A fast algorithm for particle simulations
Journal of Computational Physics
A fast algorithm for the evaluation of Legendre expansions
SIAM Journal on Scientific and Statistical Computing
Numerical Methods
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Simulation methods for RF integrated circuits
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
System level signal and power integrity analysis methodology for system-in-package applications
Proceedings of the 43rd annual Design Automation Conference
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We describe an efficient algorithm for the time-domain simulation of elements described by causal impulse responses. The computational bottleneck in the simulation of such elements is the need to compute convolutions at each time point. Hence, direct approaches for the simulation of such elements require time O(N^2), where N is the length of the simulation. We apply ideas from approximation theory to reduce this complexity to O(N \log N) while maintaining double-precision accuracy. The only restriction imposed by our method is that the impulse response h(t) gets ``smoother'' as t goes to infinity. Essentially all physically reasonable impulse responses have this characteristic. The ideas presented can also be applied to time-domain simulation of elements described in the frequency domain, including those characterized by measured data. In this paper, we demonstrate the efficiency of the algorithm by applying it to the simulation of lossy transmission lines.