A Hierarchical Multiresolution Adaptive Mesh Refinement for the Solution of Evolution PDEs

In this paper, we propose a novel multiresolution adaptive mesh refinement algorithm for solving initial-boundary value problems (IBVP) for evolution PDEs. The proposed algorithm dynamically adapts the grid to any existing or emerging irregularities in the solution, by refining the grid only at thos...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2008-01, Vol.31 (2), p.1221-1248
Main Authors: Jain, S., Tsiotras, P., Zhou, H.-M.
Format: Article
Language:English
Subjects:
Adaptation
Algorithms
Boundary conditions
Boundary value problems
Conservation laws
Data compression
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Summary:In this paper, we propose a novel multiresolution adaptive mesh refinement algorithm for solving initial-boundary value problems (IBVP) for evolution PDEs. The proposed algorithm dynamically adapts the grid to any existing or emerging irregularities in the solution, by refining the grid only at those places where the solution exhibits sharp features. The main advantage of the proposed grid adaptation method is that it results in a grid with a fewer number of nodes when compared to adaptive grids generated by existing multiresolution-based mesh refinement techniques. Several examples show the robustness and stability of the proposed algorithm.
ISSN:1064-8275
1095-7197
DOI:10.1137/070708329