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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, 79-116 p.Article 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, 29-38 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    Identifiers
    urn:nbn:se:uu:diva-112977 (URN)000276898600003 ()
    Available from: 2010-01-24 Created: 2010-01-24 Last updated: 2011-11-30Bibliographically 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 Science
    Identifiers
    urn:nbn:se:uu:diva-110133 (URN)
    Available from: 2009-11-04 Created: 2009-11-04 Last updated: 2011-11-26Bibliographically 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, 4216-4231 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    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: 2013-01-23Bibliographically 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, 61-68 p.Conference 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)978-3-642-11794-7 (ISBN)
    Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2011-11-26Bibliographically 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, 416-423 p.Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    South African Association for Theoretical and Applied Mechanics, 2010
    National Category
    Computational Mathematics Computer Science
    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: 2011-11-09Bibliographically approved
  • 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, 29-38 p.Article 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, 52-62 p.Conference 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, 61-68 p.Conference paper (Refereed)
  • 9.
    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, 2185-2199 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    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: 2014-09-03Bibliographically 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, 650-673 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    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: 2011-11-29Bibliographically 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, 28-34 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    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: 2016-01-28Bibliographically 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 Science
    Identifiers
    urn:nbn:se:uu:diva-93590 (URN)
    Projects
    GEMS
    Available from: 2005-10-11 Created: 2005-10-11 Last updated: 2011-11-10Bibliographically approved
  • 10. 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, 2185-2199 p.Article in journal (Refereed)
  • 11.
    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, 28-34 p.Article 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
    Johansson, Christer
    Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method2005Report (Other academic)
  • 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.
    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, 220-226 p.Conference paper (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
    Modeling of inhomogeneous waveguides using hybrid methods2005Manuscript (preprint) (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.
    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, 650-673 p.Article in journal (Refereed)
  • 16. 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, 4- p.Conference paper (Refereed)
  • 17.
    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, 51-69 p.Article in journal (Refereed)
  • 18.
    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, 367-391 p.Article in journal (Refereed)
  • 19. 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, 93-98 p.Conference paper (Refereed)
  • 20.
    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, 417-435 p.Article 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: 2016-05-16Bibliographically 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, 2135-2152 p.Article 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: 2016-05-16Bibliographically 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, 1-19 p.Article 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: 2016-05-16Bibliographically 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
  • 21.
    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)
  • 22.
    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, 417-435 p.Article in journal (Refereed)
  • 23.
    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)
  • 24.
    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, 4281-4325 p.Article in journal (Other academic)
  • 25.
    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, 2135-2152 p.Article in journal (Refereed)
  • 26.
    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, 1-19 p.Article in journal (Refereed)
  • 27.
    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)
  • 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.
    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, 633-649 p.Article in journal (Refereed)
  • 29. 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?2017In: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 76Article in journal (Refereed)
  • 30. 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)
  • 31. 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, ISSN 1999-4893, E-ISSN 1999-4893, Vol. 9, 5:1-10 p., 5Article in journal (Refereed)
  • 32.
    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, 418-442 p.Article 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: 2016-12-11Bibliographically 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, 91-111 p.Article 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: 2016-12-11Bibliographically 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, 255-279 p.Article 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, 369-397 p.Article 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: 2016-12-11Bibliographically 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, 86-103 p.Article 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: 2016-12-11Bibliographically 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, 052108:1-5 p., 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: 2016-12-11Bibliographically 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, A2020-A2048 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-310123 (URN)10.1137/16M1084407 (DOI)
    Available from: 2017-09-14 Created: 2016-12-11 Last updated: 2017-09-29Bibliographically approved
  • 33.
    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, 369-397 p.Article in journal (Refereed)
  • 34.
    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)
  • 35.
    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, 86-103 p.Article in journal (Refereed)
  • 36.
    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, 213-214 p.Conference paper (Other academic)
  • 37.
    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, A2020-A2048 p.Article in journal (Refereed)
  • 38. Amani Rad, Jamal
    et al.
    Höök, Josef
    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.
    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.
    von Sydow, Lina
    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.
    Forward deterministic pricing of options using Gaussian radial basis functions2017In: Journal of Computational Science, ISSN 1877-7503, E-ISSN 1877-7511Article in journal (Refereed)
    The full text will be freely available from 2018-05-25 23:59
  • 39.
    Amoignon, Olivier
    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.
    Adjoint-based aerodynamic shape optimization2003Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    An adjoint system of the Euler equations of gas dynamics is derived in order to solve aerodynamic shape optimization problems with gradient-based methods. The derivation is based on the fully discrete flow model and involves differentiation and transposition of the system of equations obtained by an unstructured and node-centered finite-volume discretization. Solving the adjoint equations allows an efficient calculation of gradients, also when the subject of optimization is described by hundreds or thousands of design parameters.

    Such a fine geometry description may cause wavy or otherwise irregular designs during the optimization process. Using the one-to-one mapping defined by a Poisson problem is a known technique that produces smooth design updates while keeping a fine resolution of the geometry. This technique is extended here to combine the smoothing effect with constraints on the geometry, by defining the design updates as solutions of a quadratic programming problem associated with the Poisson problem.

    These methods are applied to airfoil shape optimization for reduction of the wave drag, that is, the drag caused by gas dynamic effects that occur close to the speed of sound. A second application concerns airfoil design optimization to delay the laminar-to-turbulent transition point in the boundary layer in order to reduce the drag. The latter application has been performed by the author with collaborators, also using gradient-based optimization. Here, the growth of convectively unstable disturbances are modeled by successively solving the Euler equations, the boundary layer equations, and the parabolized stability equations.

  • 40.
    Amoignon, Olivier
    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.
    Moving mesh adaptation scheme for aerodynamic shape optimization2006Report (Other academic)
  • 41.
    Amoignon, Olivier
    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.
    Numerical Methods for Aerodynamic Shape Optimization2005Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances.

    When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries.

    Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation.

    In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme.

    The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

    List of papers
    1. Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization
    Open this publication in new window or tab >>Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization
    2006 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-013
    National Category
    Computational Mathematics Computer Science
    Identifiers
    urn:nbn:se:uu:diva-80174 (URN)
    Projects
    Design Optimization
    Available from: 2007-09-16 Created: 2007-09-16 Last updated: 2014-09-03Bibliographically approved
    2. Shape optimization for delay of laminar-turbulent transition
    Open this publication in new window or tab >>Shape optimization for delay of laminar-turbulent transition
    Show others...
    2006 (English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 44, 1009-1024 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    Identifiers
    urn:nbn:se:uu:diva-80640 (URN)10.2514/1.12431 (DOI)000237492000010 ()
    Projects
    Design Optimization
    Available from: 2007-01-31 Created: 2007-01-31 Last updated: 2016-01-28Bibliographically approved
    3. Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization
    Open this publication in new window or tab >>Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization
    2007 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 36, 1119-1136 p.Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Science
    Identifiers
    urn:nbn:se:uu:diva-22158 (URN)10.1016/j.compfluid.2006.11.002 (DOI)000246537700008 ()
    Projects
    Design Optimization
    Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2014-09-03Bibliographically approved
    4. Moving mesh adaptation scheme for aerodynamic shape optimization
    Open this publication in new window or tab >>Moving mesh adaptation scheme for aerodynamic shape optimization
    2006 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-014
    National Category
    Computational Mathematics Computer Science
    Identifiers
    urn:nbn:se:uu:diva-80175 (URN)
    Projects
    Design Optimization
    Available from: 2007-09-17 Created: 2007-09-17 Last updated: 2014-09-03Bibliographically approved
  • 42.
    Amoignon, Olivier
    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.
    Berggren, 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.
    Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization2006Report (Other academic)
  • 43.
    Amoignon, Olivier
    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.
    Berggren, 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.
    Discrete adjoint-based shape optimization for an edge-based finite-volume solver2003In: Computational Fluid and Solid Mechanics: 2003, Elsevier Science , 2003, 2190-2193 p.Conference paper (Refereed)
  • 44.
    Amoignon, Olivier
    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.
    Pralits, Jan
    Hanifi, Ardeshir
    Berggren, 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.
    Henningson, Dan
    Shape optimization for delay of laminar-turbulent transition2006In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 44, 1009-1024 p.Article in journal (Refereed)
  • 45. Andersson, Paul
    et al.
    Berggren, 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.
    Henningson, Dan S.
    Optimal disturbances and bypass transition in boundary layers1999In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 11, 134-150 p.Article in journal (Refereed)
  • 46.
    Apelkrans, Mats Y. T.
    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.
    On difference schemes for hyperbolic equations with discontinuous initial values1968In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 22, no 103, 525-539 p.Article in journal (Refereed)
  • 47. Appelö, Daniel
    et al.
    Hagstrom, Thomas
    Kreiss, Gunilla
    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.
    Perfectly matched layers for hyperbolic systems: General formulation, well-posedness, and stability2006In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 67, 1-23 p.Article in journal (Refereed)
  • 48. Appelö, Daniel
    et al.
    Kreiss, Gunilla
    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.
    Application of a perfectly matched layer to the nonlinear wave equation2007In: Wave motion, ISSN 0165-2125, Vol. 44, 531-548 p.Article in journal (Refereed)
  • 49. Appelö, Daniel
    et al.
    Kreiss, Gunilla
    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.
    Wang, Siyang
    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.
    An explicit Hermite–Taylor method for the Schrödinger equation2017In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 21, 1207-1230 p.Article in journal (Refereed)
  • 50. Appelö, Daniel
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    Wang, Siyang
    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.
    An energy based discontinuous Galerkin method for acoustic–elastic waves2017In: Proc. 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Minneapolis, MN: University of Minnesota Press, 2017, 389-390 p.Conference paper (Other academic)
1234567 1 - 50 of 1217
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