The analysis of coupled interconnect with process parameter variation based wavelet collocation method

In this paper, a novel approach based on fast wavelet collocation method (FWCM) is presented to solve partial differential equations (PDEs) in coupled on-chip interconnects with parameter variations. After processing PDEs by decomposing variables with wavelet functions, we transfer the PDEs into ordinary differential equations (ODEs), and then use Taylor expansion in the ODEs to approximate the partial complex expression containing inverse matrix. Consequently, we can solve the PDEs with random variables more feasibly. Moreover, this approach provides a new idea for solving other kinds of PDEs with random variables in very large scaled integrated circuits (VLSI). Comparison with HSPICE simulation results shows the method proposed in this paper is effective and accurate.