Parallelization of a Winslow variational mesh generator

Abstract

Adaptive meshes appear to be preferable to the uniform meshes for the numerical approximations of some PDEs. As the solution of large scale numerical problems often involves solving a problem on a distributed computational systems (clusters), it is desirable for a mesh adaptation method to also be deployable on such systems. We study various 1D mesh adaptation methods and theoretically explore connection between some of them. An implementation of a library for a parallel 2D Winslow adaptive mesh method is be presented. The library is written in the C++ language and uses the PETSc library and the Message Passing Interface (MPI) protocol. Also an example of using the library with a Stochastic Domain Decomposition (SDD) approach based on a Monte Carlo method is discussed with some numerical results provided.