Implementation of sparse matrix algorithms in an advection-diffusion-chemistry module

DOI10.1016/j.cam.2011.07.026zbMath1228.65184OpenAlexW2069183763WikidataQ115100157 ScholiaQ115100157MaRDI QIDQ645725

Zahari Zlatev, Krassimir Georgiev

Publication date: 10 November 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.07.026

zbMATH Keywords

algorithmsnumerical resultspreconditioningordinary differential equationssemidiscretizationpartial differential equationssystems of linear algebraic equationsenvironmental modelsadvection-diffusion-chemistry modulenon-linear chemistrysparse matrix techniques

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Classical flows, reactions, etc. in chemistry (92E20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Ecology (92D40) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Uses Software

• LAPACK
• SuperLU
• RODAS
• CGS

Cites Work

• A comparison of some GMRES-like methods
• A new family of block methods
• Accelerating with rank-one updates
• Experiences with sparse matrix solvers in parallel ODE software
• A global numerical ocean model. I
• Computational and numerical challenges in environmental modelling
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique
• Modified Diagonally Implicit Runge–Kutta Methods
• Use of Iterative Refinement in the Solution of Sparse Linear Systems
• Comparison of Two Algorithms for Solving Large Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Some A -Stable and L -Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations
• A Supernodal Approach to Sparse Partial Pivoting
• An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
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