Logo: to the web site of Uppsala University

uu.sePublikasjoner fra Uppsala universitet
Endre søk
Begrens søket
1234567 1 - 50 of 1824
RefereraExporteraLink til resultatlisten
Permanent link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Treff pr side
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sortering
  • Standard (Relevans)
  • Forfatter A-Ø
  • Forfatter Ø-A
  • Tittel A-Ø
  • Tittel Ø-A
  • Type publikasjon A-Ø
  • Type publikasjon Ø-A
  • Eldste først
  • Nyeste først
  • Skapad (Eldste først)
  • Skapad (Nyeste først)
  • Senast uppdaterad (Eldste først)
  • Senast uppdaterad (Nyeste først)
  • Disputationsdatum (tidligste først)
  • Disputationsdatum (siste først)
  • Standard (Relevans)
  • Forfatter A-Ø
  • Forfatter Ø-A
  • Tittel A-Ø
  • Tittel Ø-A
  • Type publikasjon A-Ø
  • Type publikasjon Ø-A
  • Eldste først
  • Nyeste først
  • Skapad (Eldste først)
  • Skapad (Nyeste først)
  • Senast uppdaterad (Eldste først)
  • Senast uppdaterad (Nyeste først)
  • Disputationsdatum (tidligste først)
  • Disputationsdatum (siste først)
Merk
Maxantalet träffar du kan exportera från sökgränssnittet är 250. Vid större uttag använd dig av utsökningar.
  • 1. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, s. 79-116Artikkel i tidsskrift (Fagfellevurdert)
  • 2. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000Rapport (Annet vitenskapelig)
    Abstract [en]

    This paper considers a family of spatially semi-discrete approximations, including boundary treatments, to hyperbolic and parabolic equations. We derive the dependence of the error-bounds on time as well as on mesh size.

    Fulltekst (ps)
    fulltext
  • 3.
    Abbas, Qaisar
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

    Delarbeid
    1. Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    Åpne denne publikasjonen i ny fane eller vindu >>Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    2010 (engelsk)Inngår i: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, s. 29-38Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-112977 (URN)000276898600003 ()
    Tilgjengelig fra: 2010-01-24 Laget: 2010-01-24 Sist oppdatert: 2018-01-12bibliografisk kontrollert
    2. A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    Åpne denne publikasjonen i ny fane eller vindu >>A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    2011 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.

    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-019
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-159353 (URN)
    Tilgjengelig fra: 2011-09-23 Laget: 2011-09-28 Sist oppdatert: 2024-05-30bibliografisk kontrollert
    3. Accurate and stable calculations involving shocks using a new hybrid scheme
    Åpne denne publikasjonen i ny fane eller vindu >>Accurate and stable calculations involving shocks using a new hybrid scheme
    2009 (engelsk)Inngår i: Proc. 19th AIAA CFD Conference, AIAA , 2009Konferansepaper, Publicerat paper (Fagfellevurdert)
    sted, utgiver, år, opplag, sider
    AIAA, 2009
    Serie
    Conference Proceeding Series ; 2009-3985
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-110133 (URN)
    Tilgjengelig fra: 2009-11-04 Laget: 2009-11-04 Sist oppdatert: 2018-01-12bibliografisk kontrollert
    4. A stable and conservative method for locally adapting the design order of finite difference schemes
    Åpne denne publikasjonen i ny fane eller vindu >>A stable and conservative method for locally adapting the design order of finite difference schemes
    2011 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, s. 4216-4231Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-134055 (URN)10.1016/j.jcp.2010.11.020 (DOI)000290185000007 ()
    Tilgjengelig fra: 2010-11-20 Laget: 2010-11-21 Sist oppdatert: 2018-01-12bibliografisk kontrollert
    5. Energy stability of the MUSCL scheme
    Åpne denne publikasjonen i ny fane eller vindu >>Energy stability of the MUSCL scheme
    2010 (engelsk)Inngår i: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, s. 61-68Konferansepaper, Publicerat paper (Fagfellevurdert)
    sted, utgiver, år, opplag, sider
    Berlin: Springer-Verlag, 2010
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-132925 (URN)10.1007/978-3-642-11795-4_5 (DOI)000395207900005 ()978-3-642-11794-7 (ISBN)
    Tilgjengelig fra: 2010-10-29 Laget: 2010-10-29 Sist oppdatert: 2018-06-16bibliografisk kontrollert
    6. The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    Åpne denne publikasjonen i ny fane eller vindu >>The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    2010 (engelsk)Inngår i: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, s. 416-423Konferansepaper, Publicerat paper (Fagfellevurdert)
    sted, utgiver, år, opplag, sider
    South African Association for Theoretical and Applied Mechanics, 2010
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-113571 (URN)978-0-620-49192-1 (ISBN)
    Tilgjengelig fra: 2010-01-29 Laget: 2010-01-29 Sist oppdatert: 2018-01-12bibliografisk kontrollert
    Fulltekst (pdf)
    fulltext
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    A weak boundary procedure for high order finite difference approximations of hyperbolic problems2011Rapport (Annet vitenskapelig)
    Abstract [en]

    We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.

    Fulltekst (pdf)
    fulltext
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010Inngår i: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, s. 29-38Artikkel i tidsskrift (Fagfellevurdert)
  • 6.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008Inngår i: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, s. 52-62Konferansepaper (Annet vitenskapelig)
  • 7.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009Inngår i: Proc. 19th AIAA CFD Conference, AIAA , 2009Konferansepaper (Fagfellevurdert)
  • 8.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Energy stability of the MUSCL scheme2010Inngår i: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, s. 61-68Konferansepaper (Fagfellevurdert)
  • 9.
    Abdulle, Assyr
    et al.
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    Arjmand, Doghonay
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    Paganoni, Edoardo
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    A parabolic local problem with exponential decay of the resonance error for numerical homogenization2021Inngår i: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 31, nr 13, s. 2733-2772Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in 𝜀/𝛿𝜀/δ, where 𝜀<𝛿𝜀<δ represents the characteristic length of the small scale oscillations and 𝛿𝑑δd is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in 𝜀/𝛿𝜀/δ. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

  • 10.
    Abdulle, Assyr
    et al.
    Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    Arjmand, Doghonay
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys. Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    Paganoni, Edoardo
    Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    AN ELLIPTIC LOCAL PROBLEM WITH EXPONENTIAL DECAY OF THE RESONANCE ERROR FOR NUMERICAL HOMOGENIZATION2023Inngår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 21, nr 2, s. 513-541Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These effective data need to be computed by running local microscale simulations followed by a local averaging of the microscopic information. Motivated by the classical homogenization theory, it is a common practice to use local elliptic cell problems for computing the missing homogenized coefficients in the macro model. Such a consideration results in a first order error O(E/8), where E represents the wavelength of the microscale variations and 8 is the size of the microscopic simulation boxes. This error, called ``resonance error,"" originates from the boundary conditions used in the microproblem and typically dominates all other errors in a multiscale numerical method. Optimal decay of the resonance error remains an open problem, although several interesting approaches reducing the effect of the boundary have been proposed over the last two decades. In this paper, as an attempt to resolve this problem, we propose a computationally efficient, fully elliptic approach with exponential decay of the resonance error.

  • 11. Abdulle, Assyr
    et al.
    Arjmand, Doghonay
    Paganoni, Edoardo
    Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems2019Inngår i: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, nr 6, s. 545-551Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.

  • 12.
    Abenius, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain2005Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment. Different topics for time-domain finite-difference (FDTD) and finite-element (FETD) methods for Maxwell's equations are treated in this thesis.

    Subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid. A novel model for thin sheets using shell elements is proposed. This approach has the advantage of taking into account discontinuities in the normal component of the electric field, unlike previous models based on impedance boundary conditions (IBCs). Several results are presented to illustrate the capabilities of the shell element approach.

    Waveguides are of fundamental importance in many microwave applications, for example in antenna feeds. The key issues of excitation and truncation of waveguides are addressed. A complex frequency shifted form of the uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) in FETD is developed. Prism elements are used to promote automatic grid generation and enhance the performance. Results are presented where reflection errors below -70dB are obtained for different types of waveguides, including inhomogeneous cases. Excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency-domain mode solver for the vector Helmholtz equation. Huygens surfaces are used in both FDTD and FETD for excitation in waveguide ports.

    Inverse problems have received an increased interest due to the availability of powerful computers. An important application is non-destructive evaluation of material. A time-domain, minimization approach is presented where exact gradients are computed using the adjoint problem. The approach is applied to a general form of Maxwell's equations including dispersive media and UPML. Successful reconstruction examples are presented both using synthetic and experimental measurement data. Parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem. Gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry.

    Delarbeid
    1. Hybrid time domain solvers for the Maxwell equations in 2D
    Åpne denne publikasjonen i ny fane eller vindu >>Hybrid time domain solvers for the Maxwell equations in 2D
    Vise andre…
    2002 (engelsk)Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, s. 2185-2199Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-44333 (URN)10.1002/nme.380 (DOI)
    Prosjekter
    GEMS
    Tilgjengelig fra: 2007-01-26 Laget: 2007-01-26 Sist oppdatert: 2018-01-11bibliografisk kontrollert
    2. Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
    Åpne denne publikasjonen i ny fane eller vindu >>Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
    2005 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    An important part of numerical waveguide modeling is the termination of the waveguide using artificial boundaries. In this paper we develop a perfectly matched layer (PML) for waveguides in the finite-element time-domain method (FETD). The PML is discretized by prism elements aligned with the direction of propagation of the waveguide. Assuming that the waveguide is discretized by tetrahedra such a grid is easily generated from a cross-sectional surface in the waveguide. The proposed method has the advantage of being general with regard to the geometry and material of the waveguide. Previous works on PML for FETD have reported problems with late-time instability. While still present in the current approach, our results indicate that the instability is less severe for the prism element PML compared to a tetrahedral PML. Moreover, it may be controlled by increasing the number of grid points in the absorbing layer. It should be noted that the instability appears long after the energy has been attenuated and therefore pose no problems in practical computations. The performance of the suggested scheme is demonstrated for several waveguide problems, including an inhomogeneous case.

    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-026
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-80256 (URN)
    Prosjekter
    GEMS
    Tilgjengelig fra: 2007-02-03 Laget: 2007-02-03 Sist oppdatert: 2024-05-31bibliografisk kontrollert
    3. Solving inverse electromagnetic problems using FDTD and gradient-based minimization
    Åpne denne publikasjonen i ny fane eller vindu >>Solving inverse electromagnetic problems using FDTD and gradient-based minimization
    2006 (engelsk)Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, s. 650-673Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-80802 (URN)10.1002/nme.1731 (DOI)000241713800003 ()
    Prosjekter
    GEMS
    Tilgjengelig fra: 2007-01-26 Laget: 2007-01-26 Sist oppdatert: 2018-01-13bibliografisk kontrollert
    4. Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
    Åpne denne publikasjonen i ny fane eller vindu >>Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
    2006 (engelsk)Inngår i: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, s. 28-34Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-80325 (URN)10.1109/TAP.2005.861554 (DOI)000235016700004 ()
    Prosjekter
    GEMS
    Tilgjengelig fra: 2007-01-26 Laget: 2007-01-26 Sist oppdatert: 2018-01-13bibliografisk kontrollert
    5. Modeling of inhomogeneous waveguides using hybrid methods
    Åpne denne publikasjonen i ny fane eller vindu >>Modeling of inhomogeneous waveguides using hybrid methods
    2005 (engelsk)Manuskript (preprint) (Annet vitenskapelig)
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-93590 (URN)
    Prosjekter
    GEMS
    Tilgjengelig fra: 2005-10-11 Laget: 2005-10-11 Sist oppdatert: 2018-01-13bibliografisk kontrollert
    Fulltekst (pdf)
    FULLTEXT01
  • 13. Abenius, Erik
    et al.
    Andersson, Ulf
    Edelvik, Fredrik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Eriksson, Lasse
    Ledfelt, Gunnar
    Hybrid time domain solvers for the Maxwell equations in 2D2002Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, s. 2185-2199Artikkel i tidsskrift (Fagfellevurdert)
  • 14.
    Abenius, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Edelvik, Fredrik
    Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method2006Inngår i: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, s. 28-34Artikkel i tidsskrift (Fagfellevurdert)
  • 15.
    Abenius, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Edelvik, Fredrik
    Johansson, Christer
    Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method2005Rapport (Annet vitenskapelig)
    Abstract [en]

    An important part of numerical waveguide modeling is the termination of the waveguide using artificial boundaries. In this paper we develop a perfectly matched layer (PML) for waveguides in the finite-element time-domain method (FETD). The PML is discretized by prism elements aligned with the direction of propagation of the waveguide. Assuming that the waveguide is discretized by tetrahedra such a grid is easily generated from a cross-sectional surface in the waveguide. The proposed method has the advantage of being general with regard to the geometry and material of the waveguide. Previous works on PML for FETD have reported problems with late-time instability. While still present in the current approach, our results indicate that the instability is less severe for the prism element PML compared to a tetrahedral PML. Moreover, it may be controlled by increasing the number of grid points in the absorbing layer. It should be noted that the instability appears long after the energy has been attenuated and therefore pose no problems in practical computations. The performance of the suggested scheme is demonstrated for several waveguide problems, including an inhomogeneous case.

    Fulltekst (pdf)
    fulltext
  • 16.
    Abenius, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Johansson, Christer
    A General Approach for Time-Domain Simulation of Waveguides in 3D2004Inngår i: Proc. EMB 04, Computational Electromagnetics: Methods and Applications, Göteborg, Sweden: Department of Electromagnetics, Chalmers University of Technology , 2004, s. 220-226Konferansepaper (Annet vitenskapelig)
  • 17.
    Abenius, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Johansson, Christer
    Modeling of inhomogeneous waveguides using hybrid methods2005Manuskript (preprint) (Annet vitenskapelig)
  • 18.
    Abenius, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Strand, Bo
    Solving inverse electromagnetic problems using FDTD and gradient-based minimization2006Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, s. 650-673Artikkel i tidsskrift (Fagfellevurdert)
  • 19. Abenius, Erik
    et al.
    Strand, Bo
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Alestra, Stephane
    Inverse Electromagnetic Scattering Using the Finite-Difference Time-Domain Method2000Inngår i: Proc. Millennium Conference on Antennas and Propagation, Noordwijk, The Netherlands: ESA Publications , 2000, s. 4-Konferansepaper (Fagfellevurdert)
  • 20.
    Abrahamsson, Leif R.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A priori estimates for solutions of singular perturbations with a turning point1977Inngår i: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 56, s. 51-69Artikkel i tidsskrift (Fagfellevurdert)
  • 21.
    Abrahamsson, Leif R.
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Keller, Herbert B.
    Kreiss, Heinz-Otto
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Difference approximations for singular perturbations of systems of ordinary differential equations1974Inngår i: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 22, s. 367-391Artikkel i tidsskrift (Fagfellevurdert)
  • 22. Aceto, Lidia
    et al.
    Mazza, Mariarosa
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis2020Inngår i: Calcolo, ISSN 0008-0624, E-ISSN 1126-5434, Vol. 57, artikkel-id 27Artikkel i tidsskrift (Fagfellevurdert)
  • 23.
    Adler, Jonas
    et al.
    KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden.;DeepMind, 6 Pancras Sq, London N1C 4AG, England..
    Lunz, Sebastian
    Univ Cambridge, Ctr Math Sci, Cambridge CB3 0WA, England..
    Verdier, Olivier
    KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden.;Western Norway Univ Appl Sci, Dept Comp Math & Phys, Bergen, Norway..
    Schonlieb, Carola-Bibiane
    Univ Cambridge, Ctr Math Sci, Cambridge CB3 0WA, England..
    Öktem, Ozan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden.
    Task adapted reconstruction for inverse problems2022Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 38, nr 7, artikkel-id 075006Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper considers the problem of performing a post-processing task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and post-processing as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the post-processing task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any post-processing that can be encoded as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation.

    Fulltekst (pdf)
    fulltext
  • 24.
    Adlmann, Franz A.
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Fysiska sektionen, Institutionen för fysik och astronomi, Materialfysik.
    Pálsson, Gunnar Karl
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Fysiska sektionen, Institutionen för fysik och astronomi, Materialfysik.
    Bilheux, J. C.
    Oak Ridge Natl Lab, Spallat Neutron Source, Oak Ridge, TN USA..
    Ankner, J. F.
    Oak Ridge Natl Lab, Spallat Neutron Source, Oak Ridge, TN USA..
    Gutfreund, P.
    Inst Laue Langevin, BP 156, F-38042 Grenoble, France..
    Kawecki, M.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Fysiska sektionen, Institutionen för fysik och astronomi, Materialfysik.
    Wolff, Max
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Fysiska sektionen, Institutionen för fysik och astronomi, Materialfysik.
    Överlåtaren: a fast way to transfer and orthogonalize two-dimensional off-specular reflectivity data2016Inngår i: Journal of applied crystallography, ISSN 0021-8898, E-ISSN 1600-5767, Vol. 49, s. 2091-2099Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Reflectivity measurements offer unique opportunities for the study of surfaces and interfaces, and specular reflectometry has become a standard tool in materials science to resolve structures normal to the surface of a thin film. Off-specular scattering, which probes lateral structures, is more difficult to analyse, because the Fourier space being probed is highly anisotropic and the scattering pattern is truncated by the interface. As a result, scattering patterns collected with (especially time-of-flight) neutron reflectometers are difficult to transform into reciprocal space for comparison with model calculations. A program package is presented for a generic two-dimensional transformation of reflectometry data into q space and back. The data are represented on an orthogonal grid, allowing cuts along directions relevant for theoretical modelling. This treatment includes background subtraction as well as a full characterization of the resolution function. The method is optimized for computational performance using repeatable operations and standardized instrument settings.

  • 25. Adriani, Andrea
    et al.
    Bianchi, Davide
    Ferrari, Paola
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Asymptotic spectra of large (grid) graphs with a uniform local structure, Part II: Numerical applications2024Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 437, artikkel-id 115461Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω ⊂ Rd , d ≥ 1. When Ω = [0, 1], such graphs include the standard Toeplitz graphs and, for Ω = [0,1]d, the considered class includes d-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences, Finite Elements, and Isogeometric Analysis. Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure.

  • 26. Adriani, Andrea
    et al.
    Bianchi, Davide
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Asymptotic Spectra of Large (Grid) Graphs with a Uniform Local Structure (Part I): Theory2020Inngår i: Milan Journal of Mathematics, ISSN 1424-9286, E-ISSN 1424-9294, Vol. 88, nr 2, s. 409-454Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We are mainly concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain omega subset of Rd, d >= 1. When omega=[0,1] , such graphs include the standard Toeplitz graphs and, for omega=[0,1](d), the considered class includesd-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and we show that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides many information on the eigenvalue structure, of localization, spectral gap, clustering, and distribution type.

    Few generalizations are also considered in connection with the notion of generalized locally Toeplitz sequences and applications are discussed, stemming e.g. from the approximation of differential operators via numerical schemes. Nevertheless, more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks

    Fulltekst (pdf)
    fulltext
  • 27. Adriani, Andrea
    et al.
    Semplice, Matteo
    Serra, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Generalized Locally Toeplitz matrix-sequences and approximated PDEs on submanifolds: the flat case2023Inngår i: Linear and multilinear algebra, ISSN 0308-1087, E-ISSN 1563-5139, s. 1-23Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the present paper, we consider a class of elliptic partial differential equations with Dirichlet boundary conditions where the operator is the Laplace-Beltrami operator Δ over   Ω¯, Ω being an open and bounded submanifold of   Rν,   ν=2,3. We will take into consideration the classical   Pk Finite Elements, in the case of Friedrichs-Keller triangulations, leading to sequences of matrices of increasing size. We are interested in carrying out a spectral analysis of the resulting matrix-sequences. The tools for our derivations are mainly taken from the Toeplitz technology and from the rather new theory of Generalized Locally Toeplitz (GLT) matrix-sequences. The current contribution is only quite an initial step, where a general programme is provided, with partial answers leading to further open questions: indeed the analysis is performed on special flat submanifolds and hence there is room for wide generalizations, with a final picture which is still unclear with respect to, e.g. the role of the submanifold curvature.

  • 28.
    Adriani, Andrea
    et al.
    Univ Insubria, Dept Sci & High Technol, Via Valleggio 11, I-22100 Como, Italy..
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys. Univ Insubria, Dept Sci & High Technol, Via Valleggio 11, I-22100 Como, Italy..
    Tablino-Possio, Cristina
    Univ Milano Bicocca, Dept Math & Applicat, Via Cozzi 53, I-20125 Milan, Italy..
    Clustering/Distribution Analysis and Preconditioned Krylov Solvers for the Approximated Helmholtz Equation and Fractional Laplacian in the Case of Complex-Valued, Unbounded Variable Coefficient Wave Number μ2024Inngår i: Algorithms, E-ISSN 1999-4893, Vol. 17, nr 3, artikkel-id 100Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number 𝜇, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a 𝜏 preconditioning when the variable coefficient wave number 𝜇 is uniformly bounded. Here, we extend the analysis to the unbounded case by focusing on the case of a power singularity. Several numerical experiments concerning the spectral behavior and convergence of the related preconditioned GMRES are presented.

    Fulltekst (pdf)
    FULLTEXT01
  • 29. Ahlberg, Ragnar
    et al.
    Gustafsson, Bertil
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A note on parallel algorithms for partial differential equations1984Inngår i: Parallel Computing: 83, Amsterdam, The Netherlands: Elsevier Science , 1984, s. 93-98Konferansepaper (Fagfellevurdert)
  • 30.
    Ahlkrona, Josefin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Computational Ice Sheet Dynamics: Error control and efficiency2016Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated.

    Delarbeid
    1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    Åpne denne publikasjonen i ny fane eller vindu >>A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    2013 (engelsk)Inngår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, s. 417-435Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-205727 (URN)10.1093/qjmam/hbt009 (DOI)000327457200001 ()
    Prosjekter
    eSSENCE
    Tilgjengelig fra: 2013-08-09 Laget: 2013-08-22 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    Åpne denne publikasjonen i ny fane eller vindu >>Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    2013 (engelsk)Inngår i: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, s. 2135-2152Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-213571 (URN)10.5194/gmd-6-2135-2013 (DOI)000329050500017 ()
    Prosjekter
    eSSENCE
    Tilgjengelig fra: 2013-12-19 Laget: 2013-12-28 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    Åpne denne publikasjonen i ny fane eller vindu >>Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    2016 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, s. 1-19Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-269822 (URN)10.1016/j.jcp.2015.12.025 (DOI)000369086700001 ()
    Prosjekter
    eSSENCE
    Tilgjengelig fra: 2015-12-17 Laget: 2015-12-18 Sist oppdatert: 2017-12-01bibliografisk kontrollert
    4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    Åpne denne publikasjonen i ny fane eller vindu >>The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    2016 (engelsk)Rapport (Annet vitenskapelig)
    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-006
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-283438 (URN)
    Prosjekter
    eSSENCE
    Tilgjengelig fra: 2016-04-19 Laget: 2016-04-13 Sist oppdatert: 2024-05-29bibliografisk kontrollert
    5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    Åpne denne publikasjonen i ny fane eller vindu >>A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    2016 (engelsk)Rapport (Annet vitenskapelig)
    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-005
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-283437 (URN)
    Prosjekter
    eSSENCE
    Tilgjengelig fra: 2016-04-19 Laget: 2016-04-13 Sist oppdatert: 2024-05-29bibliografisk kontrollert
    Fulltekst (pdf)
    fulltext
    Download (jpg)
    preview image
  • 31.
    Ahlkrona, Josefin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation2016Rapport (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 32.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling2013Inngår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, s. 417-435Artikkel i tidsskrift (Fagfellevurdert)
  • 33.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A numerical study of the validity of Shallow Ice Approximations2012Rapport (Annet vitenskapelig)
    Abstract [en]

    Improving numerical ice sheet models is a very active field of research. In part, this is because ice sheet modelling has gained societal relevance in the context of predictions of future sea level rise. Ice sheet modelling is however also a challenging mathematical and computational subject. Since the exact equations governing ice dynamics, the full Stokes equations, are computationally expensive to solve, approximations are crucially needed for many problems. Shallow ice approximations are a family of approximations derived by asymptotic expansion of the exact equations in terms of the aspect ratio, epsilon. Retaining only the zeroth order terms in this expansion yields the by far most frequently used approximation; the Shallow Ice Approximation (SIA). Including terms up to second order yields the Second Order Shallow Ice Approximation (SOSIA), which is a so-called higher order model. Here, we study the validity and accuracy of shallow ice approximations beyond previous analyses of the SIA. We perform a detailed analysis of the assumptions behind shallow ice approximations, i.e. of the order of magnitude of field variables. We do this by using a numerical solution of the exact equations for ice flow over a sloping, undulating bed. We also construct analytical solutions for the SIA and SOSIA and numerically compute the accuracy for varying epsilon by comparing to the exact solution. We find that the assumptions underlying shallow ice approximations are not entirely appropriate since they do not account for a high viscosity boundary layer developing near the ice surface as soon as small bumps are introduced at the ice base. This boundary layer is thick and has no distinct border. Other existing theories which do incorporate the boundary layer are in better, but not full, agreement with our numerical results. Our results reveal that neither the SIA nor the SOSIA is as accurate as suggested by the asymptotic expansion approach. Also, in SOSIA the ice rheology needs to be altered to avoid infinite viscosity, though both our analytical and numerical solutions show that, especially for high bump amplitudes, the accuracy of the SOSIA is highly sensitive to this alternation. However, by updating the SOSIA solution in an iterative manner, we obtain a model which utilises the advantages of shallow ice approximations, while reducing the disadvantages.

    Fulltekst (pdf)
    fulltext
  • 34.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Accuracy of the zeroth and second order shallow ice approximation: numerical and theoretical results2013Inngår i: Geoscientific Model Development Discussions, ISSN 1991-9611, E-ISSN 1991-962X, Vol. 6, s. 4281-4325Artikkel i tidsskrift (Annet vitenskapelig)
  • 35.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results2013Inngår i: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, s. 2135-2152Artikkel i tidsskrift (Fagfellevurdert)
  • 36.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, s. 1-19Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 37.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Shcherbakov, Victor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2017Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, s. 633-649Artikkel i tidsskrift (Fagfellevurdert)
  • 38.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Shcherbakov, Victor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2016Rapport (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 39. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2018Inngår i: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 78, s. 867-893Artikkel i tidsskrift (Fagfellevurdert)
  • 40. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2017Rapport (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 41. Ahmad, Fayyaz
    et al.
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Zaka Ullah, Malik
    Al-Fhaid, A. Saleh
    A family of iterative methods for solving systems of nonlinear equations having unknown multiplicity2016Inngår i: Algorithms, E-ISSN 1999-4893, Vol. 9, s. 5:1-10, artikkel-id 5Artikkel i tidsskrift (Fagfellevurdert)
  • 42. Ahmad, Fayyaz
    et al.
    Soleymani, Fazlollah
    Khaksar Haghani, Farhad
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations2017Inngår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 314, s. 199-211Artikkel i tidsskrift (Fagfellevurdert)
  • 43.
    Ahmad, Masood
    et al.
    University of Engineering and Technology, Peshawar, Pakistan.
    Islam, Siraj-ul
    University of Engineering and Technology, Peshawar, Pakistan.
    Larsson, Elisabeth
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Local meshless methods for second order elliptic interface problems with sharp corners2020Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 416, artikkel-id 109500Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 44. Akbari, Hesam
    et al.
    Sadiq, Muhammad Tariq
    Jafari, Nastaran
    Too, Jingwei
    Mikaeilvand, Nasser
    Cicone, Antonio
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys. Department of Science and High Technology, Division of Mathematics, University of Insubria, Como, Italy.
    Recognizing seizure using Poincaré plot of EEG signals and graphical features in DWT domain2023Inngår i: Bratislava Medical Journal, ISSN 0006-9248, E-ISSN 1336-0345, Vol. 124, nr 1, s. 12-24Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Electroencephalography (EEG) signals are considered one of the oldest techniques for detecting disorders in medical signal processing. However, brain complexity and the non-stationary nature of EEG signals represent a challenge when applying this technique. The current paper proposes new geometrical features for classification of seizure (S) and seizure-free (SF) EEG signals with respect to the Poincaré pattern of discrete wavelet transform (DWT) coefficients. DWT decomposes EEG signal to four levels, and thus Poincaré plot is shown for coefficients. Due to patterns of the Poincaré plot, novel geometrical features are computed from EEG signals. The computed features are involved in standard descriptors of 2-D projection (STD), summation of triangle area using consecutive points (STA), as well as summation of shortest distance from each point relative to the 45-degree line (SSHD), and summation of distance from each point relative to the coordinate center (SDTC). The proposed procedure leads to discriminate features between S and SF EEG signals. Thereafter, a binary particle swarm optimization (BPSO) is developed as an appropriate technique for feature selection. Finally, k-nearest neighbor (KNN) and support vector machine (SVM) classifiers are used for classifying features in S and SF groups. By developing the proposed method, we have archived classification accuracy of 99.3 % with respect to the proposed geometrical features. Accordingly, S and SF EEG signals have been classified. Also, Poincaré plot of SF EEG signals has more regular geometrical shapes as compared to S group. As a final remark, we notice that the Poincaré plot of coefficients in S EEG signals has occupied more space as compared to SF EEG signals (Tab. 3, Fig. 11, Ref. 57).

  • 45.
    Alghamdi, Azza
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Klimek, Maciej
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Approximation of pluricomplex Green functions based on Monte Carlo integrationManuskript (preprint) (Annet vitenskapelig)
  • 46.
    Almquist, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Efficient Simulation of Wave Phenomena2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Wave phenomena appear in many fields of science such as acoustics, geophysics, and quantum mechanics. They can often be described by partial differential equations (PDEs). As PDEs typically are too difficult to solve by hand, the only option is to compute approximate solutions by implementing numerical methods on computers. Ideally, the numerical methods should produce accurate solutions at low computational cost. For wave propagation problems, high-order finite difference methods are known to be computationally cheap, but historically it has been difficult to construct stable methods. Thus, they have not been guaranteed to produce reasonable results.

    In this thesis we consider finite difference methods on summation-by-parts (SBP) form. To impose boundary and interface conditions we use the simultaneous approximation term (SAT) method. The SBP-SAT technique is designed such that the numerical solution mimics the energy estimates satisfied by the true solution. Hence, SBP-SAT schemes are energy-stable by construction and guaranteed to converge to the true solution of well-posed linear PDE. The SBP-SAT framework provides a means to derive high-order methods without jeopardizing stability. Thus, they overcome most of the drawbacks historically associated with finite difference methods.

    This thesis consists of three parts. The first part is devoted to improving existing SBP-SAT methods. In Papers I and II, we derive schemes with improved accuracy compared to standard schemes. In Paper III, we present an embedded boundary method that makes it easier to cope with complex geometries. The second part of the thesis shows how to apply the SBP-SAT method to wave propagation problems in acoustics (Paper IV) and quantum mechanics (Papers V and VI). The third part of the thesis, consisting of Paper VII, presents an efficient, fully explicit time-integration scheme well suited for locally refined meshes.

    Delarbeid
    1. A solution to the stability issues with block norm summation by parts operators
    Åpne denne publikasjonen i ny fane eller vindu >>A solution to the stability issues with block norm summation by parts operators
    2013 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 253, s. 418-442Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-205418 (URN)10.1016/j.jcp.2013.07.013 (DOI)000323610500022 ()
    Tilgjengelig fra: 2013-07-24 Laget: 2013-08-16 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    2. Optimal diagonal-norm SBP operators
    Åpne denne publikasjonen i ny fane eller vindu >>Optimal diagonal-norm SBP operators
    2014 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 264, s. 91-111Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-215785 (URN)10.1016/j.jcp.2013.12.041 (DOI)000331717100005 ()
    Tilgjengelig fra: 2014-01-15 Laget: 2014-01-16 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    3. A high-order accurate embedded boundary method for first order hyperbolic equations
    Åpne denne publikasjonen i ny fane eller vindu >>A high-order accurate embedded boundary method for first order hyperbolic equations
    2017 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 334, s. 255-279Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-310122 (URN)10.1016/j.jcp.2016.12.034 (DOI)000395210500015 ()
    Tilgjengelig fra: 2016-12-28 Laget: 2016-12-11 Sist oppdatert: 2017-06-30bibliografisk kontrollert
    4. Atmospheric sound propagation over large-scale irregular terrain
    Åpne denne publikasjonen i ny fane eller vindu >>Atmospheric sound propagation over large-scale irregular terrain
    2014 (engelsk)Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, s. 369-397Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-218680 (URN)10.1007/s10915-014-9830-4 (DOI)000343215600007 ()
    Tilgjengelig fra: 2014-02-14 Laget: 2014-02-14 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    5. High-fidelity numerical solution of the time-dependent Dirac equation
    Åpne denne publikasjonen i ny fane eller vindu >>High-fidelity numerical solution of the time-dependent Dirac equation
    2014 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, s. 86-103Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-215119 (URN)10.1016/j.jcp.2013.12.038 (DOI)000330955200006 ()
    Tilgjengelig fra: 2014-01-09 Laget: 2014-01-10 Sist oppdatert: 2017-12-06bibliografisk kontrollert
    6. Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Åpne denne publikasjonen i ny fane eller vindu >>Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Vise andre…
    2015 (engelsk)Inngår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, nr 5, s. 052108:1-5, artikkel-id 052108Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-246721 (URN)10.1103/PhysRevA.92.052108 (DOI)000364468300002 ()
    Forskningsfinansiär
    Swedish Research Council, D0413201
    Tilgjengelig fra: 2015-11-12 Laget: 2015-03-09 Sist oppdatert: 2017-12-04bibliografisk kontrollert
    7. Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    Åpne denne publikasjonen i ny fane eller vindu >>Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    2017 (engelsk)Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, s. A2020-A2048Artikkel i tidsskrift (Fagfellevurdert) Published
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-310123 (URN)10.1137/16M1084407 (DOI)000415797300064 ()
    Tilgjengelig fra: 2017-09-14 Laget: 2016-12-11 Sist oppdatert: 2018-03-02bibliografisk kontrollert
    Fulltekst (pdf)
    fulltext
    Download (jpg)
    preview image
  • 47.
    Almquist, Martin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Dunham, Eric M.
    Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions2021Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 424Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Summation-by-parts (SBP) finite difference methods have several desirable properties for second-order wave equations. They combine the computational efficiency of narrow-stencil finite difference operators with provable stability on curvilinear multiblock grids. While several techniques for boundary and interface conditions exist, weak imposition via simultaneous approximation terms (SATs) is perhaps the most flexible one. Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature. We fill this gap by deriving energy-stable self-adjoint SBP-SAT methods for general anisotropic materials on curvilinear multiblock grids. The methods are based on fully compatible SBP operators. Although this paper focuses on classical SBP finite difference operators, the presented boundary and interface treatments are general and apply to a range of methods that satisfy an SBP property. We demonstrate the stability and accuracy properties of a particular set of fully compatible SBP-SAT schemes using the method of manufactured solutions. We also demonstrate the utility of the new method in elastodynamic cloaking and seismic imaging in mountainous regions.

  • 48.
    Almquist, Martin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Dunham, Eric M.
    Non-stiff boundary and interface penalties for narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids2020Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 408Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine computational efficiency with provable stability on curvilinear multiblock grids. However, the existing SBP-SAT discretization of the Laplacian quickly becomes prohibitively stiff as grid skewness increases. The stiffness stems from the SATs that impose inter-block couplings and Dirichlet boundary conditions. We resolve this issue by deriving stable SATs whose stiffness is almost insensitive to grid skewness. The new discretization thus allows for large time steps in explicit time integrators, even on very skewed grids. It also applies to the variable-coefficient generalization of the Laplacian. We demonstrate the efficacy and versatility of the new SATs by applying them to acoustic wave propagation problems inspired by marine seismic exploration and infrasound monitoring of volcanoes.

  • 49.
    Almquist, Martin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Karasalo, Ilkka
    Mattsson, Ken
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Atmospheric sound propagation over large-scale irregular terrain2014Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, s. 369-397Artikkel i tidsskrift (Fagfellevurdert)
  • 50.
    Almquist, Martin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Karasalo, Ilkka
    Mattsson, Ken
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Atmospheric sound propagation over large-scale irregular terrain2013Rapport (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
1234567 1 - 50 of 1824
RefereraExporteraLink til resultatlisten
Permanent link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf