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Exact transformation of a wide variety of domain integrals into boundary integrals in boundary element method. (English) Zbl 1156.65099
Summary: A sufficient condition for transforming domain integrals into boundary integrals is described. The transformation is accomplished by Green’s and Gauss’ theorems. It is shown that a wide range of domain integrals including some integrals in the boundary element method satisfy this sufficient condition and can be simply transformed into the boundary.
Although emphasis is made on potential and elastostatic problems, this method can also be used for many other applications. Using the present method, a wide range of 2D and 3D domain integrals over simply or multiply connected regions can be transformed exactly into the boundary. The resultant boundary integrals are numerically evaluated using an adaptive version of the Simpson integration method. Several examples are provided to show the efficiency and accuracy of the present method.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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