Direct methods for sparse matrices
Direct methods for sparse matrices
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Running Large-Scale Air Pollution Models on Message Passing Machines
Proceedings of the 4th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
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Mathematical models are indispensable tools in different environmental studies. Such models are usually described by systems of partial differential equations (PDE's). The number of equations in the PDE system is equal to the number of the chemical species involved in the model. The application of different discretization and splitting techniques transforms the system of partial differential equations into five very large systems of ordinary differential equations (ODE's). The treatment of the ODE systems leads to the solution of several large systems of linear algebraic equations at every time-step. Sparse matrix technique can be used in order to reduce the number of arithmetic operations. The efficiency can be further increased by applying parallel algorithms. The use of a special sparse matrix algorithm and the parallelization of the computational process will be discussed in this paper.