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Krylov Deferred Correction and Fast Elliptic Solvers for Time Dependent Partial Differential Equations

Jingfang Huang
Department of Mathematics, UNC Chapel Hill


In this talk, we discuss a new class of numerical methods for the accurateand efficient integration of time dependent partial differential equations.Unlike traditional method of lines (MoL), the new Krylov deferred correction(KDC) accelerated method of lines transpose (Mol^T) first discretizes thetemporal direction using Gaussian type nodes and spectral integration, andthe resulting coupled elliptic system is solved iteratively usingNewton-Krylov techniques such as Newton-GMRES method, in which eachfunction evaluation is simply one low order time stepping approximationof the error by solving a decoupled system using available fast ellipticequation solvers. Preliminary numerical experiments show that the KDCaccelerated MoL^T technique is unconditionally stable, can be spectrallyaccurate in both temporal and spatial directions, and allows optimal timestep sizes in long-time simulations. Numerical experiments for parabolictype equations including the Schrodinger equation will be discussed.

Tuesday, March 11, 2008
11:00AM AP&M 2402