[Colloq] Monday October 5th 2009 -- MIT Applied Math Colloquium And Numerical Methods for Partial Differential Equations Seminar -- Kai Schneider -- 4:30 PM in 4-370

[Rachel Kalweit]

JOINT EVENT

Applied Mathematics Colloquium and Numerical Methods for Partial 
Differential Equations Seminar

Monday October 5th 2009

Time: 4:30 PM

Location: MIT, Building 4, Room 370
Refreshments are available in Building 2, Room 290
(Math Common Room) between 3:30 – 4:30 PM

Speaker: Kai Schneider (Universite de Provence, Marseille, France)

Title: Adaptive Space-time Multiresolution Techniques for Nonlinear PDEs

ABSTRACT: We present efficient fully adaptive numerical schemes for 
evolutionary partial differential equations based on a finite volume 
(FV) discretization with explicit time discretization. A multiresolution 
strategy allows local grid refinement while controlling the 
approximation error in space. The costly fluxes are evaluated on the 
adaptive grid only. For time discretization we use an explicit 
Runge-Kutta scheme of second-order with a scale-dependent time step. On 
the finest scale the size of the time step is imposed by the stability 
condition of the explicit scheme. On larger scales, the time step can be 
increased without violating the stability requirement of the explicit 
scheme. Embedded Runge-Kutta methods of second and third order are then 
used to choose automatically the new time step while controlling the 
approximation error in time. Non-admissible choices of the time step are 
avoided by limiting
its variation.

The implementation of the multiresolution representation uses a dynamic 
tree data structure, which allows memory compression and CPU time 
reduction. This new numerical scheme is validated using different 
classical test problems in one, two and three space dimensions. The gain 
in memory and CPU time with respect to the finite volume scheme on a 
regular grid is reported, which demonstrates the efficiency of the new 
method.

This work is joint work with M. Domingues, S. Gomes and O. Roussel

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Applied Math Colloquium Website: http://math.mit.edu/amc/fall09/
Applied Math Colloquium poster: 
http://math.mit.edu/amc/fall09/Kai_Schneider.pdf

Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139
http://math.mit.edu
http://web.mit.edu/facilities/maps/Campus_Basemap_R2009.pdf

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