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Biconjugate Gradient Stabilized and V-cycle Multigrid Methods for Discretized Helmholtz Equation: A Comparative Study |
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PP: 1039-1048 |
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doi:10.18576/amis/190506
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Author(s) |
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N. H. Sweilam,
Ibrahim M. Hanafy,
Moutaz Ramadan,
Azza Eseily,
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Abstract |
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| In this work, a comparison between two numerical techniques for solving the discretized scheme of Helmholtz equation is conducted: the first technique is the V-cycle multigrid method combined with the Generalized Minimal Residual Method as a smoother and the second technique is the Biconjugate Gradient Stabilized Method. On the other side, Helmholtz equation will be discretized using the finite difference method, converting the continuous problem to a linear system of equations. The multigrid method leverages a hierarchical, multi-level framework to accelerate convergence by addressing errors across various spatial scales, while Biconjugate Gradient Stabilized Method is an independent iterative technique known for its stability and convergence efficiency. Through this comparative study, we evaluate the performance of both approaches based on the convergence rate, computational cost, and iteration count to achieve a specified accuracy. Numerical experiments are conducted across multiple grid sizes to assess effectiveness. |
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