On a fast direct elliptic solver by a modified Fourier method

被引：0
作者：
A. Averbuch
L. Vozovoi
M. Israeli
机构：
[1] Tel Aviv University,School of Mathematical Sciences
[2] Technion,Faculty of Computer Science
来源：
Numerical Algorithms | 1997年 / 15卷
关键词：
Helmholtz equation; Fourier method; fast solver; subtraction technique; corner singularities;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We describe high order numerical algorithms for the solution of second order elliptic equations in rectangular domains. These algorithms are based on the Fourier method in combination with a subtraction procedure. The singularities at the corner points, arising due to non-smoothness of the boundaries, are treated explicitly using properly constructed singular corner functions. The present algorithm is a generalization of the Fast Poisson Solver developed in our previous paper.
引用
收藏
页码：287 / 313
页数：26
相关论文
共 50 条
[31]   The Fourier-Nitsche-mortaring for elliptic problems with reentrant edges [J].
B. Heinrich ;
B. Jung .
Computing, 2007, 80 :221-246
[32]   A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions [J].
Lai, Jun ;
Kobayashi, Motoki ;
Barnett, Alex .
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 :194-208
[33]   A split-step Fourier method for the complex modified Korteweg-de Vries equation [J].
Muslu, GM ;
Erbay, HA .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) :503-514
[34]   A fast Fourier-Galerkin method solving boundary integral equations for the Helmholtz equation with exponential convergence [J].
Jiang, Ying ;
Wang, Bo ;
Yu, Dandan .
NUMERICAL ALGORITHMS, 2021, 88 (03) :1457-1491
[35]   A fast Fourier-Galerkin method solving boundary integral equations for the Helmholtz equation with exponential convergence [J].
Ying Jiang ;
Bo Wang ;
Dandan Yu .
Numerical Algorithms, 2021, 88 :1457-1491
[36]   An Efficient Modified Haar Wavelet Collocation Method for Numerical Solution of Two-Dimensional Elliptic PDEs [J].
Aziz I. ;
Siraj-ul-Islam .
Differential Equations and Dynamical Systems, 2017, 25 (2) :347-360
[37]   A fast 3D Poisson solver of arbitrary order accuracy [J].
Braverman, E ;
Israeli, M ;
Averbuch, A ;
Vozovoi, L .
JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 144 (01) :109-136
[38]   H-Matrix Accelerated Direct Matrix Solver using Chebyshev-based Nystrom Boundary Integral Equation Method [J].
Hu, Jin ;
Sever, Emrah ;
Babazadeh, Omid ;
Gholami, Reza ;
Okhmatovski, Vladimir ;
Sideris, Constantine .
2022 IEEE/MTT-S INTERNATIONAL MICROWAVE SYMPOSIUM (IMS 2022), 2022, :16-19
[39]   A fast algorithm for two-dimensional elliptic problems [J].
Badea, L ;
Daripa, P .
NUMERICAL ALGORITHMS, 2002, 30 (3-4) :199-239
[40]   A Fast Algorithm for Two-Dimensional Elliptic Problems [J].
Lori Badea ;
Prabir Daripa .
Numerical Algorithms, 2002, 30 :199-239
12345