Boundary Element Dual Reciprocity Method
With Overlapping Sub-domains
Author(s)
B. Thanh Tu & V. Popov
Abstract
In this paper a numerical approach based on the Boundary Element Method
(BEM) with overlapping sub-domains is presented. The approach simplifies the
assembly of the equations arising from the BEM sub-domain methods and at the
same time reduces the problems with near-singular or singular integrals that may
arise in the integral equations. The overlapping numerical approach is tested on a
convection-diffusion problem. The approach is implemented in combination with
the Dual Reciprocity Method (DRM) with two different Radial Basis Functions
(RBFs) and the results are compared with the previous results obtained using the
DRM-MD approach, showing good accuracy and convergence.
Keywords: boundary element method, domain decomposition, overlapping subdomains.
1 Introduction
The present formulation employs domain decomposition, but unlike the previous
BEM sub-domain methods it applies an overlapping approach which eliminates
the Interface Boundary Conditions (IBCs), simplifies assembly of the equations
and reduces the problems arising from near-singular or singular integrals. It also
leads to a closed system of equations while the BEM sub-domain techniques
with continuous elements lead to over-determined systems.
When using domain decomposition in three dimensions (3D) and for the case
where the number of sub-domains is large, imposing the IBCs may be
complicated since several sub-domains would generally share the same node
(vertex). In the BEM the IBCs include the flux conservation, which increases the
Keywords
boundary element method, domain decomposition, overlapping subdomains.
Related Book
Other papers in this volume
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