On superconvergence of Runge-Kutta convolution quadrature for the wave equation

被引:3
|
作者
Melenk, Jens Markus [1 ]
Rieder, Alexander [2 ]
机构
[1] Tech Univ Wien, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
[2] Univ Wien, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
关键词
65M38; 65L06; 65M12;
D O I
10.1007/s00211-020-01161-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are compared: one relies on the incoming wave as input data and the other one is based on its temporal derivative. The convergence rate of the latter is shown to be higher than previously established in the literature. Numerical results indicate sharpness of the analysis. The proof hinges on a novel estimate on the Dirichlet-to-Impedance map for certain Helmholtz problems. Namely, the frequency dependence can be lowered by one power of |s| (up to a logarithmic term for polygonal domains) compared to the Dirichlet-to-Neumann map.
引用
收藏
页码:157 / 188
页数:32
相关论文
共 50 条
  • [1] On superconvergence of Runge–Kutta convolution quadrature for the wave equation
    Jens Markus Melenk
    Alexander Rieder
    [J]. Numerische Mathematik, 2021, 147 : 157 - 188
  • [2] Runge-Kutta convolution quadrature for operators arising in wave propagation
    Banjai, Lehel
    Lubich, Christian
    Melenk, Jens Markus
    [J]. NUMERISCHE MATHEMATIK, 2011, 119 (01) : 1 - 20
  • [3] An error analysis of Runge-Kutta convolution quadrature
    Banjai, Lehel
    Lubich, Christian
    [J]. BIT NUMERICAL MATHEMATICS, 2011, 51 (03) : 483 - 496
  • [4] Runge-Kutta Based Generalized Convolution Quadrature
    Lopez-Fernandez, Maria
    Sauter, Stefan
    [J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM-2015), 2016, 1738
  • [5] Runge-Kutta convolution quadrature for the Boundary Element Method
    Banjai, Lehel
    Messner, Matthias
    Schanz, Martin
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 245 : 90 - 101
  • [6] Generalized convolution quadrature based on Runge-Kutta methods
    Lopez-Fernandez, M.
    Sauter, S.
    [J]. NUMERISCHE MATHEMATIK, 2016, 133 (04) : 743 - 779
  • [7] Runge-Kutta convolution quadrature based on Gauss methods
    Banjai, Lehel
    Ferrari, Matteo
    [J]. NUMERISCHE MATHEMATIK, 2024,
  • [8] Generalized convolution quadrature based on Runge-Kutta methods
    M. Lopez-Fernandez
    S. Sauter
    [J]. Numerische Mathematik, 2016, 133 : 743 - 779
  • [9] RUNGE-KUTTA METHODS FOR PARABOLIC EQUATIONS AND CONVOLUTION QUADRATURE
    LUBICH, C
    OSTERMANN, A
    [J]. MATHEMATICS OF COMPUTATION, 1993, 60 (201) : 105 - 131
  • [10] Sparsity of Runge-Kutta convolution weights for the three-dimensional wave equation
    Banjai, Lehel
    Kachanovska, Maryna
    [J]. BIT NUMERICAL MATHEMATICS, 2014, 54 (04) : 901 - 936