This talk consists of two parts. In the first part, we discuss the convergence of finite volume method for solving non-linear aggregation-breakage equation. The pro of re lie s on showing the consistency of the scheme and Lipschitz continuity of numerical fluxes. It is investigated that the technique is second order convergent independently of the meshes for pure breakage problem while for aggregation and coupled problems, it depends on the type of grids chose n for the computations. Next, we show the efficient representation of d-point correlation functions for a Gaussian random field. To avoid the curse of dimensionality for d > 2, a truncated KarhunenLo´eve expansion of the random field is used together with the low rank Tensor Train decomposition. The target application of this work is the computation of statistics ofthe solution of linear PDEs with random Gaussian forcing terms.
School of Mathematical Sciences
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