A Multi-Dimensional Complex Variable Boundary Element Method Book

	Acknowledgements
	Contents
	List of Figures
1	Overview of the complex variable boundary element method (CVBEM)
	Abstract	1
1	Introduction	1
2	A complex variable boundary element model using linear polynomial trial functions	2
3	The analytic function defined by the approximator [omega](z)	17
4	A constant boundary element method	19
5	The complex variable boundary element method	20
6	Approximation error from the CVBEM	25
7	A strategy to reduce approximation error	27
8	Expansion of the H[subscript k] approximation function	29
2	Advanced topics in the CVBEM
1	Higher-order basis functions	39
2	Multiply connected domains	53
3	Application of the CVBEM to multiply connected regions	60
4	Expansion of the CVBEM into a series using fractals	72
3	CVBEM: A Hilbert space setting
1	Introduction	79
2	Mathematical development	81
3	The CVBEM and W[subscript [Omega]]	84
4	The best approximation method and the CVBEM	92
5	Representation of the CVBEM approximation function by a dimension mn vector space	97
4	Extension of the CVBEM to higher dimensions
1	Approximating three-dimensional potential problems using the CVBEM	99
5	Applications of the CVBEM to higher dimensions
1	Two potential function approximations	121
2	Approximating three-dimensional potential problems on a sphere	132
3	Approximating three-dimensional potential problems using the CVBEM and domain rotations	139
4	A generalized 3D complex variable boundary element method	151
6	Conclusions	183
App. A	3D CVBEM Computer Program	185
	App. B: Papers written during the course of this research	203
	References	205