Monday April 15, 2019 at 4:00 PM in Yost 306

Speaker: Maureen M. Morton, Stark State College (mmorton@starkstate.edu)

Abstract

Integral Deferred Correction (IDC) methods are high order numerical time integrators whose structure leads to simple construction of arbitrary order integrators. High order numerical time
integrators, such as IDC, provide a valuable partnership with existing or new high order spatial methods. They ensure that results in both space and time attain similar quality, and neither limits the other. IDC methods involve a low order prediction step and correction of the prediction through solving an error equation. Certain modifications to IDC allow high order numerical solutions to multi-scale and/or nonlinear problems in plasma physics, such as the Vlasov-Poisson system. These modifications include incorporating semi-implicit methods to solve an IVP (arising from method of lines discretization) with a stiff and nonstiff term, or employing operator splitting into IDC’s prediction and correction steps. Such high order IDC methods are efficient when compared with Runge-Kutta methods. Also, despite introducing a CFL condition comparable to Eulerian methods, split IDC in time with conservative semi-Lagrangian WENO interpolation in space proves effective at preserving the expected physical properties in classic plasma physics problems.