MC 5417
Candidate
Khalida ParveenÌý| Applied Math, University of À¶Ý®ÊÓƵ
Title
Explicit Runge-Kutta time-stepping with the discontinuous Galerkin method
Abstract
Ìý In this thesis, the discontinuous Galerkin method is used to solve the hyperbolic equations.Ìý
Ìý The DG method discretizes a system into semi-discrete system and a system of ODEs is
Ìý obtained. To solve this system of ODEs efficiently, numerous time-stepping techniques
Ìý can be used. The most popular choice is Runge-Kutta methods. Classical Runge-Kutta
Ìý methods need a lot of space in the computer memory to store the required information.Ìý
Ìý The 2N-storage time-steppers store the values in two registers, where N is the dimension
Ìý of the system. The 2N-storage schemes have more stages than classical RK schemes but
Ìý are more efficient than classical RK schemes.Ìý
Ìý Several 2N-storage time-stepping techniques have been used reported in the literature.Ìý
Ìý The linear stability condition is found by using the eigenvalue analysis of DG method and
Ìý spectrum of DG method has been scaled to fit inside the absolute stability regions of 2N-
Ìý storage schemes. The one-dimensional advection equation has been solved using RK-DG
Ìý pairings. It is shown that these high-order 2N-storage RK schemes are a good choice for
Ìý use with the DG method to improve efficiency and accuracy over classical RK schemes.Ìý