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Approximating three‐dimensional potential problems using the complex variable boundary element method (CVBEM)
Author(s) -
Hromadka T. V.
Publication year - 2000
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 - 10.1002/1098-2426(200011)16:6<535::aid-num3>3.0.co;2-p
Subject(s) - mathematics , dimension (graph theory) , focus (optics) , boundary element method , domain (mathematical analysis) , variable (mathematics) , boundary (topology) , residual , element (criminal law) , approximations of π , finite element method , algorithm , geometry , mathematical analysis , calculus (dental) , pure mathematics , political science , law , medicine , physics , dentistry , optics , thermodynamics
In the current research, the primary focus is to extend the CVBEM to solving potential problems in three dimensions (3D). This is achieved by applying the CVBEM to three coupled projections of the 3D problem domain, in 2D planes, and then superimposing the resulting corresponding 2D CVBEM solutions. The new 3D CVBEM technique is also applied towards improving 3D problem approximations, which are based on the usual 3D boundary element method (BEM) techniques, by approximating the 3D BEM residual error. Finally, a technique to extend a 3D problem geometry into higher geometric dimensions is introduced, and a corresponding numeric error reduction technique is advanced for use in superimposing multiple dimension approximations to improve 3D approximations. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 535–560, 2000.