Master's Defence | Khalida Parveen, Explicit Runge-Kutta time-stepping with the discontinuous Galerkin methodExport this event to calendar

Friday, April 13, 2018 — 10:00 AM EDT

MC 5417

Candidate

Khalida Parveen | Applied Math, University of Waterloo

Title

Explicit Runge-Kutta time-stepping with the discontinuous Galerkin method

Abstract

  In this thesis, the discontinuous Galerkin method is used to solve the hyperbolic equations. 

  The DG method discretizes a system into semi-discrete system and a system of ODEs is

  obtained. To solve this system of ODEs efficiently, numerous time-stepping techniques

  can be used. The most popular choice is Runge-Kutta methods. Classical Runge-Kutta

  methods need a lot of space in the computer memory to store the required information. 

  The 2N-storage time-steppers store the values in two registers, where N is the dimension

  of the system. The 2N-storage schemes have more stages than classical RK schemes but

  are more efficient than classical RK schemes. 

  Several 2N-storage time-stepping techniques have been used reported in the literature. 

  The linear stability condition is found by using the eigenvalue analysis of DG method and

  spectrum of DG method has been scaled to fit inside the absolute stability regions of 2N-

  storage schemes. The one-dimensional advection equation has been solved using RK-DG

  pairings. It is shown that these high-order 2N-storage RK schemes are a good choice for

  use with the DG method to improve efficiency and accuracy over classical RK schemes. 

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