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- Benedusi, Pietro, et al.
(författare)
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Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation
- 2021
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Ingår i: Journal of Scientific Computing. - : Springer. - 0885-7474 .- 1573-7691. ; 89:1
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Tidskriftsartikel (refereegranskat)abstract
- We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.
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- Benedusi, Pietro, et al.
(författare)
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Modeling Excitable Cells with the EMI Equations : Spectral Analysis and Iterative Solution Strategy
- 2024
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Ingår i: Journal of Scientific Computing. - : Springer. - 0885-7474 .- 1573-7691. ; 98:3
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we are interested in solving large linear systems stemming from the extra-membrane-intra model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial differential equations equipped with proper boundary conditions, we provide its finite element discretization and focus on the resulting large linear systems. We first give a relatively complete spectral analysis using tools from the theory of Generalized Locally Toeplitz matrix sequences. The obtained spectral information is used for designing appropriate preconditioned Krylov solvers. Through numerical experiments, we show that the presented solution strategy is robust w.r.t. problem and discretization parameters, efficient and scalable.
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