Friday, November 23, 13:00-14:00 in Celestijnenlaan 200A room 00.144, 3001 Leuven-Heverlee
Numerical simulation of the macroscopic behaviour of multiscale systems
By Giovanni Samaey (Scientific Computing Research Group)
We discuss patch dynamics schemes as a means to perform simulation of an effective, macroscopic PDE, when the most accurate model of the system is given on a more microscopic scale. The schemes estimate the time derivative (for finite differences) or flux (for finite volumes) by performing a local simulation with the microscopic model in small patches around the macroscopic grid points. We discuss how to initialize these microscopic simulations, as well as how to choose the size of the patches and the boundary conditions and the simulated microscopic time. We present convergence results for classical homogenization problems and illustrate the method on a number of examples. Since the resulting macroscopic time-stepper can be used to estimate matrix-vector products with the macroscopic Jacobian, fixed points can be computed using standard multigrid techniques with polynomial smoothing.