Boundary Integral Equation Method

**Ken-ichi Yoshida ^{1}
Dept. of Global Environment Eng.
Kyoto Univ.,
Japan**

**March 2001**

- Contents
- List of Figures
- Introduction
- Overview of Fast Multipole Method (FMM)
- Applications of FMM to three-dimensional crack problems
- Crack
- Crack problems for three-dimensional Laplace's equation
- Crack problems for three-dimensional elastostatics with collocation method
- Crack problems for three-dimensional elastostatics with Galerkin's method
- Three-dimensional scattering of scalar waves by cracks
- Three-dimensional scattering of elastic waves by a crack
- Concluding remarks

- Applications of the new FMM to three-dimensional problems
- Final remarks
- Series expansion of
- Relations between solid harmonics
*R*_{n,m}and*S*_{n,m} - Recurrence formulae for
*R*_{n,m}and*S*_{n,m} - Derivatives of
*R*_{n,m}and*S*_{n,m} - M2M, M2L, L2L in three-dimensional Laplace's equation
- Series expansion of |
*x*-*y*| - Series expansion of the fundamental solution of three-dimensional elastostatics
- M2M, M2L, L2L in three-dimensional elastostatics
- M2M, M2L, L2L in three-dimensional Helmholtz's equation
- M2X, X2X, X2L in three-dimensional Laplace's equation
- M2X, X2X, X2L in three-dimensional elastostatics
- Regularisation of integral equations
- Bibliography
- About this document ...