Solving PDEs with Random Data by Sparse Grid Stochastic Collocation Methods

Eman Almoalim (The University of Manchester)

ATB Frank Adams 1,

There are many areas of science where the uncertainties are critical for modeling scientific phenomena such as: climate models, weather models and nuclear reactor designs. My work aims to study the numerical solution of PDEs with random data using sparse grid stochastic collocation methods with three different choices of interpolation abscissas. These choices are Clenshaw-Curtis, Chebyshev-Gauss-Lobatto and Gauss-Patterson. We study the numerical solution for these linear and nonlinear models: convection-diffusion where the diffusion coefficient is a random variable, Navier-Stokes where the viscosity is a random variable and the diffusion problem where the diffusion coefficient is a random field. In this talk, I will introduce the numerical methods that I used to solve these models. Then, I will present the numerical results and error estimate for each case.

There are many areas of science where the uncertainties are critical for modeling scientific phenomena such as: climate models, weather models and nuclear reactor designs. My work aims to study the numerical solution of PDEs with random data using sparse grid stochastic collocation methods with three different choices of interpolation abscissas. These choices are Clenshaw-Curtis, Chebyshev-Gauss-Lobatto and Gauss-Patterson. We study the numerical solution for these linear and nonlinear models: convection-diffusion where the diffusion coefficient is a random variable, Navier-Stokes where the viscosity is a random variable and the diffusion problem where the diffusion coefficient is a random field. In this talk, I will introduce the numerical methods that I used to solve these models. Then, I will present the numerical results and error estimate for each case.

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