Applied Mathematics Colloquium: Dr. Heyrim Cho

Title: Numerical methods for uncertainty quantification - from noise parameterization to efficient simulation of parameterized stochastic PDE

Speaker: Heyrim Cho, University of Maryland, College Park

Abstract: For a reliable simulation of systems subject to noise, it is necessary to characterize the noise properly and develop efficient algorithms. In the first part of this talk, I will present a numerical technique to model and simulate multiple correlated random processes. The method finds the appropriate expansion for each correlated random process by generalizing the Karhunen-Loeve (K-L) expansion, in particular, by releasing the bi-orthogonal condition of the K-L expansion. I will address the convergence and computational efficiency, in addition to some explicit formulae and analytical results. In the second part, I will present an adaptive reduced basis method that enables an efficient simulation of parameterized stochastic PDEs. The method is employed by using an adaptive ANOVA and probabilistic collocation method to automatically identify the important dimensions and appropriate resolution in each dimension. The effectiveness of the method is demonstrated in anisotropic high-dimensional stochastic PDEs.