Spectral-Prism Element for Multi-Scale Layered Package-Chip Co-Simulations Using the Discontinuous Galerkin Time-Domain Method

Abstract

A new kind of prism element with a triangular base is presented for discretization of multi-scale layered structures within the discontinuous Galerkin time-domain framework. Mixed-order curl-conforming vector basis functions are used in the triangular bases of the prismatic element. The height of the prism adopts spectral basis functions based on Gauss–Lobatto–Legendre polynomials, with an arbitrary order of interpolation. This method combines the flexibility of triangles with the accuracy of spectral elements for layered structures. Eigenvalues obtained show better results than traditional finite elements using tetrahedrons and hexahedrons. For transient analysis, the implicit Crank–Nicholson method is implemented for sequential sub-domains. This kind of arrangement of sub-domains produces a block tridiagonal linear system, thus allowing a block Thomas algorithm to solve the system efficiently. A package-to-chip example shows the efficacy of this method.