My motto for software testing is quite the opposite of "go big or go home." With the
reconstruction of the 3-D "HexMesh" class (mesh of hexahedrons), the Discontinuous
Galerkin SEM needed a fresh set of tests. A simple place to start is with the linear
advection equation. The video shows the advection of a Gaussian spot through a
2x2x2 spectral element mesh with a 10th degree polynomial where the boundary
conditions are provided by the exact solution. Documentation of this test, and other
similar tests, is currently in production where the error convergence rates are
verified and the timing of the algorithm is recorded to inform decision making when
using this module in future applications.
Do you have a video or short article on your use of the SELF ?
Send an e-mail to Joe.
The software is built off of a basic set of Lagrange interpolation routines (interp/).
These routines are used to construct discrete differentiation operators that are
spectrally accurate (nodal/). The geometry (geom/) and solution storage (dgsem/ and cgsem/)
data-structures are constructed so that they can be applied to either structured
or unstructured spectral element meshes. Nonlinear PDEs can suffer from instabilities
associated aliasing errors. Because of this, a set of modal-cutoff and roll-off
filter modules (filters/) are provided for polynomial deliasing or solution smoothing.
Elliptic and parabolic PDEs, approximated by the CGSEM, can be efficiently solved using
iterative solvers (iterativesolve/). These solvers are provided in a highly
reusable OO module and currently include preconditioned Conjugate Gradient
and GMRES. A small set of "high-end" modules are provided with driver programs
in order to demonstrate the use of the libraries and to provide modelers with a
"jumping-off-point" for their own research.