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Microstructural Decomposition Error Estimates
Author(s) -
Zohdi T.,
Wriggers P.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19990791341
Subject(s) - domain decomposition methods , decoupling (probability) , mortar methods , boundary value problem , a priori and a posteriori , finite element method , computational complexity theory , partition (number theory) , computer science , algorithm , mathematical optimization , mathematics , mathematical analysis , philosophy , physics , epistemology , combinatorics , control engineering , engineering , thermodynamics
Abstract Computational simulations of interacting microstructure in solid structures, with methods such as the finite element method, require solutions to numerically enormous boundary value problems. The primary objective of this work is to introduce a‐posteriori error bounds for a domain decomposition which can be used to reduce the computational complexity of boundary value problems associated with such simulations. The approach is to partition and decouple the heterogeneous body into more computationally tractable, nonoverlapping, subdomains whose union forms the entire domain under analysis. This is achieved by computing a relatively inexpensive auxiliary „decoupling problem” with regularized coefficients but with the same external geometry and loading as the original body. The solution to the decoupling problem is then used to construct local boundary data for the subdomains, which can thereafter be solved independently, possibly in parallel.