Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

Parallel Computations in a Large-Scale Air Pollution Model

Author(s): Zahari Zlatev, Krassimir Georgiev and Ivan Dimov

Pp: 166-202 (37)

DOI: 10.2174/9781608057788113010010

* (Excluding Mailing and Handling)


Large-scale air pollution models, which are normally described mathematically as systems of partial differential equations, must very often be run efficiently on high-speed computer architectures. The requirement for efficiency is especially important when some fine discretization of the spatial domain is to be applied. In practice, this means that an efficient implementation of such a model on fast modern computers must nearly always be achieved, because as a rule fine grids are needed in the efforts to avoid the appearance of numerical errors that are comparable with or even larger than the errors which are caused by other reasons (uncertainties of the meteorological data, of the emission data, of the rates of the involved chemical reactions, etc.). The organization of the parallel computations will be discussed in this chapter of the eBook. The major principles, on which the parallelization is based, are rather general and, therefore, some of the discussed techniques can also be applied in connection with some large-scale models arising in other areas of science and engineering.

Keywords: Balkan Peninsula, Bulgaria, Denmark, England, Hungary, boundary condition, initial condition, Semi-discretization, sub-models, advection, semi- Lagrangian discretization, pseudo-spectral discretization, trigonometric polynomials, truncated Fourier series, Taylor series, QSSA (Quasi-Steady-State-Approximation), Trapezoidal Rule, Runge-Kutta method, A-stable, Strongly A-stable, L-stable method, BLAS (Basic Linear Algebra Subroutines), LAPACK, quasi-Newton iterative method, Cache memory, MPI, OpenMP.

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