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An efficient boundary element method for a class of parabolic differential equations using discretization in time
Author(s) -
Ingber M. S.
Publication year - 1987
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690030304
Subject(s) - mathematics , discretization , mathematical analysis , boundary element method , time derivative , boundary value problem , finite element method , parabolic partial differential equation , boundary knot method , term (time) , boundary (topology) , partial differential equation , physics , quantum mechanics , thermodynamics
A new boundary element method using discretization in time is proposed to solve a class of parabolic differential equations. The method treats the term containing the time derivative as a forcing term. This necessitates the introduction of additional unknowns in the interior of the domain. At the same time, however, values for the dependent variable are determined directly in the interior. The boundary element formulation is reduced to essentially solving a Poisson equation. The accuracy and efficiency of the method are demonstrated with several examples.