High-Order Conformal Perfectly Matched Layer for the DGTD Method

Based on the discontinuous Galerkin time-domain (DGTD) method, a new conformal perfectly matched layer (PML) is introduced to truncate the 3-D open domain. Compared with the traditional (rectangular or cubic) PML, the conformal PML is a smooth convex shell, which significantly reduces the buffer space in the computational domain. In this article, we construct the conformal PML in an orthogonal curvilinear coordinate system. Conductivities are defined to absorb the outgoing waves, depending on the distance from the sampling point to the non-PML region and the principal curvature radii of the sampling point, which are calculated utilizing the Weingarten transformation. The analytical expression of 3-D conformal PML is derived with the complex coordinate stretching technique. Furthermore, to reduce the total degrees of freedom (DoFs) while maintaining accuracy, the hierarchical vector basis functions are chosen to discretize the conformal PML and physical region. Numerical results validate its good absorption performance.