A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation
TL;DR: In this article, a domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented, where interface values between subdomains are found by an explicit finite difference formula, and interior values are determined by backward differencing in time.
read more
Abstract: A domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented. In this procedure, interface values between subdomains are found by an explicit finite difference formula. Once these values are calculated, interior values are determined by backward differencing in time. A natural extension of this method allows for the use of different time steps in different subdomains. Maximum norm error estimates for these procedures are derived, which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Additive Schwarz algorithms for parabolic convection-diffusion equations
TL;DR: Three additive Schwarz type domain decomposition methods for general, not necessarily selfadjoint, linear, second order, parabolic partial differential equations are introduced and the convergence rates of these algorithms are studied.
190
Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems
TL;DR: Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman-Jones interface condition; the unconditional stability and convergence of the first method is proved and illustrated through numerical experiments.
Explicit/implicit, conservative domain decomposition procedures for parabolic problems based on block-centered finite differences
Clint Dawson,Todd F. Dupont +1 more
TL;DR: Domain decomposition procedures for solving parabolic equations are considered, and a priori error estimates are presented, and numerical results examining the stability, accuracy, and parallelism of the scheme are presented.
Explicit-/implicit conservative Galerkin domain decomposition procedures for parabolic problems
Clint Dawson,Todd F. Dupont +1 more
TL;DR: Several domain decomposition methods for approximating solutions of parabolic problems using implicit Galerkin procedures in the subdomains and explicit flux calculation on the inter-domain boundaries are given.
Efficient Parallel Algorithms for Parabolic Problems
TL;DR: Domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation, showing that the resulting schemes are of second order global accuracy in space, and stable in the sense of Osher or in $L_{\infty }$.
References
New algorithms for approximate realization of implicit difference schemes
TL;DR: The construction of estimates for Green's mesh function of finite difference and finite element operators involved in solving non-stationary heat conduction equations by implicit methods are treated and a new approach to approximate realization of implicit difference schemes is suggested on the basis of partitioning the spatial mesh domain into small mesh subdomains.
82
A domain decomposition method for parabolic problems
TL;DR: A domain decomposition preconditioner used with the conjugate gradient method for solving linear systems arising from parabolic partial differential equations in two-dimensional domains that relies on patching local overlapping solutions and on estimates of decay of inverses of matrices to approximately compute the amount of overlapping.
46
•Journal Article
The construction of preconditioners for elliptic problems by substructuring
TL;DR: Developpement d'une methode iterative preconditionnee pour la solution des problemes elliptiques as discussed by the authors, a.k.a. iterative pre-condition.
26
A Finite Element Domain Decomposition Method for Parabolic
Clint Dawson,Qiang Du +1 more
- 01 Oct 1990
8
Mixed finite element methods for elliptic problems
TL;DR: In this paper, the basic ideas of mixed finite element methods at an introductory level are discussed, and the concepts of convergence, approximability and stability and their interrelations are developed, and a resume is given of the stability theory which governs the performance of mixed methods.