Domain decomposition methods for domain composition purpose: Chimera, overset, gluing and sliding mesh methods

Domain composition methods (DCM) consist in obtaining a solution to a problem, from the formulations of the same problem expressed on various subdomains. These methods have therefore the opposite objective of domain decomposition methods (DDM). Indeed, in contrast to DCM, these last techniques are usually applied to matching meshes as their purpose consists mainly in distributing the work in parallel environments. However, they are sometimes based on the same methodology as after decomposing, DDM have to recompose. As a consequence, in the literature, the term DDM has many times substituted DCM. DCM are powerful techniques that can be used for different purposes: to simplify the meshing of a complex geometry by decomposing it into different meshable pieces; to perform local refinement to adapt to local mesh requirements; to treat subdomains in relative motion (Chimera, sliding mesh); to solve multiphysics or multiscale problems, etc. The term DCM is generic and does not give any clue about how the fragmented solutions on the different subdomains are composed into a global one. In the literature, many methodologies have been proposed: they are mesh-based, equation-based, or algebraic-based. In mesh-based formulations, the coupling is achieved at the mesh level, before the governing equations are assembled into an algebraic system (mesh conforming, Shear-Slip Mesh Update, HERMESH). The equation-based counterpart recomposes the solution from the strong or weak formulation itself, and are implemented during the assembly of the algebraic system on the subdomain meshes. The different coupling techniques can be formulated for the strong formulation at the continuous level, for the weak formulation either at the continuous or at the discrete level (iteration-by-subdomains, mortar element, mesh free interpolation). Although the different methods usually lead to the same solutions at the continuous level, which usually coincide with the solution of the problem on the original domain, they have very different behaviors at the discrete level and can be implemented in many different ways. Eventually, algebraic- based formulations treat the composition of the solutions directly on the matrix and right-hand side of the individual subdomain algebraic systems. The present work introduces mesh-based, equation-based and algebraicbased DCM. It however focusses on algebraic-based domain composition methods, which have many advantages with respect to the others: they are relatively problem independent; their implicit implementation can be hidden in the iterative solver operations, which enables one to avoid intensive code rewriting; they can be implemented in a multi-code environment

Convergence analysis of domain decomposition algorithms with full overlapping for the advection-diffusion problems

Programme 6 - Calcul scientifique, modelisation et logiciel numerique. Projet MENUSINSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1994 n.2435 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Convergence Analysis of Domain Decomposition algorithms with full overlapping for the advection-diffusion problems.

: The aim of this paper is to study the convergence properties of a Time Marching Algorithm solving Advection-Diffusion problems on two domains using incompatible discretizations. The basic algorithm is first presented, and theoretical or numerical results illustrate its convergence properties. This study is based on spectral theory, a priori estimates and a Di-Giorgi-Nash maximum principle . Key-words: non symmetric elliptic operators, domain decomposition, incompatible grids, advection-diffusion, time marching algorithms, overlapping, maximun principle. (R'esum'e : tsvp) Universit'e Paris-Dauphine and INRIA, Domaine de Voluceau- Rocquencourt- B.P. 105- Le Chesnay Cedex (France) email: [email protected] Department of Mechanical Engineering, Yale University, New Haven, CT 06520 email: tidriri @icase.edu. This work has been done in 1991 at INRIA and has been supported by the Hermes Research program under grant number RDAN 86.1/3. The author is presently supported by the Na..

NASA Langley Scientific and Technical Information Output: 1996

This document is a compilation of the scientific and technical information that the Langley Research Center has produced during the calendar year 1996. Included are citations for Formal Reports, High-Numbered Conference Publications, High-Numbered Technical Memorandums, Contractor Reports, Journal Articles and Other Publications, Meeting Presentations, Technical Talks, Computer Programs, Tech Briefs, and Patents