Krylov Subspace Spectral Methods with Coarse-Grid Residual Correction for Solving Time-Dependent, Variable-Coefficient PDEs

Abstract

Krylov Supspace Spectral (KSS) methods provide an efficient approach to the solution of time-dependent, variable-coefficient partial differential equations by using an interpolating polynomial with frequency-dependent interpolation points to approximate a solution operator for each Fourier coefficient. KSS methods are high-order accurate time-stepping methods that also scale effectively to higher spatial resolution. In this paper, we will demonstrate the effectiveness of using coarse-grid residual correction, generalized to the time-dependent case, to improve the accuracy and efficiency of KSS methods. Numerical experiments demonstrate the effectiveness of this correction.