Solving advection equations by applying the crank-nicolson scheme combined with the richardson extrapolation

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples. Copyright Zahari Zlatev et al

Parallel performance and scalability experiments with the Danish Eulerian Model on the EPCC supercomputers

The Danish Eulerian Model (DEM) is a powerful air pollution model, designed to calculate the concentrations of various dangerous species over a large geographical region (e.g. Europe). It takes into account the main physical and chemical processes between these species, the actual meteorological conditions, emissions, etc.. This is a huge computational task and requires significant resources of storage and CPU time. Parallel computing is essential for the efficient practical use of the model. Some efficient parallel versions of the model were created over the past several years. A suitable parallel version of DEM by using the Message Passing Interface library (AIPI) was implemented on two powerful supercomputers of the EPCC - Edinburgh, available via the HPC-Europa programme for transnational access to research infrastructures in EC: a Sun Fire E15K and an IBM HPCx cluster. Although the implementation is in principal, the same for both supercomputers, few modifications had to be done for successful porting of the code on the IBM HPCx cluster. Performance analysis and parallel optimization was done next. Results from bench marking experiments will be presented in this paper. Another set of experiments was carried out in order to investigate the sensitivity of the model to variation of some chemical rate constants in the chemical submodel. Certain modifications of the code were necessary to be done in accordance with this task. The obtained results will be used for further sensitivity analysis Studies by using Monte Carlo simulation

APPARC PaA6a Deliverable ESPRIT BRA III Contract 6634 PARASPAR: A Package for the Solution of Large and Sparse Systems of Linear Algebraic Equations, on Parallel Computers with Shared Memory

Package PARASPAR is a set of FORTRAN subroutines for solving linear systems of algebraic equations Ax = b whose coefficient matrices are assumed to be 1. real, 2. large 3. general sparse. It is not assumed that the matrix has any special property (such as symmetry or positive definiteness) or any special pattern (such as bandedness). The subroutines of the package PARASPAR are optimized for parallel computers with shared memory and with not too many tightly connected processors. In fact the subroutines were extensively tested on FX/80 and FX/2800 ALLIANT computers, but the most important processes that can be carried out in parallel are well-separated (in subroutines that can be called concurrently in loops). Therefore it is easy to optimize the package on other computers. The subroutines from package PARASPAR have already been National Environmental Research Institute Frederiksborgvej 399, DK-4000 Roskilde, Denmark, e-mail address: [email protected] y The Danish Computer Cent..