A k-d tree based solution cache for the non-linear equation of circuit simulations
Martin Holters, Udo Zölzer · 2016
In the digital simulation of non-linear audio effect circuits, the arising non-linear equation generally poses the main challenge for a computationally cheap implementation. For any but the simplest circuits, using an iterative solver at execution time will be too slow, while exhaustive look-up tables quickly grow intolerably large. To better cope with the situation, in this paper we propose to store solutions non-uniformly sampled from the parameter space to enable an iterative solver to quickly converge when being started from the closest initial solution. Efficient look-up of this closest solution is realized by using a k-d tree. The method is supported by a step to reduce the dimension of the parameter space and a linear extrapolation from the closest solution stored to the actually needed parameter vector.