A key based parallel adaptive refinement technique for finite element methods

摘要

Many computatonal problems such as finite element analysis and computational fluid dynamics are solved by discretising the geometry of the problem into a mesh. Such problems may become very large. Splitting a geometry-based problem into small pieces and computing the solutio all at once (parallel programming) should result in a much faster turnaround. Unfortunately these problems are not particularly conducive to such fine-grain parallelism since the solutions have many interdependencies, which means that there will be a great deal of inter-processor communication which slows computation. However, coarse-grain parallelism can be used efficiently so long as each processor holds a large enough continuous piece of the mesh, and each processor sends and receives updates on the boundaries to and from its neighbours. To improve the accuracy of many such problems adaptive refinement may be used to refine those parts of he mesh in which the accuracy is deficient.