Sergej Rjasanow, Olaf Steinbach
The Fast Solution of Boundary Integral Equations.
Mathematical and Analytical Techniques with Applications to Engineering, Springer, 2007.
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Table of Contents
1Boundary Integral Equations
1.1Laplace Equation
1.2Lame Equation
1.3Stokes System
1.4Helmholtz Equation
2Boundary Element Methods
2.1Boundary Elements
2.2Basis Functions
2.3Laplace Equation
2.4Lame Equations
2.5Helmholtz Equation
3Approximation of Boundary Element Matrices
3.1Hierarchical Matrices
3.2Block Approximation Methods
4Implementation and Numerical Examples
4.1Geometry Description
4.2Laplace Equation
4.3Linear Elastostatics
4.4Helmholtz Equation
AMathematical Foundations
A.1Function Spaces
A.2Fundamental Solutions
A.3Mapping Properties
BNumerical Analysis
B.1Variational Methods
B.2Approximation Properties
CNumerical Algorithms
C.1Numerical Integration
C.2Analytic Integration
C.3Iterative Solution Methods