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2004 - 2005
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Scientific Computation,
Numerical Analysis And Applications
January - July, 2005
(with special reference to Numerical Simulation,
Control, Noise Modelling, and Optimization of Systems
Governed by Hyperbolic Partial Differential Equations
and Differential-Algebraic Equations)
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Scientific computation is a multidisciplinary subject of
growing importance. In this program, the main focus will
be on a very active branch of research, namely
- Hyperbolic partial differential equations (HPDE) - theory,
numeric and computation - simulation, control and optimization:
attention will also be paid to general ideas of scientific
computation as a branch of applied mathematics.
- Differential-Algebraic Equations (DAE) -- Theory and
Computational Aspects, High Index Cases, Noisy Models,
Delay DAEs, Partial DAE, Algorithms and Software for simulation,
control and optimization in various application areas.
Hyperbolic systems of partial differential
equations appear as a natural system governing a large number
of physical phenomena and form an important branch of active
research due to its wide application from gas dynamics,
water waves and oil exploration to astrophysics. Hyperbolic
conservation laws play an important role in these areas.
They not only provide a sophisticated mathematical framework
to discuss discontinuous solutions in the form of shocks
but also unify many areas of applications from the point
of view of developing powerful numerical schemes. India
has excellent research groups on computational fluid dynamics
to support research and development in DRDO and ISRO and
in other industries if needed. It has also has good theoretical
groups working on hyperbolic equations in mathematics departments
of various universities and research institutions. However,
the former needs a strong theoretical support from the latter
to develop further the numerical methods, and the latter
needs informed inputs from the application areas. The underlying
connection between the two is numerical analysis and experimentation
of new numerical techniques to nontrivial problems in areas
of application.
DAEs arise in constrained dynamical systems.
They occur naturally in discretized PDEs, in modeling of
mechanical multibody systems, trajectory design of space
and atmospheric vehicles, molecular dynamical simulation
for studying macro-molecules in bio-chemistry, and circuit
simulation and device optimization tools for Microelectronics
Design Automation. The computational study of high index
DAEs for trajectory optimization and cost-effective design
of control and guidance is of natural interest to space
mission planners (ISRO) and long range atmospheric vehicle
trajectory designers (DRDO). The study of DAEs arising out
of hyperbolic PDEs (partial DAEs) are of interest to high-pressure
physicists (Department Of Atomic Energy). Computational
scientists solving proteomics and drug design problems use
results from multibody dynamical systems approach involving
DAEs. Engineers designing computer-aided-design (CAD) tools
for microelectronics industry use computational models described
by delay and noisy DAEs. The last aspect is of interest
to many CAD tool companies setting up development centers
in India.
As part of the semester-long programme, the
following activities are planned:
- Workshop
1 on Scientific Computation, Numerical Analysis and
Applications
(January 24 - February 04, 2005)
- Indo-French
Workshop on Partial Differential Equations and their
Applications
(February 07 - 12, 2005)
- Workshop
2 on Scientific Computation, Numerical Analysis and
Applications
(July 04 - 15, 2005)
- International
Conference on Scientific Computation, Numerical Analysis
and Applications
(July 18 - 21, 2005)
Please note: The dates mentioned above
are tentative
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