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Convergence of the high-accuracy algorithm for solving the Dirichlet problem of the modified Helmholtz equation. (English) Zbl 1440.65261

Summary: In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is developed to deal with weakly singular integrals. The convergence of the algorithm is proved based on Anselone’s collective compact theory. Moreover, an asymptotic error expansion shows that the algorithm is of order \(O \left(h_0^3\right)\). The numerical examples support the theoretical analysis.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
65D30 Numerical integration
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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