Fast dynamic force computation for electrostatic and electromagnetic conductors

This thesis presents an improved method for dynamic force computation applicable to both electrostatic and electromagnetic conductors with complex 3D geometries. During the transient simulation of electrostatic actuated MEMS, the positions of the conductors as well as the potential applied to the conductors may change, necessitating recalculation of electrostatic forces at each time step of computation. Similarly, during the simulation of electromagnetic actuated MEMS, the current re-distribution in the conductors requires recalculation of electromagnetic forces at each time step. In this thesis, a simple method based on the principles of fast multipole algorithm is explored to effectively recalculate the potential coefficients to compute the surface charges and thereby forces during transient simulation of electrostatic conductors. The proposed method improves the speed of electrostatic force computation by 15 - 60% at each time step, depending on the displacement, with an error less than 3%. Electromagnetic forces are also computed by the same method. In addition, an efficient method is also presented for electrostatic analysis of dummy metal filled interconnects

Improving Boundary Element Methods for Parasitic Extraction

We improve the accuracy and speed of boundary element method (BEM) or multipole accelerated BEM for interconnect parasitic extraction. Three techniques are presented and applied to capacitance extraction: selective coefficient ehancement, variable order multipole and multigrid. Experimental results show that the techniques are effective for extracting parasitics between all pairs of conductors, or between selected pairs of conductors