An hp-Adaptive Scheme of Discontinuous Galerkin Time-Domain Method With Fast Error Estimation

In this article, a highly efficient
hp
-adaptive scheme has been developed for the discontinuous Galerkin time-domain (DGTD) method. In order to achieve the
${h}$
- and
${p}$
-adaptive behaviors, a hierarchical octree-based recursive meshing procedure has been introduced. In the
hp
-adaptive scheme, the transformation method of the basis function is developed to convert the fields between the parent element and the child elements and between the higher- and the lower-order bases. Instead of the time-consuming field update process according to the governing equations, the error based on modified reference solutions can be rapidly and accurately calculated in the
${h}$
- and
${p}$
-adaptions by using the proposed transformation, thus flexibly manipulating the
hp
-adaptive procedure. Some 3-D radiation and scattering examples are given to demonstrate the good accuracy and high efficiency of the proposed
hp
-adaptive DGTD method.