Időpont:
2016. 10. 13. 10:15
Hely:
BME H épület 306-os terem
Előadó:
dr. Karátson János
MEGHÍVÓ
Szeretettel várjuk a BME-ELTE Alkalmazott Analízis Szemináriumára
Előadás részletei:
2016. október 13. (csütörtök) 10:15, BME H306-os teremben
Előadó:
dr. Karátson János - ELTE
Equivalent operator preconditioning for elliptic problems
Absztrakt:
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
matrix.
A class of efficient preconditioners for discretized elliptic problems
can be obtained via equivalent operator preconditioning. This means
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
matrix.
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)
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, for
streamline diffusion preconditioning of convection-diffusion problems,
and to achieve superlinear convergence under shifted Laplace
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, for
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