A Variational Max Ensemble Numerical Algorism for a Transient Heat Model with Random Inputs

Abstract

A variational MAX ensemble-based time stepping numerical method is proposed to simulate a transient heat equation with uncertain Robin boundary and diffusion coefficients. Instead of employing ensemble means for Robin coefficients as well as diffusion coefficients, the maximums of these coefficients are utilized at per time-step. This is a new variational ensemble Monte Carlo  numerical method which we call variational MAX ensemble Monte Carlo (VMEMC) method. In contrast with related methodologies, the novelty of this algorithm is that it is unconditional stability. And also, the error estimates are proved. Numerical tests illustrate the theoretical properties for the VMEMC method.

Keywords: Transient heat equation, Robin coefficient, Diffusion coefficient, Uncertain inputs, Variational MAX ensemble, Monte Carlo sampling