Schedule: February 5, 7, 12, 14, 19, 2002, 2:00 pm - 4:30 pm
The problems connected with the environmental pollution are becoming
more and more important. It is necessary to use advanced mathematical
models in order to give adequate answers to the numerous questions arising
in this field. These models are described by systems of partial differential
equations (PDEs). The number of equations is equal to the number of
chemical species involved in the model. In the attempts to obtain more
reliable results one tries (i) to incorporate more chemical species
in the model and/or (ii) to use finer grids in the discretization of
the spatial derivatives. This leads to very large computational task.
Furthermore, long sequences of scenarios are, as a rule, needed in most
of the environmental studies. This is why many challenging problems
are to be resolved in order to prepare reliable answers to the asked
questions. The solution of some of the problems when systems of PDEs
arising in environmental models are handled on modern high-speed computers
will be the major topic of this course. Several applications of the
models, including the impact of future climate changes (the green house
effects) on pollution levels, will also be described. Finally, a series
of problems, which are still open, will be presented and discussed.
Most of the problems treated in this course are also discussed in: Zahari
Zlatev: "Computer Treatment of Large Air Pollution Models",
Kluwer Academic Publishers, Dordrecht-Boston-London, 1995. However,
some new results will be presented (copies of relevant materials will
be made available as postscript and pdf files).
Contents of lectures:
General discussion of the systems of PDEs arising in environmental
models and justification of the need of high-speed computers.
Use of splitting techniques in the numerical treatment of the models.
Treatment of the advection (the horizontal transport) part in an
Treatment of the chemical part: general ideas and major numerical
methods used in this sub-model.
Partitioning of the ODE system describing the chemical reactions
in the model.
Optimizing the matrix computations (types of matrices arising
in the treatment of the different parts of an environmental model).
Parallel computations: need for parallel computations and major
requirements (standard tools + portability). Use of templates.
Discussion of some typical applications related to different environmental
Impact of future climate changes on high pollution levels.
Open problems and plans for future research efforts.