A RUNGE-KUTTA BASED DISCONTINUOUS GALERKIN METHOD WITH TIME ACCURATE LOCAL TIME STEPPING

2011 ◽  
pp. 95-118 ◽  
Author(s):  
Gregor J. Gassner ◽  
Florian Hindenlang ◽  
Claus-Dieter Munz
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Discontinuous Galerkin Method ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Runge Kutta

scholarly journals Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwellʼs equations

2014 ◽  
Vol 256 ◽  
pp. 678-695 ◽  
Author(s):  
L.D. Angulo ◽  
J. Alvarez ◽  
F.L. Teixeira ◽  
M.F. Pantoja ◽  
S.G. Garcia
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Discontinuous Galerkin Method ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Causal Path

scholarly journals A p-Strategy with a Local Time-Stepping Method in a Discontinuous Galerkin Approach to Solve Electromagnetic Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Benoit Mallet ◽  
Xavier Ferrieres ◽  
Sebastien Pernet ◽  
Jean-Baptiste Laurent ◽  
Bernard Pecqueux ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Discontinuous Galerkin Method ◽  
Computational Time ◽  
Electromagnetic Problems ◽  
Time Stepping ◽  
Local Time Stepping ◽  
The Time Domain ◽  
Spatial Approximation

We present a local spatial approximation or p-strategy Discontinuous Galerkin method to solve the time-domain Maxwell equations. First, the Discontinuous Galerkin method with a local time-stepping strategy is recalled. Next, in order to increase the efficiency of the method, a local spatial approximation strategy is introduced and studied. While preserving accuracy and by using different spatial approximation orders for each cell, this strategy is very efficient to reduce the computational time and the required memory in numerical simulations using very distorted meshes. Several numerical examples are given to show the interest and the capacity of such method.

Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

2016 ◽  
Vol 9 (1) ◽  
pp. 73-91 ◽  
Author(s):  
Haitian Lu ◽  
Jun Zhu ◽  
Chunwu Wang ◽  
Ning Zhao
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Front Tracking ◽  
Unstructured Meshes ◽  
Interfacial Region ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Medium Flow ◽  
Runge Kutta

AbstractIn this paper, we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible two-medium flow on unstructured meshes. A Riemann problem is constructed in the normal direction in the material interfacial region, with the goal of obtaining a compact, robust and efficient procedure to track the explicit sharp interface precisely. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

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