A parallel iterative algorithm for solving the two-dimensional Helmholtz equation with discontinuous coefficients using a high-order compact finite difference scheme

Jinyang Zheng and Xiufang Feng

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 179-188

Abstract: This paper considers the two-dimensional Helmholtz equation with discontinuous coefficients and constructs a fourth-order compact finite difference scheme based on the immersed interface method. The component-averaged row projection-conjugate gradient (CARP-CG) algorithm is applied to solve the discretized system of linear equations. Numerical experiments demonstrate that the CARP-CG algorithm exhibits superior convergence characteristics compared with the traditional successive over-relaxation algorithm while maintaining fourth-order accuracy. The computation times with various numbers of processors are measured, allowing the optimal number of processors to be determined. The results demonstrate that the CARP-CG algorithm achieves good parallel performance, providing an efficient and reliable computational solution for large and complex problems.

Keywords: Helmholtz equation; Immersed interface method; CARP-CG; Parallel processing (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:179-188

DOI: 10.1016/j.matcom.2025.04.030

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