Extreme-scale Discontinuous Galerkin Environment (EDGE)
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README.md

EDGƎ Build Status codecov FOSSA Status

Equations

  • advection (1D):

    Solves the one-dimensional advection equation. q(x,t) is a scalar. The scalar advection speed a(x) can be set per element, but has to be either positive or negative for the entire domain.

    q_t + a * q_x = 0
    
  • advection (2D):

    Solves the two-dimensional advection equation. q(x,y,t) is a scalar. The scalar advection speeds a(x,y) and b(x,y) can be set per element. Each has to be either positive or negative for the entire domain.

    q_t + a * q_x + b * q_y = 0
    
  • advection (3D):

    Solves the three-dimensional advection equation. q(x,y,z,t) is a scalar. The scalar advection speeds a(x,y,z), b(x,y,z) and c(x,y,z) can be set per element. Each has to be either positive or negative for the entire doman.

    q_t + a * q_x + b * q_y + c q_z = 0
    
  • elastics (2D):

    Solves the two-dimensional elastic wave equations. The vector of quantities q(x,y,t)=(sigma_xx, sigma_yy, sigma_xy, u, v ) contains the normal stress components sigma_xx and sigma_yy, the shear stress sigma_xy and the two particle velocities u and v in x- and y-direction respectively. The Jacobians A(x,y) and B(x,y) are allowed to be set per element and summarize the material parameters.

    q_t + A q_x + B q_y = 0
    
  • elastics (3D):

    Solves the three-dimensional elastic wave equations. The vector of quantities q(x,y,z,t)=(sigma_xx, sigma_yy, sigma_zz, sigma_xy, sigma_xz, sigma_yz, u, v, w ) contains the normal stress components sigma_xx, sigma_yy and sigma_zz, the shear stresses sigma_xy, sigma_xz and sigma_yz and the three particle velocities u, v w in x-, y- and z-direction respectively. The Jacobians A(x,y,z), B(x,y,z) and C(x,y,z) are allowed to be set per element and summarize the material parameters.

    q_t + A q_x + B q_y + C q_z = 0
    
  • swe (1D):

    Solves the one-dimensional Shallow Water Equations (SWE) in conservative form. The conserved quantities q(x,t)=(h,hu) are the water height h and the momentum hu. The flux function is nonlinear. Bathymetry is supported.

    q_t + f(q)_x = 0,
    
           |         hu           |
    f(q) = |                      |
           | hu^2 + 1/2 * g * h^2 |
    
  • swe (2D):

    Solves the two-dimensional Shallow Water Equations (SWE) in conservative form. The conserved quantities q(x,t)=(h,hu,hv) are the water height h, the momentum hu in x-direction and the momentum hv in y-direction. The flux function is nonlinear. Bathymetry is supported.

    q_t + f(q)_x + g(q)_y = 0,
    
           |         hu           |         |          hv          |
           |                      |         |                      |
    f(q) = | hu^2 + 1/2 * g * h^2 |, g(q) = |          huv         |
           |                      |         |                      |
           |         huv          |         | hv^2 + 1/2 * g * h^2 |
    

Elements

  • line (1D):

    Line element. Element width dx is allowed to change in every element.

  • quad4r (2D):

    Rectangular, 4-node quadrilaterals. Widths dx and dy are allowed to change on a per-row/per-column basis (conforming mesh).

  • tria3 (2D):

    3-node triangles. Arbitrary, conforming triangulations of the computational domain are supported.

  • hex8r (3D):

    Rectangular, 8-node hexahedrons (bricks). Widths dx, dy and dz are allowed to change on a conforming mesh basis.

  • tet4 (3D):

    4-node tetrahedrons. Arbitrary, conforming tetrahedralization are allowed.

Feature table

Based on the equations and the element type, the following table shows the implemented features:

equations element types CFR FV ADER-DG LIBXSMM
advection line, quad4r, tria3, hex8r, tet4 x x x
elastics quad4r, tria3, hex8r, tet4 x x x x
swe line, quad4r, tria3 x x

High Performance Support

Microarchitecture Machine(s)
Sandy Bridge Stampede 1
Bulldozer Blue Waters
Haswell Comet, Cori Phase 1
Knights Landing Stampede 2, Cori Phase 2, Theta
Skylake Amazon Elastic Compute Cloud, Google Cloud Platform, Stampede 2
EPYC packet
Knights Mill -