Wavelets for efficient algorithms in electronic design automation

With current advances in electronics, numerical methods once applicable only to analog design are becoming essential for digital design as well. The scale of present day analog and, particularly, digital design requires that the traditional numerical techniques for analysis and simulation be much more effective than in the past. Development of not only efficient, but gracefully scalable numerical methods is a top priority in Electronics Design Automation. This work attempts to treat the problem of efficient and scalable numerical methods for EDA in the scope of multiresolution analysis. It shows how analysis and simulation problems can be treated in a systematic way based on the generalized operator equation formulation. Wavelet bases are presented within this framework. The thesis puts particular emphasis on the circuit analysis and simulations applications. The thesis presents a newly developed Harmonic Balance-like method for steady state analysis of nonlinear circuits under periodic excitations, which is representative of the class of problems described by nonlinear differential equations. The technique features sparse representation of both derivative operator and nonlinear term and shows significant advantage over traditional methods, particularly for analysis of large scale, highly nonlinear, multitone and broadband circuits. A number of other applications are also considered, namely transient analysis of nonlinear circuits, interconnect macromodelling and capacitance extraction for multiconductor transmission lines. A new approach to capacitance extraction using wavelets is presented featuring extremely aggressive thresholding of the stiffness matrix.