DCIM-accelerated SMFMA for capacitance extraction

Recent advances in very large scale integration (VLSI) technology heighten the need for fast and accurate calculations of the capacitance and inductance matrices of complex 3D multiconductor structures in the presence of a layered dielectric medium. A stratified medium fast multipole algorithm (SMFMA) was developed to speedup capacitance extractions for the large-number-of-unknowns case with O(N) cost (Pan, Y.C., "Development of the fast multipole method for stratified medium", Ph.D thesis, Univ. of Illinois, 2002). But in the multilayer medium, the translators and near field interactions have no closed form. Therefore, the numerical integral computation for the translator preparations makes the SMFMA setup stage very time consuming. We derive a set of identities based on extended spherical harmonic functions in the complex plane. Combined with the discrete complex image method (DCIM), the multipole translators can be represented by simple closed-form expressions. The technique can make the SMFMA setup stage one to two-orders faster compared to the old method. It provides excellent accuracy with little computation costs.