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On the numerical solution of sparse linear systems emerging in finite volume discretizations of 2D Boussinesq-type models

Abstract : This work supplements the realization and validation of a higher-order well balanced finite volume (FV) scheme developed for numerically simulating, on triangular meshes, weakly non-linear weakly dispersive water waves over varying bathymetries. The scheme has been recently presented by Kazolea et al. \textit{(Coastal Eng. 69:42-66, 2012 and J. Comp. Phys. 271:281-305, 2014)}. More precisely, we investigate and develop solution strategies for the sparse linear system that occurs during this FV discretisation of a set of Boussinesq-type equations on unstructured meshes. The resultant system of equations must be solved at each time step as to recover the actual velocity field of the flow. The system's coefficient matrix is sparse, un-symmetric and often ill-conditioned. Its characteristics are affected by physical quantities of the problem to be solved, such as the un-disturbed water depth and the mesh topology. This work investigates the application of different iterative techniques, with and without the usage of preconditioners and reordering, for the solution of this sparse linear system. Two different iterative methods, three preconditioning techniques, including different ILU factorizations and two different reordering techniques are implemented and discussed. An optimal strategy, in terms of computational efficiency and robustness, is proposed.
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https://hal.inria.fr/hal-01202983
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Submitted on : Tuesday, September 22, 2015 - 9:49:23 AM
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Maria Kazolea, M Gaitani, Argiris I. Delis. On the numerical solution of sparse linear systems emerging in finite volume discretizations of 2D Boussinesq-type models. [Research Report] RR-8778, INRIA Bordeaux, équipe CARDAMOM. 2015, pp.28. ⟨hal-01202983⟩

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