Hierarchical bases for non-hierarchic 3Dtriangular meshes

We describe a novel basis of hierarchical, multiscale functions that are linear combinations of standard Rao-Wilton- Glisson (RWG) functions. When the basis is used for discretizing the electric field integral equation (EFIE) for PEC objects it gives rise to a linear system immune from low-frequency breakdown, and well conditioned for dense meshes. The proposed scheme can be applied to any mesh with triangular facets, and therefore it can be used as if it were an algebraic preconditioner. The properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers, significantly better than those for the loop-tree basis. As a byproduct of the basis generation, a generalization of the RWG functions to nonsimplex cells is introduced

Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques

Process variations are a major concern in today's chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit's performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014. arXiv admin note: text overlap with arXiv:1407.302