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A wavelet–Galerkin scheme for analysis of large‐scale problems on simple domains
Author(s) -
Díaz Alejandro R.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990420)44:11<1599::aid-nme556>3.0.co;2-p
Subject(s) - preconditioner , mathematics , galerkin method , conjugate gradient method , boundary value problem , lagrange multiplier , wavelet , mathematical optimization , simple (philosophy) , domain (mathematical analysis) , mathematical analysis , finite element method , linear system , computer science , philosophy , physics , epistemology , artificial intelligence , thermodynamics
A wavelet–Galerkin scheme tailored to address the numerical solution of large‐scale boundary value problems defined on domains of simple geometry is presented. The variation of parameters, e.g. material properties, within the domain is arbitrary but the method is specifically designed to solve problems where parameters vary in raster‐like fashion. Boundary conditions are imposed via Lagrange multipliers using a fictitious domain approach. A preconditioner specially designed for this problem is developed to guarantee that convergence of conjugate gradient algorithms is quick and insensitive to problem size. The strategy is applied to the solution of steady state, heat conduction problems in 2‐D, but it can be generalized without conceptual changes to 3‐D problems and to problems in linear elasticity. Copyright © 1999 John Wiley & Sons, Ltd.