一、課程簡介:
1. Introduction
2. Mathematical preliminary
2.1 vectors
2.2 integral equations
2.3 Green’s second identity
2.4 Fundamental solution
2.5 Gauss guadrature

3. Indirect method (potential problem)
3.1 Elements of potential theory
3.2 Indirection formulation
3.3 Constant element

4. Direct method (Laplace equation)
4.1 Derivation of the singular boundary integral equation
4.2 BEM- constant element
4.3 Linear element (2D)
4.4 Quadratic element (2D)
4.5 Mixed type boundary condition
4.6 Boundary elements for 3D problems
4.7 Sub-regions
4.8 Infinite region---exterior problem
4.9 Special fundamental solution ( Semi-infinite region)
4.10 Poisson equation

5. Helmholtz equation
5.1 Preliminary consideration
5.2 Boundary integral equation
5.3 Dual reciprocity method
5.4 The non-unique problem
5.5 Frequency interpolation
5.6 Multiple reciprocity method
5.7 Arbitrary-order boundary element method

6. Elasticstatic problem
6.1 Stress and tractions
6.2 Reciprocal work theorem
6.3 Boundary integral equation

7. Introduction to the hypersingular integral equation)
7.1 Response-gradient boundary integral equations
7.2 Hypersingular boundary integral equations
7.3 Regularization of Hypersingular boundary integral equations


二、先修課程:工程數學、數值分析

三、參考書目:

1. C. A. Brebbia, J. C. F. Telles and L. C. Wrobel `Boundary
Element Techniques Theory and application in Engineering`
2. A. A. Becker, `The Boundary Element Method in Engineering`,
McMraw-Hill Book Company.
3. P. K. Kytbe, “An introduction to Boundary Element methods”
CRC Press.