Numerical solution of 2D Helmholtz Equation by Bicubic B-spline Collocation with SOR Iteration

Claire NC Motiun; Jumat Sulaiman; Aini Janteng; Asep Kuswandi Supriatna.

Two-dimensional Helmholtz equations arise in various fields, including acoustics, electromagnetics, and fluid dynamics, in which their numerical solutions are essential for modeling wave propagation phenomena. This study presents a numerical approach based on the Bicubic B-spline collocation method combined with the Successive Overrelaxation (SOR) iterative solver to efficiently solve the 2D Helmholtz equation. The method involves constructing a system of equations by discretizing the domain using Bicubic B-spline interpolation and collocation techniques. The resulting linear system is solved iteratively, and the performance of the SOR method is compared with the classical Gauss-Seidel (GS) iteration. Numerical experiments on three test cases demonstrate that the SOR iteration significantly reduces the number of iterations and computational time compared to the GS method, highlighting the effectiveness and efficiency of the proposed approach.

KEYWORDS: SOR Iteration; Gauss Seidel Iteration; B-spline Collocation Solution; Two-Dimensional Helmholtz Equation.



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