A Zooming Technique for Wind Transport of Air Pollution

In air pollution dispersion models, typically systems of millions of equations that describe wind transport, chemistry and vertical mixing have to be integrated in time. To have more accurate results over specific fixed areas of interest---usually highly polluted areas with intensive emissions---a local grid refinement or zoom is often required. For the wind transport part of the models, i.e.\ for finite volume discretizations of the transport equation, we propose a zoom technique that is positive, mass-conservative and allows to use smaller time steps as enforced by the CFL restriction in the zoom regions only

On the diagonal approximation of full matrices

AbstractIn this paper the construction of diagonal matrices, in some sense approximating the inverse of a given square matrix, is described. The matrices are constructed using the well-known computer algebra system Maple. The techniques we show are applicable to square matrices in general. Results are given for use in Parallel diagonal-implicit Runge-Kutta (PDIRK) methods. For an s-stage Radau IIA corrector we conjecture s! possibilities for the diagonal matrices

Test set for initial value problem solvers

The CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differential equations. This test set can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application field and numerical mathematics. This document contains the descriptive part of the test set. It describes the test problems and their origin, and reports on the behavior of a few state-of-the-art solvers on these problems. The latest version of this document and the software part of the test set is available via the world wide web at url{http://www.cwi.nl/cwi/projects/IVPtestset/. The software part serves as a platform on which one can test the performance of a solver on a particular test problem oneself. Instructions how to use this software are in this paper as well. The idea to develop this test set was discussed at the workshop ODE to NODE, held in Geiranger, Norway, 19--22 June~1995