4.1. Variable polynomial degree (p-adaption)

The field solver of PICLas for Maxwell’s and Poisson’s equations supports a variable, element-local polynomial degree. This functionality can be enabled with

pAdaptionType = non-periodic-BC

The currently available options are:

Option	Description
none (0)	Default for setting all elements to \(N\)
random (1)	Elements get random polynomial degree between \(N_{\mathrm{min}}\) and \(N_{\mathrm{max}}\)
non-periodic-BC (2)	Refinement of elements with non-periodic boundary conditions, see Section Refining boundary elements (pAdaptionType = non-periodic-BC)
half-half (3)	Elements in the lower half domain in x-direction are set to \(N_{\mathrm{min}}\) and the upper half are set to \(N_{\mathrm{max}}\). The domain must be centered around \(x=0\).

An option to adapt the polynomial degree based on the Debye length is currently in development.

4.1.1. Refining boundary elements (pAdaptionType = non-periodic-BC)

To refine elements at a non-periodic boundary condition, which can be enabled by

pAdaptionBCLevel = 1st-and-2nd-NMin+1

Several options are available:

Option	Description
1st-and-2nd-NMin+1 (-2)	Elements with non-periodic boundary conditions receive \(N_{\mathrm{max}}\), 2\(^{\mathrm{nd}}\) layer receives \(N_{\mathrm{min}}+1\)
directly-connected-NMin+1 (-1)	Elements with non-periodic boundary conditions receive \(N_{\mathrm{min}}+1\)
directly-connected-NMax (1)	Elements with non-periodic boundary conditions receive \(N_{\mathrm{max}}\)
1st-and-2nd-NMax (2)	First two layers of elements with non-periodic boundary conditions receive \(N_{\mathrm{max}}\)

An example is available in the regression tests, e.g. in regressioncheck/NIG_PIC_poisson_Leapfrog_single_node/box_VDL_and_linPhi