Rapid solution of integral equations of scattering theory in two dimensions. (English) Zbl 0686.65079

Rokhlin, V.

J. Comput. Phys. 86, No. 2, 414-439 (1990).

The author considers the two-dimensional problem of scattering by a homogeneous obstacle. He points out that the problem, originally expressed in terms of the Helmholtz equation, can be reformulated in integral equation form. He discusses the error in the truncation of infinite series of Bessel functions and develops an iterative algorithm for solving the integral equation system. He indicates that, when these are n nodes, the amount of work required is of order \(n^{4/3}\). This is an improvement on previous methods where the order is \(n^ 2\).

Reviewer: Ll.G.Chambers

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
65R20	Numerical methods for integral equations
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35C15	Integral representations of solutions to PDEs
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
76Q05	Hydro- and aero-acoustics

Keywords:

rapid solution; two-dimensional scattering; Helmholtz equation; series of Bessel functions; iterative algorithm

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