TY - JOUR

T1 - Accelerated Algorithm for Solving the Direct Scattering Problem for the Wave Equation

AU - Frumin, L. L.

AU - Chernyavsky, A. E.

N1 - Frumin, L.L., Chernyavsky, A.E. Accelerated Algorithm for Solving the Direct Scattering Problem for the Wave Equation. Optoelectron.Instrument.Proc. 61, 737–743 (2025). This work was supported by the Russian Science Foundation, project no. 24-22-00183.

PY - 2025/12

Y1 - 2025/12

N2 - Direct scattering problem for the one-dimensional Helmholtz equation is numerically solved. The transfer matrix method and the integral method are used to obtain a second-order accurate implicit difference scheme for the transfer matrix. A duplication strategy, a convolution theorem, and a fast Fourier transform are used to develop an algorithm for accelerated solution of the Helmholtz equation, asymptotically requiring only arithmetic operations. The scattering problem is numerically solved using the example of an exponential smooth layer, the solution to which is known. The numerical simulation confirmed that the proposed algorithm is accurate and fast, which is necessary in practical applications for optical and acoustic sensing of media in applied optics and acoustics.

AB - Direct scattering problem for the one-dimensional Helmholtz equation is numerically solved. The transfer matrix method and the integral method are used to obtain a second-order accurate implicit difference scheme for the transfer matrix. A duplication strategy, a convolution theorem, and a fast Fourier transform are used to develop an algorithm for accelerated solution of the Helmholtz equation, asymptotically requiring only arithmetic operations. The scattering problem is numerically solved using the example of an exponential smooth layer, the solution to which is known. The numerical simulation confirmed that the proposed algorithm is accurate and fast, which is necessary in practical applications for optical and acoustic sensing of media in applied optics and acoustics.

KW - Helmholtz equation

KW - direct scattering problem

KW - implicit scheme

KW - transfer matrix

UR - https://www.scopus.com/pages/publications/105035421368

UR - https://www.mendeley.com/catalogue/1b5f68b3-c5f2-366e-8409-6ae55c1e5ff5/

U2 - 10.3103/S8756699025700840

DO - 10.3103/S8756699025700840

M3 - Article

VL - 61

SP - 737

EP - 743

JO - Optoelectronics, Instrumentation and Data Processing

JF - Optoelectronics, Instrumentation and Data Processing

SN - 8756-6990

IS - 6

ER -