Title
Choosing an efficient conjugate gradient-based method to solve the dense systems of equations arising from the boundary element method

Affiliations
Iman Farahbakhsh¹ · Benyamin Barani Nia^1
1 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract
Solving the linear system of equations with nonsymmetric, dense, and typically ill-conditioned matrices can be considered a critical subject in BEM. Applying direct methods like Gauss elimination, Gauss-Jordan, and LU decomposition will be computationally expensive for the large-scale system of equations, and a rule of thumb shows that iterative methods are efficient. The present study considers the numerical solution of the Laplace equation with various boundary conditions. The numerical investigations on some Krylov subspace methods as bi-conjugate gradient (BiCG), conjugate gradient squared (CGS), and bi-conjugate gradient stabilized (BiCGSTAB) have been carried out, and convergence plots and CPU-time of these methods are compared. Results demonstrated the superiority of the Krylov subspace methods in the case of dense matrices.

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