In search of optimal high-order semi-implicit time-integrators for continuous and discontinuous spatial discretization of hyperbolic equations

Event Sponsor: 
LANS Informal Seminar
Start Date: 
Oct 29 2008 (All day)
Building 221 Conference Room A261
Argonne National Laboratory
Francis X. Giraldo
Speaker(s) Title: 
Naval Postgraduate School

This talk will give the audience an overview of the implicit-explicit (IMEX) time-integration methods that we have been pursuing for simulating the time-evolution of systems of nonlinear hyperbolic and hyperbolic-elliptic equations (e.g., Euler, shallow water, and compressible Navier-Stokes). The goal is to develop the most efficient and accurate time-integration methods when used in conjunction with certain spatial discretization methods - specifically, we are looking at high-order continuous and discontinuous Galerkin methods. Because the spatial discretization methods that we use are high-order accurate, we are then looking to use high-order time-integration methods in order to balance the space and time errors.

So far we have only explored IMEX linear multi-step methods (such as the backward difference formulas) with and without Operator-Integration-Factor-Splitting, semi-Lagrangian methods, fully implicit methods, and semi-implicit Runge-Kutta methods. We would like to consider the feasibility of multi-rate methods and spectral deferred correction methods within our framework.
In this talk I will show results obtained with the linear multi-step IMEX methods and will discuss the challenges posed by the spatial discretization methods to the efficient construction of semi-implicit methods.

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