# Adaptive Simulation of a Folded Patch Antenna with Dynamical hp-meshes

This is another example of a dynamically adapted hp-mesh using SMOVE. The example is part of a paper I will submit soon (preprint link). It shows a triple slot patch antenna. The structure is included in the examples of CST MICROWAVE STUDIO.

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The absolute value of the electric field is on the left and the hp-mesh using embedded triangles for visualizing the tensor product orders (cf. Demkowicz, Solin) is on the right. The adaptation strategy is HP_ANISO, i.e., allowing for anisotropic refinement in the mesh step size and the polynomial order. The computation and adaptation is done in a three-dimensional domain. The viewplane is located at the bottom of the antenna substrate.

Electric farfield in the azimuth plane.

Electric farfield in the elevation plane.

# Dynamical hp-mesh with SMOVE

Here is an example of a dynamically adapted hp-mesh using SMOVE. I presented the example at the SCEE conference in Sep 2012. The respective slides can be found here.

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The top panel shows the y-component of the electric field, below is the estimated element error, next is the adaptation flag (-2: irreducible, -1: reduce, 0: fine, 1: refine, 2: non-refinable) and last is the hp-mesh using embedded triangles for visualizing the tensor product orders (cf. Demkowicz, Solin). The adaptation strategy is HP_ANISO, i.e., allowing for anisotropic refinement in the mesh step size and the polynomial order. The computation and adaptation is done in a three-dimensional domain, the visualizations show cut views.

After finding the initial mesh the mesh step sizes, h, and elementwise approximation orders, p, are adapted autonomously such that the prescribed error tolerance of 1E-5 is met throughout the time-domain simulation (see below or page 70 of the talk).

# 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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