A curvelet method for numerical solution of partial differential equations

This paper proposes a fast curvelet based finite difference method for numerical solutions of partial differential equations (PDEs). The method uses finite difference approximations for differential operators involved in the PDE5. After the approximation, the curvelet is used for the compression of the finite difference matrices and subsequently for computing the dyadic powers of these matrices required for solving the PDE in a fast and efficient manner. As a prerequisite, compression and reconstruction errors for the curvelet have been tested against different parameters. The developed method has been applied on five test problems of different nature. For each test problem the convergence of the method is examined. Moreover, to measure the performance of the proposed method the computational time taken by the proposed method is compared to that of the finite difference method. It is observed that the proposed method is computationally very efficient. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.