Domain decomposition approaches for the generation of equidistributing grids

Abstract

To solve boundary value problems whose solutions contain moving fronts or sharp variations, moving mesh methods can be used to achieve reasonable solution resolution with a fixed, moderate number of mesh points. Such meshes are obtained by solving nonlinear elliptic differential equations which are governed by an equidistribution principle. In this thesis we combine the moving mesh technique with several Schwarz domain decomposition methods, which allow elliptic boundary value problems to be solved by parallel computation. Convergence results are established for both parallel and alternating iterations using classical, optimal, or optimized Schwarz transmission conditions. Results for multidomain and time-dependent variations are also presented. Four potential sets of optimized transmission conditions are proposed for a 2D mesh generation algorithm. Numerical results are provided to illustrate typical behavior of the proposed algorithms.