TitleA Survey on the Performance of Krylov Subspace Methods in High Order Compact Schemes for Solving Poisson’s Equation for Application in Incompressible Fluid Flow Solvers AffiliationsIman Farahbakhsh1 · Benyamin Barani Nia1. Mehdi Dehghan21 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran.2 Department of Applied Mathematics, Faculty of Mathematics andComputer Sciences, Amirkabir University of Technology (TehranPolytechnic), Tehran, Iran. AbstractThe efficiency of three Krylov subspace methods with their ILU0- preconditioned version in solving the systems with the nonadiagonal sparse matrix is examined. The systems have arisen from the discretization of Poisson’s equation using the 4th and 6th-order compact schemes. Four matrix-vector multiplication techniques based on four …

TitleChoosing an efficient conjugate gradient-based method to solve the dense systems of equations arising from the boundary element method AffiliationsIman Farahbakhsh1 · Benyamin Barani Nia11 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran AbstractSolving 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 …

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