14 Result(s)
within
Chapter
Ernst P. Stephan
Partial Differential Equations
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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...
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Chapter
Two-Level Methods: The hp-Version on Rectangular Elements
IIn this chapter, we study different two-level methods for the hp-version of the Galerkin method with rectangular elements. Both the hypersingular and weakly-singular integral equations on a screen in three dimen...
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Chapter
FEM–BEM Coupling
The coupling of boundary elements and finite elements is a powerful tool for the numerical treatment of boundary value problems on unbounded domains, and in particular, of interface problems. It allows us to b...
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Chapter
General Framework of Preconditioners
This chapter provides the general framework of preconditioning by additive and multiplicative Schwarz operators. Preconditioners are viewed from different angles: in the matrix form, variational form, and oper...
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Chapter
Two-Level Methods: The Hp-Version on Triangular Elements
In this chapter we report on the paper [111] by Heuer, Leydecker, and Stephan, which analyses a two-level additive Schwarz method for the hp-version on triangular elements applied to the hypersingular integral eq...
