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Efficiency considerations in triangular adaptive mesh refinement. (English) Zbl 1192.86005

Summary: Locally or adaptively refined meshes have been successfully applied to simulation applications involving multi-scale phenomena in the geosciences. In particular, for situations with complex geometries or domain boundaries, meshes with triangular or tetrahedral cells demonstrate their superior ability to accurately represent relevant realistic features. On the other hand, these methods require more complex data structures and are therefore less easily implemented, maintained and optimized. Acceptance in the Earth-system modelling community is still low. One of the major drawbacks is posed by indirect addressing due to unstructured or dynamically changing data structures and correspondingly lower efficiency of the related computations. In this paper, we will derive several strategies to circumvent the mentioned efficiency constraint. In particular, we will apply recent computational sciences methods in combination with results of classical mathematics (space-filling curves) in order to linearize the complex data and access structure.

MSC:

86-08 Computational methods for problems pertaining to geophysics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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