Heat conduction in a 2D domain with geometrical uncertainty using intrusive polynomial chaos method

The primary objective of this work is to understand geometrical uncertainty based on the intrusive polynomial chaos method which allows computing the statistical output for geometrical uncertainty. Currently, very few techniques are available for such computations and this makes these computations a very active research topic. This article deals with the computation of some statistics of the solution of the heat equation in a 2D domain with a given geometrical uncertainty on the top surface. This article explains an implementation of geometrical uncertainty and shows the variation in the output temperature with the mesh size and polynomial order of approximation. The polynomial chaos method produced results are compared with the Monte Carlo results. Keywords— Intrusive polynomial chaos, Geometrical uncertainty, Stochastic modeling.