Fig. 16

Illustration of the integration sub-cells resulting from the B-QTD. On each refinement level a certain number of sub-cells is created and different labels are assigned indicated by the color-coding: The sets of green (\(\varvec{\mathcal {B}}_{\mathrm {full}}^+\)) and red sub-cells (\(\varvec{\mathcal {B}}_{\mathrm {full}}^-\)) represent integration domains where the discontinuity is not taken into account. The blue (\(\varvec{\mathcal {B}}_{\mathrm {cut}}^+\)) and orange (\(\varvec{\mathcal {B}}_{\mathrm {cut}}^-\)) sub-cells are located at \(k=k_{\mathrm {max}}=5\) exclusively, and they denote integration domains, where the discontinuity is actually taken into account, but only IPs in the physical (blue) or fictitious (orange) domain are considered