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A new method for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM. (English) Zbl 1302.65264
Summary: This work presents a new method for numerical computation of the two-dimensional nearly singular integrals by using the eight-node second-order quadrilateral surface elements in a 3D boundary element method (BEM). A new indirect regularized boundary element formulation excluding the Cauchy principal value and Hadamard-finite-part integrals is proposed. Based on this, a new approximation formula of the distance from the fixed calculation point to a generic point of the aforementioned surface geometry elements is developed firstly, and then the exponential transformation, which has been widely employed in the 2D BEM, is extended to the 3D BEM to remove the near singularities of integrands for the considered integrals. Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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