**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

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Friday, April 13, 2018 — 10:00 AM EDT

MC 5417

Khalida Parveen | Applied Math, University of Waterloo

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

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.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1