Preconditioned CG Methods for a Variable-Coefficient Nonlocal Diffusion Model

Abstract

A variable-coefficient nonlocal diffusion model is discretized by an improved fast collocation scheme. The resulting linear system has a symmetric positive definite Toeplitz-like coefficient matrix. The preconditioned CG methods with Toeplitz and circulant preconditioners are used for solving the discretized linear system. Numerical experiments demonstrate the effectiveness of the preconditioned CG methods.