This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite diffe...This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.展开更多
Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
A novel overlapping domain decomposition splitting algorithm based on a CrankNicolson method is developed for the stochastic nonlinear Schrödinger equation driven by a multiplicative noise with non-periodic bound...A novel overlapping domain decomposition splitting algorithm based on a CrankNicolson method is developed for the stochastic nonlinear Schrödinger equation driven by a multiplicative noise with non-periodic boundary conditions.The proposed algorithm can significantly reduce the computational cost while maintaining the similar conservation laws.Numerical experiments are dedicated to illustrating the capability of the algorithm for different spatial dimensions,as well as the various initial conditions.In particular,we compare the performance of the overlapping domain decomposition splitting algorithm with the stochastic multi-symplectic method in[S.Jiang et al.,Commun.Comput.Phys.,14(2013),393-411]and the finite difference splitting scheme in[J.Cui et al.,J.Differ.Equ.,266(2019),5625-5663].We observe that our proposed algorithm has excellent computational efficiency and is highly competitive.It provides a useful tool for solving stochastic partial differential equations.展开更多
From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical propertie...From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.展开更多
In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the dist...In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the distributed lattice Boltzmann method are analyzed.展开更多
文摘This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.
基金supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171047,11971458).
文摘A novel overlapping domain decomposition splitting algorithm based on a CrankNicolson method is developed for the stochastic nonlinear Schrödinger equation driven by a multiplicative noise with non-periodic boundary conditions.The proposed algorithm can significantly reduce the computational cost while maintaining the similar conservation laws.Numerical experiments are dedicated to illustrating the capability of the algorithm for different spatial dimensions,as well as the various initial conditions.In particular,we compare the performance of the overlapping domain decomposition splitting algorithm with the stochastic multi-symplectic method in[S.Jiang et al.,Commun.Comput.Phys.,14(2013),393-411]and the finite difference splitting scheme in[J.Cui et al.,J.Differ.Equ.,266(2019),5625-5663].We observe that our proposed algorithm has excellent computational efficiency and is highly competitive.It provides a useful tool for solving stochastic partial differential equations.
文摘From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.
文摘In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the distributed lattice Boltzmann method are analyzed.
