New stochastic simulation algorithms, and applications in coagulation processes and porous flow simulation
I will present stochastic simulation algorithms for solving partial differential equations with random parameters - random coefficients, or random sources. I will illustrate the method for two classes of applied problems: coagulation processes, and flows in porous media. There are two difficult aspects in the problem under study: (i) construction of efficient simulation algorithms for homogeneous or inhomogeneous random fields with a desired correlation structure, and (2) find an appropriate numerical scheme for solving the PDE with the random fields entries constructed in (i). Both aspects will be discussed in the present talk.