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Georgiev, Krassimir; Zlatev, Zahari

Implementation of sparse matrix algorithms in an advection-diffusion-chemistry module. (English) Zbl 1228.65184

J. Comput. Appl. Math. 236, No. 3, 342-353 (2011).
Summary: A two-dimensional advection-diffusion-chemistry module of a large-scale environmental model is taken. The module is described mathematically by a system of partial differential equations. Sequential splitting is used in the numerical treatment. The non-linear chemistry is the most time-consuming part and it is handled by six implicit algorithms for solving ordinary differential equations. This leads to the solution of very long sequences of systems of linear algebraic equations. It is crucial to solve these systems efficiently. This is achieved by applying four different algorithms. The numerical results indicate that the algorithms based on a preconditioned sparse matrix technique and on a specially designed algorithm for the particular problem under consideration perform best.

Cited in 2 Documents

MSC:

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

Keywords:

environmental models; advection-diffusion-chemistry module; partial differential equations; ordinary differential equations; systems of linear algebraic equations; sparse matrix techniques; preconditioning; semidiscretization; non-linear chemistry; algorithms; numerical results

Software:

RODAS; CGS; LAPACK; SuperLU
PDFBibTeX XMLCite
\textit{K. Georgiev} and \textit{Z. Zlatev}, J. Comput. Appl. Math. 236, No. 3, 342--353 (2011; Zbl 1228.65184)
Full Text: DOI

References:

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