Impedance extraction for 3-D structures with multiple dielectrics using preconditioned boundary element method

In this paper, we present the first BEM impedance extraction algorithm for multiple dielectrics. The effect of multiple dielectrics is significant and efficient modeling is challenging. However, previous BEM algorithms, including Fastlmp and EastPep, assume uniform dielectric, thus causing considerable errors. The new algorithm introduces a circuit formulation which makes it possible to utilizes either multilayer Green's function or equivalent charge method to extract impedance in multiple dielectrics. The novelty of the formulation is the reduction of the number of unknowns and the application of the hierarchical data structure. The hierarchical data structure permits efficient sparsification transformation and preconditioners to accelerate the linear equation solver. Experimental results demonstrate that the new algorithm is accurate and efficient. For uniform dielectric problems, the new algorithm is one magnitude faster than Fastlmp, while its results differ from Fastlmp within 2%. For multiple dielectrics problems, its relative error with respect to HFSS is below 3%.