WCSE

An Adaptive Mesh Refinement Method, Based on Gershgorin Circle Theorem

Abstract— A new algorithm of dynamic local Adaptive Mesh Refinement (AMR) with support for arbitrary unstructed meshes, as well as for two and three dimensional computation is developed. The new mesh adaptation based on the discretization matrix eigenvalues estimation by Gershgorin Circle Theorem. The implementation of the algorithm is done within the framework of the OpenFOAM library for Computational Continuum Mechanics (CCM) using C++ programming language with modern policy based design for high program code modularity. It is possible to combine mesh adaptation criteria. Two numerical examples illustrate the effectiveness of new adaptive mesh refinement algorithm.

Index Terms— Adaptive mesh refinement, Gershgorin circle theorem, OpenFOAM.

Avdeev Evgeniy, Fursov Vladimir, Minaev Evgeniy
Department of supercomputers and general informatics, Samara State Aerospace University, RUSSIA
Ovchinnikov Valeriy
Laduga Ltd., RUSSIA

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Cite: Avdeev Evgeniy, Fursov Vladimir, Minaev Evgeniy, Ovchinnikov Valeriy, "An Adaptive Mesh Refinement Method, Based on Gershgorin Circle Theorem," 2015 The 5th International Workshop on Computer Science and Engineering-Information Processing and Control Engineering (WCSE 2015-IPCE), pp. 174-178, Moscow, Russia, April 15-17, 2015.