ACCELERATED ALGORITHM FOR SOLVING THE DIRECT SCATTERING PROBLEM FOR THE WAVE EQUATION
L.L. Frumin1, A.E. Chernyavsky1,2
1Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
Keywords: Helmholtz equation, direct scattering problem, implicit scheme, transfer matrix
Abstract
A numerical solution of the direct scattering problem for the one-dimensional Helmholtz equation is considered. Within the framework of the transfer matrix method, an implicit difference scheme for the transfer matrix of the second order of approximation accuracy is obtained by the integral method. Based on the duplication strategy, the convolution theorem, and the fast Fourier transform, an algorithm for the accelerated solution of the Helmholtz equation is presented, which asymptotically requires only O(Nlog2N) arithmetic operations. Numerical modeling of the scattering problem is performed using the example of an exponential smooth layer whose solution is known. Numerical simulation has confirmed the accuracy and high speed of the proposed algorithm, which is necessary in practical applications for optical and acoustic sensing of media in applied optics and acoustics.
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