The Boundary Element Method

1 Introduction
1.1 Why the boundary element method?
1.2 Typical applications of the boundary element method
1.3 Emergence of the boundary element method
1.4 History of boundary element eigenformulations
1.5 Organization of the book
2 Boundary Element Method Fundamentals
2.1 Introduction
2.2 Direct method: weighted residuals
2.3 Examples
2.4 Direct method: Green's integral theorem
2.5 Indirect method
2.6 Body forces
3 Isoparametric Boundary Elements
3.1 Introduction
3.2 Two-dimensional linear boundary elements
3.3 Higher-order elements in 2-D
3.4 Boundary elements in 3-D
3.5 Examples
4 Anisotropy, Axisymmetry and Zoning
4.1 Introduction
4.2 Anisotropic materials
4.3 Axisymmetric problems
4.4 Inhomogeneous regions and zoning
5 Time-Harmonic Analysis in Acoustics and Elasticity
5.1 Introduction
5.2 Acoustics
5.3 Elasticity
6 Dynamic Analysis: Acoustics and Elasticity
6.1 Introduction
6.2 Eigenvalue problem in acoustics
6.3 Eigenvalue problem in elasticity
6.4 Characteristic equation for eigenvalues
7 Basics of Algebraic Eigenvalue Problem Formulation
7.1 Introduction
7.2 Development of BE algebraic eigenvalue problem
7.3 Formulation of Internal Cell Method
7.4 Example of internal cell method: rectangular plate vibration
8 Algebraic Eigenvalue Problem in Boundary Elements
8.1 Introduction
8.2 Eigenproblem using dual reciprocity method in acoustics
8.3 Eigenproblem using particular integral method in elasticity
9 Advanced Concepts in Boundary Element Algebraic Eigenproblem
9.1 Introduction
9.2 Algebraic eigenvalue formulation using fictitious function
method
9.3 Example problems using fictitious function method
9.4 Effect of internal collocation points on eigensolutions
9.5 Polynomial-based particular integral method
9.6 Multiple reciprocity method (MRM)
9.7 Series expansion methods (SEM) with matrix augmentation
10 Acoustic Fluid-Structure Interaction Problems
10.1 Introduction
10.2 Boundary element-finite element coupled eigenanalysis of
fluid-structure system
10.3 Acoustic eigenproblem for enclosures with dissipative boundaries
10.4 Examples of acoustic eigenproblem with sound absorption
11 Solution Methods of Eigenvalue Problems
11.1 Introduction
11.2 Lanczos-based subspace approach
11.3 Lanczos recursion method
11.4 Example problems
11.5 Summary statements on the non-symmetric Lanczos eigensolver
11.6 Damped system eigenvalue problem solution
11.7 Lanczos two-sided recursion for the quadratic eigenvalue problem
11.8 Summary statements on eigenvalue computation algorithms
12 Discussion and Future Research
12.1 Discussion on boundary element eigenvalue methodologies
12.2 Comparison of eigenanalysis using BEM and FEM
12.3 Topics not covered in the book
12.4 Future research on BEM eigenanalysis