Name
Abstract | ||
|---|---|---|
The main purpose of this paper is to develop a fast fully discrete Fourier–Galerkin method for solving the boundary integral equations reformulated from the modified Helmholtz equation with boundary conditions. We consider both the nonlinear and the Robin boundary conditions. To tackle the difficulties caused by the two types of boundary conditions, we provide an improved version of the Galerkin method based on the Fourier basis. By employing a matrix compression strategy and efficient numerical quadrature schemes for oscillatory integrals, we obtain fully discrete nonlinear or linear system. Finally, we use the multilevel augmentation method to solve the resulting systems. We point out that the proposed method enjoys an optimal convergence order and a nearly linear computational complexity. The theoretical estimates are confirmed by the performance of this method on several numerical examples. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s10915-014-9975-1 | Journal of Scientific Computing |
Keywords | Field | DocType |
Modified Helmholtz equation, Fourier–Galerkin methods, Multilevel augmentation methods, 65M38, 45L05 | T-matrix method,Boundary value problem,Robin boundary condition,Mathematical optimization,Nonlinear system,Mathematical analysis,Helmholtz equation,Singular boundary method,Boundary element method,Mathematics,Mixed boundary condition | Journal |
Volume | Issue | ISSN |
65 | 2 | 1573-7691 |
Citations | PageRank | References |
1 | 0.38 | 16 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rui Wang | 1 | 8 | 5.36 |
| Xiangling Chen | 2 | 6 | 2.26 |