Parallelization of a Winslow variational mesh generator

Abramov, Oleksandr (2018) Parallelization of a Winslow variational mesh generator. Masters thesis, Memorial University of Newfoundland.

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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.

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