Equivalent operator preconditioning for elliptic problems

2016. 10. 13. 10:15
BME H épület 306-os terem
dr. Karátson János

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2016. október 13. (csütörtök) 10:15, BME H306-os teremben


dr. Karátson János - ELTE

Equivalent operator preconditioning for elliptic problems


For a vast number of models for real-life problems, including various
partial differential equations, the numerical solution is ultimately
reduced to the solution of linear algebraic systems. The efficiency of
this last step often depends on the proper choice of a preconditioning
A class of efficient preconditioners for discretized elliptic problems
can be obtained via equivalent operator preconditioning. This means
that the preconditioner is chosen as the discretization of a suitable
auxiliary operator that is equivalent to the original one.
Under proper conditions one can thus achieve mesh independent
convergence rates. Hence, if the discretized auxiliary problems
possess efficient optimal
order solvers (e.g. of multigrid type)
regarding the number of arithmetic operations, then the overall iteration
also yields an optimal order solution, i.e. the cost O(N) is
proportional to the degrees of freedom.
In this talk first some theoretical background is summarized,
including both linear and superlinear mesh independent convergence,
then various applications are shown. The results can be applied, among
other things, for parallel preconditioning of transport type systems,
streamline diffusion preconditioning of convection-diffusion problems,
and to achieve superlinear convergence under shifted Laplace
preconditioners for Helmholtz equations.

(The talk will be in Hungarian.)

A szervezők

(Faragó István, Karátson János, Horváth Róbert, Mincsovics Miklós)

A szeminárium honlapja: http://math.bme.hu/AlkAnalSzemi