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Construction and application of an AMR algorithm for distributed memory computers. (English) Zbl 1065.65114
Plewa, Tomasz (ed.) et al., Adaptive mesh refinement – theory and applications. Proceedings of the Chicago workshop on adaptive mesh refinement methods, Chicago, IL, USA, September 3–5, 2003. Berlin: Springer (ISBN 3-540-21147-0/pbk). Lecture Notes in Computational Science and Engineering 41, 361-372 (2005).
Summary: While the parallelization of block-structured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed memory machines are a topic of on-going research.
In this paper, a locality-preserving domain decomposition is proposed that partitions the entire adaptive mesh refinement (AMR) hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An easily reproducible standard benchmark and a highly resolved parallel AMR simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed strategy in practice.
For the entire collection see [Zbl 1053.65002].

65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65Y05 Parallel numerical computation
80A25 Combustion
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer