26 citations · 66 across the 35 of their papers we have counts for
6 papers · 1 filter
Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients
Hoang Tran, Clayton G. Webster, Guannan Zhang
In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized el…
A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models
Hoang A. Tran, Clayton G. Webster, Guannan Zhang
There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as w…
An Efficient Meshfreee Implicit Filter for Nonlinear Filtering Problems
Feng Bao, Yanzhao Cao, Clayton Webster +1
In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The impli…
Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients
Nick Dexter, Clayton Webster, Guannan Zhang
This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM) for approximating the solution of parameterized elliptic partial di…
Accelerating stochastic collocation methods for partial differential equations with random input data
Diego Galindo, Peter Jantsch, Clayton G. Webster +1
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial diffe…
Numerical Methods for a Class of Nonlocal Diffusion Problems with the Use of Backward SDEs
Guannan Zhang, Weidong Zhao, Clayton Webster +1
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward…