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hpGEM is a C++ software package for discontinuous Galerkin method. This framework is intended to those who want to easily develop and apply discontinuous Galerkin methods for various physical problems, especially partial differential equations, arising from fluid mechancis and electro-magnetism. Using HPGEM, one can numerically solve the simplest class room examples such as linear advection and Burgers equations to the most complicated practical examples such as shallow water, Euler, Navier-Stokes and Maxwell equations.

Impact of a shock wave on a Helium bubble.
Impact of a shock wave on a Helium bubble: Coordinate setup
Impact of a shock wave on a Helium bubble: Evolution of density profile
Impact of a shock wave on a Helium bubble: Evolution of density profile
Impact of a shock wave on a Helium bubble: Final density profile and refined
grid
Segregation in granular chute flows: Homogeneous inflow t=0.7
Segregation in granular chute flows: Homogeneous inflow t=2.0
Segregation in granular chute flows: Homogeneous inflow t=4.0
Segregation in Granular Chute Flows: Normally graded inflow t=0.7.
Segregation in granular chute flows: Normally graded inflow t=2.0
Segregation in granular chute flows: Normally graded inflow t=4.0
Impact of a shock wave on a Helium bubble.
Impact of a shock wave on a Helium bubble: Coordinate setup
Impact of a shock wave on a Helium bubble: Evolution of density profile
Impact of a shock wave on a Helium bubble: Evolution of density profile
Impact of a shock wave on a Helium bubble: Final density profile and refined grid
Segregation in granular chute flows: Homogeneous inflow t=0.7
Segregation in granular chute flows: Homogeneous inflow t=2.0
Segregation in granular chute flows: Homogeneous inflow t=4.0
Segregation in Granular Chute Flows: Normally graded inflow t=0.7.
Segregation in granular chute flows: Normally graded inflow t=2.0
Segregation in granular chute flows: Normally graded inflow t=4.0

Features

Some important features of hpGEM are:

  • It can handle various mesh geometries in 1D, 2D and 3D involving triangular, quadrilateral, tetrahedral, pyramid, prism or hexahedral type of elements. Hybrid meshes involving different shapes of elements are also easily handled.
  • Some examples of space and space-time discontinuous Galerkin routines for nonlinear hyperbolic equations are availables as sample applications.
  • Higher order polynomial approximations can be built with various Gauss integration rules.
  • Inbuilt output routines for tecplot in order to visualize the numerical solutions.
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