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  • 1.
    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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  • 2. 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 functions2018In: Journal of Computational Science, ISSN 1877-7503, E-ISSN 1877-7511, Vol. 24, p. 209-217Article in journal (Refereed)
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  • 3. Bernal, Francisco
    et al.
    Heryudono, Alfa R. H.
    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.
    Numerical solution of the viscous flow past a cylinder with a non-global yet spectrally convergent meshless collocation method2017In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2016, Springer, 2017, p. 495-507Conference paper (Refereed)
  • 4. Buhmann, Martin D.
    et al.
    Dinew, Slawomir
    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.
    A note on radial basis function interpolant limits2010In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 30, p. 543-554Article in journal (Refereed)
  • 5. Cacciani, Nicola
    et al.
    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, Computational Science.
    Lauro, Alberto
    Meggiolaro, Marco
    Scatto, Alessio
    Tominec, Igor
    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.
    Villard, Pierre-Frédéric
    A first meshless approach to simulation of the elastic behaviour of the diaphragm2020In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2018, Springer, 2020, p. 501-512Conference paper (Refereed)
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  • 6. Fornberg, Bengt
    et al.
    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.
    Flyer, Natasha
    Stable computations with Gaussian radial basis functions2011In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 33, p. 869-892Article in journal (Refereed)
  • 7. Fornberg, Bengt
    et al.
    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.
    Flyer, Natasha
    Stable computations with Gaussian radial basis functions in 2-D2009Report (Other academic)
  • 8. Fornberg, Bengt
    et al.
    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.
    Wright, Grady
    A new class of oscillatory radial basis functions2006In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 51, p. 1209-1222Article in journal (Refereed)
  • 9. Fornberg, Bengt
    et al.
    Wright, Grady
    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.
    Some observations regarding interpolants in the limit of flat radial basis functions2004In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 47, p. 37-55Article in journal (Refereed)
  • 10. Grelck, Clemens
    et al.
    Niewiadomska-Szynkiewicz, Ewa
    Aldinucci, Marco
    Bracciali, Andrea
    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, Computational Science.
    Why high-performance modelling and simulation for big data applications matters2019In: High-Performance Modelling and Simulation for Big Data Applications, Springer, 2019, p. 1-35Chapter in book (Refereed)
  • 11. Heryudono, Alfa
    et al.
    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.
    Ramage, Alison
    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.
    Preconditioning for radial basis function partition of unity methods2016In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 67, p. 1089-1109Article in journal (Refereed)
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  • 12.
    Kormann, Katharina
    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, Computational Science.
    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.
    A Galerkin radial basis function method for the Schrödinger equation2013In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, p. A2832-A2855Article in journal (Refereed)
  • 13.
    Kormann, Katharina
    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, Computational Science.
    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.
    An RBF–Galerkin approach to the time-dependent Schrödinger equation2012Report (Other academic)
  • 14.
    Kormann, Katharina
    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, Computational Science.
    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.
    Radial basis functions for the time-dependent Schrödinger equation2011In: Numerical Analysis and Applied Mathematics: ICNAAM 2011, Melville, NY: American Institute of Physics (AIP), 2011, p. 1323-1326Conference paper (Refereed)
  • 15.
    Kowalewski, Markus
    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, Computational Science.
    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.
    Heryudono, Alfa
    An adaptive interpolation scheme for molecular potential energy surfaces2016In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 145, p. 084104:1-10, article id 084104Article in journal (Refereed)
  • 16.
    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.
    A domain decomposition method for the Helmholtz equation in a multilayer domain1999In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 20, p. 1713-1731Article in journal (Refereed)
  • 17.
    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.
    Book Review: A Primer on Radial Basis Functions with Applications to the Geosciences2017In: SIAM Review, ISSN 0036-1445, E-ISSN 1095-7200, Vol. 59, p. 688-689Article, book review (Other academic)
  • 18.
    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.
    Domain Decomposition and Preconditioned Iterative Methods for the Helmholtz Equation2000Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    New preconditioned iterative solution methods for the Helmholtz equation are constructed. To evaluate the performance of the methods, two-dimensional problems with a waveguide geometry are used as model problems. Second- and fourth-order accurate finite difference discretizations are used. By introducing a domain decomposition framework, problems where the physical domain consists of a number of layers of different materials can be solved. The new algorithms are shown to perform well compared with standard methods.

    First, a discretization of the Helmholtz equation in a curvilinear waveguide with smoothly varying material properties is studied. Nonlocal radiation boundary conditions are constructed for the artificial in- and outflow boundaries. A preconditioner that can be applied using fast transform methods is constructed. Experiments show that the total arithmetic complexity is much less with the fast transform preconditioner than when using a standard symmetric successive over-relaxation preconditioner. Compared with band Gaussian elimination, the gain is large both in arithmetic complexity and memory requirements.

    Next, an application with layers of different materials is considered. It is shown that nonlocal radiation boundary conditions can be constructed also in this case. A domain decomposition formulation is employed, where the fast transform preconditioner is used as a subdomain preconditioner. The performance is excellent compared with band Gaussian elimination.

    The multilayer solver is used for an investigation of the properties of the solutions of a number of underwater acoustics problems. The quality of the solutions obtained by a widely used approximation, the parabolic wave equation, is evaluated. For some problems the agreement is excellent, whereas in other cases the approximation cannot replace the full Helmholtz solution.

    A parallel version of the solver is implemented, where the algorithms are modified for increased parallel performance. With the parallel code larger problems can be solved in less computational time.

  • 19.
    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.
    Skors skönhet ur en matematikers perspektiv2013In: Skor är huvudsaken: Sjutton kvinnliga forskares funderingar om skor / [ed] Eriksson Lindvall, Carin; Rydbeck, Kerstin; Rügheimer, Louise, Uppsala universitet, 2013, p. 30-31Chapter in book (Other (popular science, discussion, etc.))
  • 20.
    Larsson, Elisabeth
    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.
    Abrahamsson, Leif
    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.
    Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics2003In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 113, p. 2446-2454Article in journal (Refereed)
  • 21.
    Larsson, Elisabeth
    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.
    Fornberg, Bengt
    A numerical study of some radial basis function based solution methods for elliptic PDEs2003In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 46, p. 891-902Article in journal (Refereed)
  • 22.
    Larsson, Elisabeth
    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.
    Fornberg, Bengt
    Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions2005In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 49, p. 103-130Article in journal (Refereed)
  • 23.
    Larsson, Elisabeth
    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.
    Fornberg, Bengt
    Theoretical and Computational Aspects of Multivariate Interpolation with Increasingly Flat Radial Basis Functions2003Report (Other academic)
  • 24.
    Larsson, Elisabeth
    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.
    Gomes, Sônia M.
    Heryudono, Alfa
    Safdari-Vaighani, Ali
    Radial basis function methods in computational finance2013In: Proc. 13th International Conference on Computational and Mathematical Methods in Science and Engineering: Volume III, Spain: Universidad de Almería , 2013, p. 895-906Conference paper (Refereed)
  • 25.
    Larsson, Elisabeth
    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.
    Holmgren, Sverker
    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 parallel domain decomposition method for the Helmholtz equation2000Report (Other academic)
    Abstract [en]

    A parallel solver for the Helmholtz equation in a domain consisting of layers with different material properties is presented. A fourth-order accurate finite difference discretization is used. The arising system of equations is solved with a preconditioned Krylov subspace method. A domain decomposition framework is employed, where fast transform subdomain preconditioners are used. Three ways of treating the Schur complement of the preconditioner are investigated, and the corresponding preconditioned iterative methods are compared with a standard direct method. It is noted that the convergence rate of the iterative methods is closely related to how the Schur complement system for the preconditioner is formed, and how accurately it is solved. However, in almost all cases, the gain in both memory requirements and arithmetic complexity is large compared with the direct method. Furthermore, the gain increases with problem size, allowing problems with many unknowns to be solved efficiently. The efficiency is further improved by parallelization using message-passing, enabling us to solve even larger Helmholtz problems in less time.

    Download full text (pdf)
    fulltext
  • 26.
    Larsson, Elisabeth
    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.
    Holmgren, Sverker
    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.
    Parallel solution of the Helmholtz equation in a multilayer domain2003In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 43, p. 387-411Article in journal (Refereed)
  • 27.
    Larsson, Elisabeth
    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.
    Lehto, 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.
    Heryudono, Alfa
    Fornberg, Bengt
    Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions2012Report (Other academic)
  • 28.
    Larsson, Elisabeth
    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.
    Lehto, 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.
    Heryudono, Alfa
    Fornberg, Bengt
    Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions2013In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, p. A2096-A2119Article in journal (Refereed)
  • 29.
    Larsson, Elisabeth
    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. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
    Mavrič, Boštjan
    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, Computational Science. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia.
    Michael, Andreas
    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, Computational Science. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Pooladi, Fatemeh
    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, Computational Science. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Dept. of Mathematics, Persian Gulf University, Bushehr, Iran.
    A numerical investigation of some RBF-FD error estimates2022In: Dolomites Research Notes on Approximation, ISSN 2035-6803, Vol. 15, no 5, p. 78-95Article in journal (Refereed)
    Abstract [en]

    In a recent paper by Tominec, Larsson and Heryudono a convergence proof for an oversampled version of the RBF-FD method, using polyharmonic spline basis functions augmented with polynomials, was derived. In this paper, we take a closer look at the individual estimates involved in this proof. We investigate how large the bounds are and how they depend on the node layout, the stencil size, and the polynomial degree. We find that a moderate amount of oversampling is sufficient for the method to be stable when Halton nodes are used for the stencil approximations, while a random node layout may require a very high oversampling factor. From a practical perspective, this indicates the importance of having a locally quasi uniform node layout for the method to be stable and give reliable results. We see an overall growth of the error constant with the polynomial degree and with the stencil size.

  • 30.
    Larsson, Elisabeth
    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.
    Pålsson, Stefan
    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.
    Rantakokko, Jarmo
    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, Computational Science.
    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.
    Thuné, Michael
    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, Computational Science.
    Gender-aware course reform in Scientific Computing2013In: International journal of engineering education, ISSN 0949-149X, Vol. 29, no 2, p. 403-414Article in journal (Refereed)
  • 31.
    Larsson, Elisabeth
    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.
    Schaback, Robert
    Institut für Numerische und Angewandte Mathematik, Universität Göttingen , Göttingen, Germany.
    Scaling of radial basis functions2023In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, p. 1-23Article in journal (Refereed)
    Abstract [en]

    This paper studies the influence of scaling on the behavior of radial basis function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The most important questions are: How does the error of a kernel-based interpolant vary with the scale of the kernel chosen? How does the standard error bound vary? And since fixed functions may be in spaces that allow scalings, like global Sobolev spaces, is there a scale of the space that matches the function best? The last question is answered in the affirmative for Sobolev spaces, but the required scale may be hard to estimate. Scalability of functions turns out to be restricted for spaces generated by analytic kernels, unless the functions are band-limited. In contrast to other papers, polynomials and polyharmonics are included as flat limits when checking scales experimentally, with an independent computation. The numerical results show that the hunt for near-flat scales is questionable, if users include the flat limit cases right from the start. When there are not enough data to evaluate errors directly, the scale of the standard error bound can be varied, up to replacing the norm of the unknown function by the norm of the interpolant. This follows the behavior of the actual error qualitatively well, but is only of limited value for estimating error-optimal scales. For kernels and functions with unlimited smoothness, the given interpolation data are proven to be insufficient for determining useful scales.

  • 32.
    Larsson, Elisabeth
    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.
    Heryudono, Alfa
    A least squares radial basis function partition of unity method for solving PDEs2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2538-A2563Article in journal (Refereed)
  • 33.
    Larsson, Elisabeth
    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.
    Sundin, Ulrika
    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, Computational Science.
    An investigation of global radial basis function collocation methods applied to Helmholtz problems2020In: Dolomites Research Notes on Approximation, ISSN 2035-6803, Vol. 13, p. 28p. 65-85Article in journal (Refereed)
    Abstract [en]

    Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution functions. At the same time, the linear systems that arise are dense and severly ill-conditioned for large numbers of unknowns and small values of the shape parameter that determines how flat the basis functions are. We use Helmholtz equation as an application problem for the theoretical analysis and numerical experiments. We analyse and characterise the convergence properties as a function of the number of unknowns and for different shape parameter ranges. We provide theoretical results for the flat limit of the PDE solutions and investigate when the non-symmetric collocation matrices become singular. We also provide practical strategies for choosing the method parameters and evaluate the results on Helmholtz problems in acurved waveguide geometry

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  • 34.
    Larsson, Elisabeth
    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, Computational Science.
    Zafari, Afshin
    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, Computational Science.
    Righero, Marco
    Francavilla, M. Alessandro
    Giordanengo, Giorgio
    Vipiana, Francesca
    Vecchi, Giuseppe
    Kessler, Christoph
    Ancourt, Corinne
    Grelck, Clemens
    Parallelization of hierarchical matrix algorithms for electromagnetic scattering problems2019In: High-Performance Modelling and Simulation for Big Data Applications, Springer, 2019, p. 36-68Chapter in book (Refereed)
  • 35.
    Larsson, Elisabeth
    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.
    Åhlander, Krister
    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.
    Hall, Andreas
    Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform2006Report (Other academic)
  • 36.
    Larsson, Elisabeth
    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.
    Åhlander, Krister
    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.
    Hall, Andreas
    Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform2008In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 222, p. 175-192Article in journal (Refereed)
  • 37.
    Ljungkvist, Karl
    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, Computational Science.
    Tillenius, 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, Computational Science.
    Black-Schaffer, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems.
    Holmgren, Sverker
    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, Computational Science.
    Karlsson, Martin
    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, Computational Science.
    Using hardware transactional memory for high-performance computing2011In: Proc. 25th International Symposium on Parallel and Distributed Processing Workshops and PhD Forum, Piscataway, NJ: IEEE , 2011, p. 1660-1667Conference paper (Refereed)
  • 38. Ljungkvist, Karl
    et al.
    Tillenius, 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, Computational Science.
    Holmgren, Sverker
    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, Computational Science.
    Karlsson, Martin
    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, Computational Science.
    Early results using hardware transactional memory for high-performance computing applications2010In: Proc. 3rd Swedish Workshop on Multi-Core Computing, Göteborg, Sweden: Chalmers University of Technology , 2010, p. 93-97Conference paper (Other academic)
    Download full text (pdf)
    FULLTEXT01
  • 39.
    Otto, Kurt
    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.
    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.
    A flexible solver of the Helmholtz equation for layered media2006In: Proc. ECCOMAS CFD Conference 2006, The Netherlands: Tech. Univ. Delft , 2006, p. 8-Conference paper (Refereed)
    Download full text (pdf)
    OttoLa06
  • 40.
    Otto, Kurt
    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.
    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.
    Iterative solution of the Helmholtz equation by a second-order method1999In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 21, p. 209-229Article in journal (Refereed)
  • 41.
    Pettersson, Ulrika
    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.
    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.
    Marcusson, Gunnar
    Persson, Jonas
    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.
    Improved radial basis function methods for multi-dimensional option pricing2006Report (Other academic)
  • 42.
    Pettersson, Ulrika
    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.
    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.
    Marcusson, Gunnar
    Persson, Jonas
    Improved radial basis function methods for multi-dimensional option pricing2008In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 222, p. 82-93Article in journal (Refereed)
  • 43.
    Pettersson, Ulrika
    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.
    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.
    Marcusson, Gunnar
    Persson, Jonas
    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.
    Option pricing using radial basis functions2005In: Proc. ECCOMAS Thematic Conference on Meshless Methods, Lisboa, Portugal: Departamento de Matemática, Instituto Superior Técnico , 2005, p. C24.1-6Conference paper (Refereed)
  • 44.
    Pooladi, Fatemeh
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology. Persian Gulf University, Department of Mathematics, Bushehr, Iran.
    Larsson, Elisabeth
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
    Stabilized interpolation using radial basis functions augmented with selected radial polynomials2024In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 437, article id 115482Article in journal (Refereed)
    Abstract [en]

    Infinitely smooth radial basis functions (RBFs) have a shape parameter that controls their shapes. When using these RBFs (e.g., the Gaussian RBF) for interpolation problems, we have ill-conditioning when the shape parameter is very small, while in some cases small shape parameters lead to high accuracy. In this study, we are going to reduce the effect of the ill-conditioning of the infinitely smooth RBFs. We propose a new basis augmenting the infinitely smooth RBFs at different locations with radial polynomials of different even powers. Numerical experiments show that the new basis is stable for all values of the shape parameter.

  • 45. Rached, Imen
    et al.
    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, Computational Science.
    Tail distribution and extreme quantile estimation using non-parametric approaches2019In: High-Performance Modelling and Simulation for Big Data Applications, Springer, 2019, p. 69-87Chapter in book (Refereed)
  • 46. Safdari-Vaighani, Ali
    et al.
    Heryudono, Alfa
    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.
    A radial basis function partition of unity collocation method for convection-diffusion equations2013Report (Other academic)
  • 47. Safdari-Vaighani, Ali
    et al.
    Heryudono, Alfa
    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.
    A radial basis function partition of unity collocation method for convection–diffusion equations arising in financial applications2015In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 64, p. 341-367Article in journal (Refereed)
    Download full text (pdf)
    fulltext
  • 48. Safdari-Vaighani, Ali
    et al.
    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.
    Heryudono, Alfa
    Radial basis function methods for the Rosenau equation and other higher order PDEs2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 75, p. 1555-1580Article in journal (Refereed)
  • 49.
    Shcherbakov, Victor
    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.
    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.
    Radial basis function partition of unity methods for pricing vanilla basket options2015Report (Other academic)
  • 50.
    Shcherbakov, Victor
    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.
    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.
    Radial basis function partition of unity methods for pricing vanilla basket options2016In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 71, p. 185-200Article in journal (Refereed)
    Download full text (pdf)
    fulltext
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