Example of an hp-Mesh obtained with SMOVE

Below you can see an example of how SMOVE automatically finds an hp-adapted initial mesh to given initial conditions (Gaussian profiles along all coordinates in this case). The left panel shows the magnitude of the electric field (please ignore the visualization artifacts occurring sometimes around the border of the field solution). The right panel shows the process of the mesh adaptation using the refinement strategy HP_ANISO, i.e., allowing for anisotropic refinement in the mesh step size h and the polynomial order p. Keep in mind that this example is meant to demonstrate the adaptation process. The final relative L2-error of the field solution reaches below 1E-9, a ludicrously small error. In a real simulation a less refined mesh would suffice. The computation and adaptation is done in a three-dimensional domain, the visualizations show cut views.

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