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National Mathematics Initiative (NMI)
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2004 - 2005

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)

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

  1. 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.

  2. 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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