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Boundary element methods. (English) Zbl 0842.65071
Computational Mathematics and Applications. London: Academic Press. xx, 646 p. (1992).
Boundary element methods (BEM) have undergone a rapid advancement in recent years. Because of their numerous advantages, such as ease of coding, small memory requirement and computational efficiency, they have become a major numerical tool. The analysis and rigor of BEM have been strengthened through the work of several mathematicians. It is now possible for the authors to fit together the many scattered contributions into a comprehensive account.
In this book, we present mathematical formulations of boundary integral equations for several of the most important linear elliptic boundary value problems, discuss their computational algorithms and the accuracy of their solutions, illustrate the numerical solutions and show some applications.
We wrote this monograph as a reference source for researchers who are concerned with numerical solutions of partial differential equations, and as a graduate text for a course in this subject.

65N38 Boundary element methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
35C15 Integral representations of solutions to PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65R20 Numerical methods for integral equations