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

• Published in: Journal of computational and applied mathematics Vol. 236; no. 3; pp. 342 - 353
• Main Authors: Georgiev, Krassimir, Zlatev, Zahari
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2011
• Subjects: Advection–diffusion–chemistry module; Algebra; Algorithms; Differential equations; Environmental models; Mathematical analysis; Mathematical models; Modules; Ordinary differential equations; Partial differential equations; Sparse matrix techniques; Splitting; Systems of linear algebraic equations; Two dimensional; Ordinary differential equations; Environmental models; Partial differential equations; Systems of linear algebraic equations; Advection–diffusion–chemistry module; Sparse matrix techniques
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2011.07.026

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 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.