Highly Efficient Methods for Scientific Computing

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Department of Mathematics

Synopsis:

Iterative methods of solving systems of linear algebraic equations. Fast algorithms. Gradient methods. CG and GMRES. Preconditioning and its methods. Multilevel Methods for Elliptical Problems (Multigrid Methods). V-cycle, W-cycle. Domain Decomposition Methods (DDM). Overlapping methods, methods without overlapping. Neumann-Neumann methods. Balanced DD method.Methods of Scwarz type (Fully Black Box Methods). Special methods for non-eliptic and indefinite problems. Typical tasks, Helmholtz equation, Navier-Stokes system. Aggregation of the Leontief System. Stationary vectors of probability of stochastic matrices. All methods and algorithms are interconnected and illustrated on non-academic examples of models of mechanics, elasticity, strength and reliability of buildings.

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