Adaptive polygon simplification basing on Delaunay triangulation and its application in high speed PCBs and IC packages simulation

As modern high speed Package Circuit Boards (PCBs) and Integrated Circuit (IC) packages become more and more complicated, the electromagnetic simulation inside the PCBs and IC packages becomes more and more difficult. The most challenge work is that complicated multiple layer shapes inside PCBs and IC packages need very huge amount of high quality meshes for electromagnetic simulation, which lead to huge memory requirement for solving the linear matrix. For most personal computers, that requirement usually lead to out of memory in matrix solution. To overcome this problem without losing the simulation precision, this article presents an algorithm to simplify complex 2-D polygons based on Delaunay triangulation. By checking the smallest angles of triangles which contain an edge of the polygons, the algorithm simplifies polygons adaptively and updates the simplified polygons´ Delaunay triangulation. Different from other simplifications which try to decrease the count of vertices, this algorithm tries to delete redundant short edges, leading to greatly reduced mesh points during the process of generating the constrained and quality Delaunay triangulation. The algorithm presented here has been applied for mesh generation for finite-element analysis of complicated PCBs and IC packages. Test results show that the proposed algorithm can reduce more than 75% in total nodes in comparison with the approach without simplification, resulting in significant reduction of computer resources in numerical computation.