Wavelet Algorithm for Circuit Simulation

TL;DR

This paper introduces an adaptive wavelet-based algorithm for circuit simulation that efficiently solves nonlinear circuit equations with minimal degrees of freedom, improving computational performance over standard methods.

Contribution

It presents a novel spline wavelet approach with adaptive refinement for circuit simulation, enhancing efficiency and accuracy compared to existing techniques.

Findings

Requires minimal degrees of freedom for accurate solutions

Enables efficient numerical computations through adaptive grid refinement

Shows promising results in initial tests on electronic circuits

Abstract

We present a new adaptive circuit simulation algorithm based on spline wavelets. The unknown voltages and currents are expanded into a wavelet representation, which is determined as solution of nonlinear equations derived from the circuit equations by a Galerkin discretization. The spline wavelet representation is adaptively refined during the Newton iteration. The resulting approximation requires an almost minimal number of degrees of freedom, and in addition the grid refinement approach enables very efficient numerical computations. Initial numerical tests on various types of electronic circuits show promising results when compared to the standard transient analysis.