Kesten and Mr. Robert E. Olson for their encouragement and support. We gratefully acknowledge the support of Dr. Carson Yates, Jr.
A Short Course on Boundary Element Methods
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FAQ Policy. About this book The Boundary Element Method BEM has become established as an effective tool for the solutions of problems in engineering science.
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Show all. Consider the boundary value problem BVP. In the modern theory of partial differential equations, the smoothness of solutions is commonly described in terms of Sobolev spaces.
They have nearly become the basic language of PDE. Detailed studies of Sobolev spaces can be found in [2, ], for example. In this section, we will briefly introduce what these spaces are and some of their basic properties, to the extent that they are sufficient for the subsequent material in this book. The most important thing here is to understand the content of Theorems 2. Their proofs, although not difficult to comprehend, do appear a little technical for an inexperienced reader and, thus, can be put off to the second reading. In the study of boundary integral equations, the theory of distributions naturally comes into use.
This theory began with the use of the Dirac delta function by the British physicist P. Dirac during the s and s.
Fast Multipole Boundary Element Method: Theory and Applications in Engineering - PDF Free Download
It was found to be extremely useful in solving ordinary and partial differential equations and became very popular, but was rejected by many mathematicians because it was not a classical function and its usage lacked mathematical rigor. In —51, the French mathematician L. Today, this theory is fundamental in the study of partial differential equations.
For a detailed account of the theory of distributions, we refer the reader to [27, 76, ]. Pseudodifferential operators are a natural extension of linear integral and partial differential operators.
This theory has found many fields of application. In particular, all the boundary integral operators corresponding to the elliptic boundary value problems studied in this book are such operators. By using such a theory, the analysis of boundary integral equations and boundary element methods can be either greatly simplified or presented in a more general and elegant form.
Finite-element method s FEM were first introduced by R. Courant  in