A fast and efficient iterative scheme for viscoelastic flow simulations with the DEVSS finite element method |
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| Authors: | Wook Ryol Hwang Mark A Walkley Oliver G Harlen |
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| Institution: | 1. Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom;2. School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom;3. School of Mechanical and Aerospace Engineering, Research Center for Aircraft Parts Technology (ReCAPT), Gyeongsang National University, Jinju 660-701, South Korea;1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa;2. Center for Research in Computational and Applied Mechanics, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa;1. Mathematics Department, Faculty of Science, Taif University, Saudi Arabia;2. Mathematics Department, Faculty of Science, Sohag, Egypt;3. Mathematics Department, Faculty of Science, SVU, Qena 83523, Egypt |
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| Abstract: | We present a new fast iterative solution technique for the large sparse-matrix system that is commonly encountered in the mixed finite-element formulation of transient viscoelastic flow simulation: the DEVSS (discrete elastic-viscous stress splitting) method. A block-structured preconditioner for the velocity, pressure and viscous polymer stress has been proposed, based on a block reduction of the discrete system, designed to maintain spectral equivalence with the discrete system. The algebraic multigrid method and the diagonally scaled conjugate gradient method are applied to the preconditioning sub-block systems and a Krylov subspace iterative method (MINRES) is employed as an outer solver. We report the performance of the present solver through example problems in 2D and 3D, in comparison with the corresponding Stokes problems, and demonstrate that the outer iteration, as well as each block preconditioning sub-problem, can be solved within a fixed number of iterations. The required CPU time for the entire problem scales linearly with the number of degrees of freedom, indicating O(N) performance of this solution algorithm. |
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