A parallelized point-shifted tetrahedral grid for the finite element method.

摘要

FRONTIER is a software package developed for the solution of partial differential equations using the front tracking technique. FRONTIER tracks a discontinuity interface and generates grids that conform to the interface. For parabolic and elliptic problems, it uses the so-called point-shifted triangular grid for the finite element method in two dimensions. In this thesis, we extend the method to three dimensions.; The point-shifted triangular grid is a hybrid structured-unstructured grid scheme, providing local unstructuring within the confines of a global rectangular-based structure. At the first stage, a structured rectangular grid is constructed and point-shifted. At the second stage, each grid block is tetrahedralized in an unstructured way.; The ideas, algorithms, theories, and implementations including data structures for the parallelized point-shifted tetrahedral grid construction will be discussed. The main focus is on the theoretical grounds for the tetrahedralization and the algorithm for the parallelization.