Direct methods for sparse matrices
Direct methods for sparse matrices
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Parallel runs of a large air pollution model on a grid of Sun computers
Mathematics and Computers in Simulation
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
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An advection-diffusion-chemistry module of a large-scale air pollution model is split into two parts: (a) advection-diffusion part and (b) chemistry part. A simple sequential splitting is used. This means that at each time-step first the advection-diffusion part is treated and after that the chemical part is handled. A discretization technique based on central differences followed by Crank-Nicolson time-stepping is used in the advection-diffusion part. The non-linear chemical reactions are treated by the robust Backward Euler Formula. The performance of the combined numerical method (splitting procedure + numerical algorithms used in the advection-diffusion part and in the chemical part) is studied in connection with six test-problems. We are interested in both the accuracy of the results and the efficiency of the parallel computations.