Analysis of numerical integration error for Bessel integral identity in fast multipole method for 2D Helmholtz equation. (English) Zbl 1219.65141
Summary: In a 2D fast multipole method for scattering problems, a square quadrature rule is used to discretize the Bessel integral identity for a diagonal expansion of the 2D Helmholtz kernel, and the numerical integration error is introduced. Taking advantage of the relationship between the Euler-Maclaurin formula and the trapezoidal quadrature rule, and the relationship between the trapezoidal and the square quadrature rule, a sharp computable bound with analytical form on the error of the numerical integration of the Bessel integral identity by the square quadrature rule is derived. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N15 | Error bounds for boundary value problems involving PDEs |
Keywords:
Bessel integral identity; fast multipole method; boundary element method; 2D Helmholtz equation; error bounds; scattering; Euler-Maclaurin formula; trapezoidal quadrature rule; square quadrature rule; numerical experimentsReferences:
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