Assessment Of The Spectral Properties Of The
Double-layer Potential Matrix H
Author(s)
N. A. Dumont
Abstract
The double-layer potential matrix H of the conventional, collocation boundary
element method (CBEM) is singular, as referred to a static problem in a bounded
continuum. This means that no rigid body displacements can be transformed
between two different reference systems – and that unbalanced forces are to
be excluded from a consistent linear algebra contragradient transformation. The
properties of HT may become quite informative, as they reflect the topology
(concavities, notches, cracks, holes) of the discretized domain as well as material
non-homogeneities, which comes from the fact that local stress gradients can be
represented by fundamental solutions only in a global sense. Symmetries and
antisymmetries are also evidenced in N(HT) as well as the spectral properties
related to simple polynomial solutions that one may propose as patch tests. In
the usual implementations of the CBEM with real fundamental solutions, all
eigenvalues λ of H are real, λ ∈ R, 0 ≥ λ < 1 for a bounded domain.
This means that H is a contraction – a paramount mechanical feature that comes
up naturally in the frame of a virtual work investigation of Kelvin’s (singular)
fundamental solution and is resorted to in a simplified variational implementation
of the boundary element method.
Keywords: boundary elements, hybrid boundary elements, spectral properties,
variational methods.
Keywords
boundary elements, hybrid boundary elements, spectral properties,
variational methods
Related Book
Other papers in this volume
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