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DGSEM-3D Advection Testing

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.

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Software Overview

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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.

See the recent blog entry on roll-off filters.