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Fast decomposition of matrices generated by the boundary element method
Author(s) -
Rezayat Mohsen
Publication year - 1992
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/nme.1620330602
Subject(s) - domain decomposition methods , diagonal , matrix (chemical analysis) , boundary element method , diagonal matrix , mathematics , finite element method , boundary (topology) , degrees of freedom (physics and chemistry) , element (criminal law) , extension (predicate logic) , coefficient matrix , algorithm , domain (mathematical analysis) , boundary value problem , mathematical optimization , mathematical analysis , computer science , geometry , engineering , physics , structural engineering , eigenvalues and eigenvectors , materials science , quantum mechanics , political science , law , composite material , programming language
A new method to reduce the solution time of matrices generated by the Boundary Element Method is presented here. The method involves converting the fully populated system into a banded system by lumping certain coefficients of the matrix into fictitious nodes and then constraining these nodes to accurately represent each coefficient. The major advantages of lumping over the substructuring method are that lumping can be applied to arbitrarily shaped geometries and infinite‐domain problems and that it preserves the diagonal‐dominance of the matrix. It is shown here that the proposed algorithm reduces the rate of increase of solution time t of an n ‐degree‐of‐freedom problem from t ∝ n 3 to t ∝ n 2 . Although the algorithm is for thermal problems, its extension to mechanical problems is straightforward. The procedure can easily be incorporated into existing boundary‐element‐based packages.