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  • 1. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000Report (Other academic)
  • 2. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, p. 79-116Article in journal (Refereed)
  • 3.
    Abbas, Qaisar
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, comprehensive summary (Other academic)
    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.

    List of papers
    1. Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    Open this publication in new window or tab >>Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    2010 (English)In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-112977 (URN)000276898600003 ()
    Available from: 2010-01-24 Created: 2010-01-24 Last updated: 2018-01-12Bibliographically approved
    2. A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    Open this publication in new window or tab >>A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    2011 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-019
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-159353 (URN)
    Available from: 2011-09-23 Created: 2011-09-28 Last updated: 2011-11-04Bibliographically approved
    3. Accurate and stable calculations involving shocks using a new hybrid scheme
    Open this publication in new window or tab >>Accurate and stable calculations involving shocks using a new hybrid scheme
    2009 (English)In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    AIAA, 2009
    Series
    Conference Proceeding Series ; 2009-3985
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-110133 (URN)
    Available from: 2009-11-04 Created: 2009-11-04 Last updated: 2018-01-12Bibliographically approved
    4. A stable and conservative method for locally adapting the design order of finite difference schemes
    Open this publication in new window or tab >>A stable and conservative method for locally adapting the design order of finite difference schemes
    2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 4216-4231Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-134055 (URN)10.1016/j.jcp.2010.11.020 (DOI)000290185000007 ()
    Available from: 2010-11-20 Created: 2010-11-21 Last updated: 2018-01-12Bibliographically approved
    5. Energy stability of the MUSCL scheme
    Open this publication in new window or tab >>Energy stability of the MUSCL scheme
    2010 (English)In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Berlin: Springer-Verlag, 2010
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-132925 (URN)10.1007/978-3-642-11795-4_5 (DOI)000395207900005 ()978-3-642-11794-7 (ISBN)
    Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2018-06-16Bibliographically approved
    6. The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    Open this publication in new window or tab >>The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    2010 (English)In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 416-423Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    South African Association for Theoretical and Applied Mechanics, 2010
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-113571 (URN)978-0-620-49192-1 (ISBN)
    Available from: 2010-01-29 Created: 2010-01-29 Last updated: 2018-01-12Bibliographically approved
    Download full text (pdf)
    fulltext
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    A weak boundary procedure for high order finite difference approximations of hyperbolic problems2011Report (Other academic)
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
  • 6.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 7.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 8.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 9.
    Abdulle, Assyr
    et al.
    Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    Arjmand, Doghonay
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. 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 HOMOGENIZATION2023In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 21, no 2, p. 513-541Article in journal (Refereed)
    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.

  • 10.
    Abenius, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain2005Doctoral thesis, comprehensive summary (Other academic)
    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.

    List of papers
    1. Hybrid time domain solvers for the Maxwell equations in 2D
    Open this publication in new window or tab >>Hybrid time domain solvers for the Maxwell equations in 2D
    Show others...
    2002 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, p. 2185-2199Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-44333 (URN)10.1002/nme.380 (DOI)
    Projects
    GEMS
    Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-11Bibliographically approved
    2. Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
    Open this publication in new window or tab >>Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
    2005 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-026
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-80256 (URN)
    Projects
    GEMS
    Available from: 2007-02-03 Created: 2007-02-03 Last updated: 2014-09-03Bibliographically approved
    3. Solving inverse electromagnetic problems using FDTD and gradient-based minimization
    Open this publication in new window or tab >>Solving inverse electromagnetic problems using FDTD and gradient-based minimization
    2006 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, p. 650-673Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-80802 (URN)10.1002/nme.1731 (DOI)000241713800003 ()
    Projects
    GEMS
    Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-13Bibliographically approved
    4. Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
    Open this publication in new window or tab >>Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
    2006 (English)In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, p. 28-34Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-80325 (URN)10.1109/TAP.2005.861554 (DOI)000235016700004 ()
    Projects
    GEMS
    Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-13Bibliographically approved
    5. Modeling of inhomogeneous waveguides using hybrid methods
    Open this publication in new window or tab >>Modeling of inhomogeneous waveguides using hybrid methods
    2005 (English)Manuscript (preprint) (Other academic)
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-93590 (URN)
    Projects
    GEMS
    Available from: 2005-10-11 Created: 2005-10-11 Last updated: 2018-01-13Bibliographically approved
    Download full text (pdf)
    FULLTEXT01
  • 11. Abenius, Erik
    et al.
    Andersson, Ulf
    Edelvik, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Eriksson, Lasse
    Ledfelt, Gunnar
    Hybrid time domain solvers for the Maxwell equations in 2D2002In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, p. 2185-2199Article in journal (Refereed)
  • 12.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edelvik, Fredrik
    Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method2006In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, p. 28-34Article in journal (Refereed)
  • 13.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edelvik, Fredrik
    Johansson, Christer
    Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method2005Report (Other academic)
  • 14.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Johansson, Christer
    A General Approach for Time-Domain Simulation of Waveguides in 3D2004In: Proc. EMB 04, Computational Electromagnetics: Methods and Applications, Göteborg, Sweden: Department of Electromagnetics, Chalmers University of Technology , 2004, p. 220-226Conference paper (Other academic)
  • 15.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Johansson, Christer
    Modeling of inhomogeneous waveguides using hybrid methods2005Manuscript (preprint) (Other academic)
  • 16.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Strand, Bo
    Solving inverse electromagnetic problems using FDTD and gradient-based minimization2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, p. 650-673Article in journal (Refereed)
  • 17. Abenius, Erik
    et al.
    Strand, Bo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Alestra, Stephane
    Inverse Electromagnetic Scattering Using the Finite-Difference Time-Domain Method2000In: Proc. Millennium Conference on Antennas and Propagation, Noordwijk, The Netherlands: ESA Publications , 2000, p. 4-Conference paper (Refereed)
  • 18.
    Abrahamsson, Leif R.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A priori estimates for solutions of singular perturbations with a turning point1977In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 56, p. 51-69Article in journal (Refereed)
  • 19.
    Abrahamsson, Leif R.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Keller, Herbert B.
    Kreiss, Heinz-Otto
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Difference approximations for singular perturbations of systems of ordinary differential equations1974In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 22, p. 367-391Article in journal (Refereed)
  • 20. Aceto, Lidia
    et al.
    Mazza, Mariarosa
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis2020In: Calcolo, ISSN 0008-0624, E-ISSN 1126-5434, Vol. 57, article id 27Article in journal (Refereed)
  • 21. Adriani, Andrea
    et al.
    Bianchi, Davide
    Ferrari, Paola
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Asymptotic spectra of large (grid) graphs with a uniform local structure, Part II: Numerical applications2024In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 437, article id 115461Article in journal (Refereed)
    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.

  • 22. Adriani, Andrea
    et al.
    Bianchi, Davide
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Asymptotic Spectra of Large (Grid) Graphs with a Uniform Local Structure (Part I): Theory2020In: Milan Journal of Mathematics, ISSN 1424-9286, E-ISSN 1424-9294, Vol. 88, no 2, p. 409-454Article in journal (Refereed)
    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

    Download full text (pdf)
    fulltext
  • 23. Adriani, Andrea
    et al.
    Semplice, Matteo
    Serra, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Generalized Locally Toeplitz matrix-sequences and approximated PDEs on submanifolds: the flat case2023In: Linear and multilinear algebra, ISSN 0308-1087, E-ISSN 1563-5139, p. 1-23Article in journal (Refereed)
    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.

  • 24.
    Adriani, Andrea
    et al.
    Univ Insubria, Dept Sci & High Technol, Via Valleggio 11, I-22100 Como, Italy..
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. 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 μ2024In: Algorithms, E-ISSN 1999-4893, Vol. 17, no 3, article id 100Article in journal (Refereed)
    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.

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  • 25. Ahlberg, Ragnar
    et al.
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A note on parallel algorithms for partial differential equations1984In: Parallel Computing: 83, Amsterdam, The Netherlands: Elsevier Science , 1984, p. 93-98Conference paper (Refereed)
  • 26.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Computational Ice Sheet Dynamics: Error control and efficiency2016Doctoral thesis, comprehensive summary (Other academic)
    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.

    List of papers
    1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    Open this publication in new window or tab >>A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    2013 (English)In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, p. 417-435Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-205727 (URN)10.1093/qjmam/hbt009 (DOI)000327457200001 ()
    Projects
    eSSENCE
    Available from: 2013-08-09 Created: 2013-08-22 Last updated: 2017-12-06Bibliographically approved
    2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    Open this publication in new window or tab >>Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    2013 (English)In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, p. 2135-2152Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-213571 (URN)10.5194/gmd-6-2135-2013 (DOI)000329050500017 ()
    Projects
    eSSENCE
    Available from: 2013-12-19 Created: 2013-12-28 Last updated: 2017-12-06Bibliographically approved
    3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    Open this publication in new window or tab >>Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-269822 (URN)10.1016/j.jcp.2015.12.025 (DOI)000369086700001 ()
    Projects
    eSSENCE
    Available from: 2015-12-17 Created: 2015-12-18 Last updated: 2017-12-01Bibliographically approved
    4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    Open this publication in new window or tab >>The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    2016 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-006
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-283438 (URN)
    Projects
    eSSENCE
    Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved
    5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    Open this publication in new window or tab >>A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    2016 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-005
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-283437 (URN)
    Projects
    eSSENCE
    Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved
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  • 27.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation2016Report (Other academic)
  • 28.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling2013In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, p. 417-435Article in journal (Refereed)
  • 29.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A numerical study of the validity of Shallow Ice Approximations2012Report (Other academic)
  • 30.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accuracy of the zeroth and second order shallow ice approximation: numerical and theoretical results2013In: Geoscientific Model Development Discussions, ISSN 1991-9611, E-ISSN 1991-962X, Vol. 6, p. 4281-4325Article in journal (Other academic)
  • 31.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results2013In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, p. 2135-2152Article in journal (Refereed)
  • 32.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    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 method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed)
    Download full text (pdf)
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  • 33.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Shcherbakov, Victor
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, p. 633-649Article in journal (Refereed)
  • 34.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Shcherbakov, Victor
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2016Report (Other academic)
  • 35. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2018In: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 78, p. 867-893Article in journal (Refereed)
  • 36. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2017Report (Other academic)
  • 37. Ahmad, Fayyaz
    et al.
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Zaka Ullah, Malik
    Al-Fhaid, A. Saleh
    A family of iterative methods for solving systems of nonlinear equations having unknown multiplicity2016In: Algorithms, E-ISSN 1999-4893, Vol. 9, p. 5:1-10, article id 5Article in journal (Refereed)
  • 38. Ahmad, Fayyaz
    et al.
    Soleymani, Fazlollah
    Khaksar Haghani, Farhad
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations2017In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 314, p. 199-211Article in journal (Refereed)
  • 39.
    Ahmad, Masood
    et al.
    University of Engineering and Technology, Peshawar, Pakistan.
    Islam, Siraj-ul
    University of Engineering and Technology, Peshawar, Pakistan.
    Larsson, Elisabeth
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Local meshless methods for second order elliptic interface problems with sharp corners2020In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 416, article id 109500Article in journal (Refereed)
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  • 40. Akbari, Hesam
    et al.
    Sadiq, Muhammad Tariq
    Jafari, Nastaran
    Too, Jingwei
    Mikaeilvand, Nasser
    Cicone, Antonio
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. 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 domain2023In: Bratislava Medical Journal, ISSN 0006-9248, E-ISSN 1336-0345, Vol. 124, no 1, p. 12-24Article in journal (Refereed)
    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).

  • 41.
    Al-Jaser, Asma
    et al.
    Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia..
    Qaraad, Belgees
    Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt..
    Ramos, Higinio
    Univ Salamanca, Sci Comp Grp, Plaza Merced, Salamanca 37008, Spain.;Escuela Politecn Super Zamora, Dept Math, Campus Viriato, Zamora 49022, Spain..
    Serra, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Univ Insubria, Dept Sci & High Technol, Via Valleggio 11, I-22100 Como, Italy..
    New Conditions for Testing the Oscillation of Solutions of Second-Order Nonlinear Differential Equations with Damped Term2024In: AXIOMS, ISSN 2075-1680, Vol. 13, no 2, article id 105Article in journal (Refereed)
    Abstract [en]

    This paper deals with the oscillatory behavior of solutions of a new class of second-order nonlinear differential equations. In contrast to most of the previous results in the literature, we establish some new criteria that guarantee the oscillation of all solutions of the studied equation without additional restrictions. Our approach improves the standard integral averaging technique to obtain simpler oscillation theorems for new classes of nonlinear differential equations. Two examples are presented to illustrate the importance of our findings.

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  • 42.
    Almquist, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Efficient Simulation of Wave Phenomena2017Doctoral thesis, comprehensive summary (Other academic)
    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.

    List of papers
    1. A solution to the stability issues with block norm summation by parts operators
    Open this publication in new window or tab >>A solution to the stability issues with block norm summation by parts operators
    2013 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 253, p. 418-442Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-205418 (URN)10.1016/j.jcp.2013.07.013 (DOI)000323610500022 ()
    Available from: 2013-07-24 Created: 2013-08-16 Last updated: 2017-12-06Bibliographically approved
    2. Optimal diagonal-norm SBP operators
    Open this publication in new window or tab >>Optimal diagonal-norm SBP operators
    2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 264, p. 91-111Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-215785 (URN)10.1016/j.jcp.2013.12.041 (DOI)000331717100005 ()
    Available from: 2014-01-15 Created: 2014-01-16 Last updated: 2017-12-06Bibliographically approved
    3. A high-order accurate embedded boundary method for first order hyperbolic equations
    Open this publication in new window or tab >>A high-order accurate embedded boundary method for first order hyperbolic equations
    2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 334, p. 255-279Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-310122 (URN)10.1016/j.jcp.2016.12.034 (DOI)000395210500015 ()
    Available from: 2016-12-28 Created: 2016-12-11 Last updated: 2017-06-30Bibliographically approved
    4. Atmospheric sound propagation over large-scale irregular terrain
    Open this publication in new window or tab >>Atmospheric sound propagation over large-scale irregular terrain
    2014 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-218680 (URN)10.1007/s10915-014-9830-4 (DOI)000343215600007 ()
    Available from: 2014-02-14 Created: 2014-02-14 Last updated: 2017-12-06Bibliographically approved
    5. High-fidelity numerical solution of the time-dependent Dirac equation
    Open this publication in new window or tab >>High-fidelity numerical solution of the time-dependent Dirac equation
    2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed) Published
    National Category
    Computational Mathematics Theoretical Chemistry
    Identifiers
    urn:nbn:se:uu:diva-215119 (URN)10.1016/j.jcp.2013.12.038 (DOI)000330955200006 ()
    Available from: 2014-01-09 Created: 2014-01-10 Last updated: 2017-12-06Bibliographically approved
    6. Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Open this publication in new window or tab >>Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Show others...
    2015 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 5, p. 052108:1-5, article id 052108Article in journal (Refereed) Published
    National Category
    Atom and Molecular Physics and Optics Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-246721 (URN)10.1103/PhysRevA.92.052108 (DOI)000364468300002 ()
    Funder
    Swedish Research Council, D0413201
    Available from: 2015-11-12 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approved
    7. Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    Open this publication in new window or tab >>Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    2017 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2020-A2048Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-310123 (URN)10.1137/16M1084407 (DOI)000415797300064 ()
    Available from: 2017-09-14 Created: 2016-12-11 Last updated: 2018-03-02Bibliographically approved
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  • 43.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Dunham, Eric M.
    Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions2021In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 424Article in journal (Refereed)
    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.

  • 44.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Dunham, Eric M.
    Non-stiff boundary and interface penalties for narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids2020In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 408Article in journal (Refereed)
    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.

  • 45.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Karasalo, Ilkka
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Atmospheric sound propagation over large-scale irregular terrain2013Report (Other academic)
  • 46.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Karasalo, Ilkka
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Atmospheric sound propagation over large-scale irregular terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed)
  • 47.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edvinsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.
    High-fidelity numerical solution of the time-dependent Dirac equation2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed)
  • 48.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edvinsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.
    Stable and accurate simulation of phenomena in relativistic quantum mechanics2013In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 213-214Conference paper (Other academic)
  • 49.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Mehlin, Michaela
    Multilevel local time-stepping methods of Runge–Kutta-type for wave equations2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2020-A2048Article in journal (Refereed)
  • 50. Almquist, Martin
    et al.
    Wang, Siyang
    Werpers, Jonatan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces2019In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, p. A1201-A1227Article in journal (Refereed)
1234567 1 - 50 of 1466
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