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A new formulation of regularized meshless method applied to interior and exterior anisotropic potential problems. (English) Zbl 1426.65201
Summary: This paper proposes a new formulation of regularized meshless method (RMM), which differs from the traditional RMM in that the traditional formulation generates the diagonal elements of influence matrix via null-field integral equations, while our new one directly employs the boundary integral equations at the domain point to evaluate the diagonal elements. We test the present RMM formulation to two-dimensional anisotropic potential problems in finite and infinite domains in comparison with the traditional RMM. Numerical results show that the present RMM sharply outperforms the traditional RMM in the solution of interior problems, while the latter is clearly superior for exterior problems. A rigorous theoretical analysis of circular domain case also corroborates such numerical experiment observations and is provided in the appendix of this paper.

MSC:
65N99 Numerical methods for partial differential equations, boundary value problems
65N38 Boundary element methods for boundary value problems involving PDEs
74E10 Anisotropy in solid mechanics
74S15 Boundary element methods applied to problems in solid mechanics
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