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,we discuss a Schwarz alternating method for a kind of unboundeddomains, which can be decomposed into a bounded domain and a half-planar domain. Finite Element Method and Natural Boudary Reduction are use...In this paper,we discuss a Schwarz alternating method for a kind of unboundeddomains, which can be decomposed into a bounded domain and a half-planar domain. Finite Element Method and Natural Boudary Reduction are used alternatively. The uniform geometric convergence of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show thatthe convergence rate of this discrete Schwarz iteration is independent of the finiteelement mesh size, but dependent on the overlapping degree of subdomains.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 discussed. This method is very effective especially for problems o...In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is discussed. This method is very effective especially for problems over unbounded domains. The geometric convergency of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show that the convergence rate of this discrete Schwarz iteration is independent of the finite element mesh size, but dependent on the frequency of the exact solution and the overlapping degree of the subdomains.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,we discuss a Schwarz alternating method for a kind of unboundeddomains, which can be decomposed into a bounded domain and a half-planar domain. Finite Element Method and Natural Boudary Reduction are used alternatively. The uniform geometric convergence of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show thatthe convergence rate of this discrete Schwarz iteration is independent of the finiteelement mesh size, but dependent on the overlapping degree of subdomains.
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 discussed. This method is very effective especially for problems over unbounded domains. The geometric convergency of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show that the convergence rate of this discrete Schwarz iteration is independent of the finite element mesh size, but dependent on the frequency of the exact solution and the overlapping degree of the subdomains.
