Seminar Details
2010-03-02 (14.00) : Numerical properties of equation-free methods for multiscale problems
At Euler building
Organized by Mathematical Engineering
Speaker :
Giovanni
SAMAEY
(CESAME)
Abstract :
In quite a number of problems, there exists a wide gap between the (microscopic) level at which a system is modeled and the (macroscopic)
space and time scales at which one would like to observe the system. Equation-free methods try to bridge this gap by constructing a coarse time-stepper
for the macroscopic observables as a three-step procedure: (1) lift (from macro to micro); (2) evolve (using the microscopic model); and (3) restrict (from micro to macro).
We will discuss both how to construct lifting operators to obtain a well-defined coarse time-stepper, as well as what macroscopic tasks can be performed once a coarse time-stepper is available.
Particular emphasis will be put on the numerical properties of the resulting methods (accuracy and efficiency) and on the use of approximate macroscopic models to accelerate the computations.
Collaborators that have contributed to this work will be acknowledged throughout the talk.