In this paper, based on natural boundary reduction suggested by Feng and Yu, an nonoverlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helmholtz equation. The c...In this paper, based on natural boundary reduction suggested by Feng and Yu, an nonoverlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helmholtz equation. The convergence of the D-N alternating algorithm and its discretization are studied. Some numerical results are given.展开更多
In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helnilioltz equation. th...In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helnilioltz equation. the convergence of the Schwarz alternating algorithm is studied. Some numerical results are given.展开更多
In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and...In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and discrete problems are studied.Error estimated and some numerical results are given.展开更多
The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and ...The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.展开更多
In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive an...In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the O（h^4） term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.展开更多
文摘In this paper, based on natural boundary reduction suggested by Feng and Yu, an nonoverlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helmholtz equation. The convergence of the D-N alternating algorithm and its discretization are studied. Some numerical results are given.
文摘In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helnilioltz equation. the convergence of the Schwarz alternating algorithm is studied. Some numerical results are given.
文摘In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and discrete problems are studied.Error estimated and some numerical results are given.
文摘The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.
基金supported by Natural Science Foundation of China under grant number 10471047
文摘In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the O（h^4） term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.
