Bayesian Numerical Homogenization for PDEs with Rough Coefficients

Monday, October 22nd 12:00, 2018
TIMON Room at DeustoTech

Xinliang Liu
DeustoTech, Bilbao, Basque Country, Spain

In this talk, Xinliang will demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) using the Bayesian formulation for elliptic problem with highly varying coefficients. This is done by solving its dual problem, a constrained convex optimization problem. We employ a P1 finite volume element scheme to approximate the $-\div a \nabla $ operator on the dual mesh of a finite element mesh. Concise algebra representation for the basis functions and efficient algebra formula are derived. We prove the exponential decay and approximation property of the obtained basis. Then he will show you several applications of this type of basis on wave equation and optimal control problems.