24 Result(s)
within
Chapter
Ernst P. Stephan
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Chapter and Conference Paper
An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc
We consider here a Dirichlet problem for the two-dimensional linear elasticity equation in the domain exterior to an open arc in the plane. It is shown that the problem can be reduced to a system of boundary i...
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Chapter
Hierarchical Basis Preconditioners for Coupled Fem-Bem Equations
The purpose of this paper is to present a nearly optimal preconditioned iterative method to solve indefinite linear systems of equations arising from h-adaptive procedures for the symmetric coupling of Finite ...
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Chapter and Conference Paper
Adaptive BEM for Contact Problems with Friction
We describe two methods for the numerical solution of two-body frictional contact problems based on pure boundary integral formulations, and corresponding automatic mesh refinement procedures. For the h-version o...
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Chapter
The hp-Version of the Boundary Element Method for the Lamé Equation in 3D
We analyze the h-p version of the BEM for Dirichlet and Neumann problems of the Lamé equation on open surface pieces. With given regularity of the solution in countably normed spaces we show that the boundary ...
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Chapter and Conference Paper
Transient Boundary Element Method and Numerical Evaluation of Retarded Potentials
We discuss the modeling of transient wave propagation with the boundary element method (BEM) in three dimensions. The special structure of the fundamental solution of the wave equation leads to a close interac...
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Chapter and Conference Paper
Domain Decomposition Algorithms for an Indefinite Hypersingular Integral Equation in Three Dimensions
In this paper we report on a non-overlap** and an overlap** domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surfa...
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Chapter
A Boundary Integral Equation on the Sphere for High-Precision Geodesy
Spherical radial basis functions are used to approximate the solution of a boundary integral equation on the unit sphere which is a reformulation of a geodetic boundary value problem. The approximate solution ...
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Chapter
Finite Element and Boundary Element Approaches to Transmission and Contact Problems in Elasticity
Under the leadership of Professor Stephan, four PhD projects were investigated during the running period of the GRK615 on the field of error controlled finite element/boundary element methods, namely on adapti...
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Chapter
Additive Schwarz Methods for the hp Version of the Boundary Element Method in ℝ3
For the Galerkin matrices of the hypersingular and weakly singular first kind integral equations on plane surfaces we present preconditioners obtained by additive Schwarz methods. When those integral equations...
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Chapter
A Discrete Collocation Method for a Hypersingular Integral Equation on Curves with Corners
This paper is devoted to the approximate solution of a hypersingular integral equation on a closed polygonal boundary in ...
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Chapter
Diagonal Scaling Preconditioner and Locally-Refined Meshes
In this chapter, we study the effect of mesh refinements on the condition numbers of the stiffness matrices arising from the h-version Galerkin boundary element discretisation of the weakly-singular and hypersing...
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Chapter
Two-Level Methods: The p-Version
Similarly to Chapter 3, this chapter deals with the same issue for the p-version.
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Chapter
Additive Schwarz Methods for the hp-Version
This chapter deals with additive Schwarz methods for the hp-version on quasi-uniform and graded meshes. Multilevel methods are also analysed.
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Chapter
Indefinite Problems
This chapter designs and analyses additive Schwarz methods for boundary integral equations arising from the Helmholtz equation in two dimensions. A general theory for indefinite problems is developed and appli...
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Chapter
Multilevel Preconditioners with Adaptive Mesh Refinements
In this chapter we study the use of multilevel methods to obtain optimal preconditioners in the case that the mesh is locally refined. Local mesh refinements, particularly important for boundary element discre...
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Chapter
Introduction
This chapter sets the scene for the problems to be studied in this book. Typical problems from which boundary integral equations arise, namely, the scattering of time harmonic waves and cracks in elastic media...
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Chapter
Two-Level Methods: The h-Version
This chapter designs and analyses non-overlap** and overlap** additive and multiplicative Schwarz methods for the h-version. The novelty of this chapter is that in order to prove the coercivity of the decompo...
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Chapter
Multilevel Methods: The h-Version
When applying the two-level methods for the h-version, we have to solve a global problem on a coarse space. However, the dimensions of this coarse space can be large. Therefore it is natural to carry out the same...
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Chapter
A Fully Discrete Method
In this chapter, non-overlap** and overlap** additive Schwarz and multilevel preconditioners are analysed for a fully-discrete and symmetric method for the weakly singular integral equation
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Chapter
Implementation Issues and Numerical Experiments
In this chapter we discuss issues with implementation for the two-dimensional problems discussed in this part of the book. First we mention some important issues in implementation of the methods and then prese...
