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Solving Diffusion Problems on Rough Surfaces with a Hierarchical Multiscale FEM
Author(s) -
Abdulle Assyr
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410328
Subject(s) - finite element method , surface (topology) , triangulation , surface roughness , scale (ratio) , computer science , diffusion , macro , surface finish , sampling (signal processing) , computational science , mathematical optimization , algorithm , mathematics , geometry , materials science , mechanical engineering , physics , engineering , structural engineering , computer vision , filter (signal processing) , quantum mechanics , composite material , thermodynamics , programming language
Diffusion on rough surfaces is a basic problem for many applications in engineering and the sciences. Solving these problems with a standard finite element method is often difficult or even impossible, due to the computational work and the amount of memory needed to triangulate the whole surface with a mesh which resolves its oscillations. We discuss in this paper a hierarchical Finite Element Method of “heterogeneous multiscale” type, which only needs to resolve the surface's fine scale on small sampling domains within a macro triangulation of the underlying smooth surface. This method converges, for periodic surface roughness and sufficiently small amplitude, at a robust (i.e. scale independent) rate, to the homogenized solution. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)