In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM...In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.展开更多
In this paper we consider domain decomposition methods with polynomial Lagrangian multipliers to two-dimentional elliptic problems, and construct a kind of simple preconditioners for the corresponding interface equat...In this paper we consider domain decomposition methods with polynomial Lagrangian multipliers to two-dimentional elliptic problems, and construct a kind of simple preconditioners for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal (namelys it has only logarithmic growth with dimension of the local interface space).展开更多
In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interf...In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interface equation.It will be shown that condition number of the preconditioned interface matrix is almost optimal.展开更多
In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will...In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.展开更多
This paper is devoted to the study of the Eulerian-Lagrangian method(ELM)for convection-diffusion equations on unstructured grids with or without accurate numerical integration.We first propose an efficient and accura...This paper is devoted to the study of the Eulerian-Lagrangian method(ELM)for convection-diffusion equations on unstructured grids with or without accurate numerical integration.We first propose an efficient and accurate algorithm to calculate the integrals in the Eulerian-Lagrangian method.Our approach is based on an algorithm for finding the intersection of two non-matching grids.It has optimal algorithmic complexity and runs fast enough to make time-dependent velocity fields feasible.The evaluation of the integrals leads to increased precision and the unconditional stability.We demonstrate by numerical examples that the ELM with our proposed algorithm for accurate numerical integration has the following two features:first it is much more accurate and more stable than the ones with traditional numerical integration techniques and secondly the overall cost of the proposed method is comparable with the traditional ones.展开更多
基金The work of this author was supported by Natural Science Foundation of China(G10371129) The work of this author was supported by the National Basic Research Program of China under the grant G19990328,2005CB321701 the National Natural Science Foundation of China.
文摘In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.
基金This work was supported partly by the Natural Science Foundation of China (No. 19801030).
文摘In this paper we consider domain decomposition methods with polynomial Lagrangian multipliers to two-dimentional elliptic problems, and construct a kind of simple preconditioners for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal (namelys it has only logarithmic growth with dimension of the local interface space).
基金This research is supported by Special Funds for Major State Basic Research Projects of China (G1999032804).
文摘In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interface equation.It will be shown that condition number of the preconditioned interface matrix is almost optimal.
基金This research is supported by the Special Funds for Major State Research Projects of China(G 1999032804)
文摘In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.
文摘This paper is devoted to the study of the Eulerian-Lagrangian method(ELM)for convection-diffusion equations on unstructured grids with or without accurate numerical integration.We first propose an efficient and accurate algorithm to calculate the integrals in the Eulerian-Lagrangian method.Our approach is based on an algorithm for finding the intersection of two non-matching grids.It has optimal algorithmic complexity and runs fast enough to make time-dependent velocity fields feasible.The evaluation of the integrals leads to increased precision and the unconditional stability.We demonstrate by numerical examples that the ELM with our proposed algorithm for accurate numerical integration has the following two features:first it is much more accurate and more stable than the ones with traditional numerical integration techniques and secondly the overall cost of the proposed method is comparable with the traditional ones.
