Using PGD to Solve Nonseparable Fractional Derivative Elliptic Problems

Abstract

A family of tensor-based methods called Proper Generalized Decomposition (PGD) methods have been recently introduced for the a priori construction of the solution of several partial differential equations. This strategy was tested with success to demonstrate the capability of representing the solution with a significant reduction of the calculation and storage cost. In this paper, we suggest to test the efficiency of a such approach in solving general nonseparable fractional derivative elliptic problem. We will illustrate by several numerical experiments the efficiency of PGD, especially when the mesh or the coefficients vary with high contrast ratio. Although the PGD scheme considered in this paper is based on spectral method, it is extendable to other methods such as finite element method.