A Spectral Boundary Element Method
Author(s)
A. Calaon, R. Adey & J. Baynham
Abstract
The Boundary Element Method (BEM) is not local and generates a full and nonsymmetric
matrix, therefore the matrix solution time could easily grow beyond
acceptable limits. Furthermore, in many cases a decoupling between geometry
description and solution approximationwould be advantageous and desirable. This
work aims at offering the BEM a new approximation capability, which could
reduce the number of degrees of freedom (dofs) needed, and at providing the
desired decoupling. The method proposed here takes advantage of the less restrictive
requirements in BEM compared with FEM for the field approximation. The
base of the new approximation becomes what has been called \“Spectral Element”
(SE): a super-entity gathering many elements, which are used only for geometry
description and numerical integration. Spectral shape functions are generated
using smooth positive definite compact supported Radial Basis Functions (RBF).
The method was applied to linear elasticity in 3D and numerical tests were performed
for different typical cases in order to highlight advantages, disadvantages
and limits of the proposed methodology.
1 Approximation field in the BEM
1.1 Some general properties of the \“finite element approximation”
Both BEM and FEM, in order to reduce the infinite dimensional space of the solution
to a finite one, use the so called finite transform. If x represents the vector of
space coordinates and u the approximation field, a set of \“generalised degrees of
freedom” in the form of a vector α must be chosen so that:
u(x) = A(x)α (1)
Keywords
Related Book
Other papers in this volume
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