A 3-d capacitance extraction algorithm based on kernel independent hierarchical method and geometric moments

A three dimensional (3-D) capacitance extraction algorithm based on a kernel independent hierarchical method and geometric moments is described. Several techniques are incorporated, which leads to a better overall performance for arbitrary interconnect systems. First, the new algorithm hierarchically partitions the bounding box of all interconnect panels to build the partition tree. Then it uses simple shapes to match the low order moments of the geometry of each box in the partition tree. Finally, with the help of a fast matrix-vector product, GMRES is used to solve the linear system. Experimental results show that our algorithm reduces the linear system's size greatly and at the same time maintains a satisfying accuracy. Compared with FastCap, the running time of the new algorithm can be reduced more than a magnitude and the memory usage can be reduced more than thirty times

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

The Cluster Multipole Algorithm for Far-Field Computations

Computer simulations of N-body systems are beneficial to study the overall behavior of a number of physical systems in fields such as astrophysics, molecular dynamics, and computational fluid dynamics. A new approach for computer simulations of N-body systems is proposed in this research. The new algorithm is called the Cluster Multipole Algorithm (CMA). The goals of the new algorithm are to improve the applicability to non-point sources and to provide more control on the accuracy over current algorithms. The algorithm is targeted to applications that do not require rebuilding the data structure about the system every time step due to current limitations in the construction of the data structure. Examples of slowly changing systems can be found in molecular dynamics, capacitance, and computational fluid dynamics simulations. As the data structure development is improved, the new algorithm will be applicable to a wider range of applications. The CMA exhibits the flexibility of both Appel\u27s algorithm and the Fast Multipole Method (FMM) without sacrificing the order of computation (O(N)) for well structured clusters. The CMA provides more control on the accuracy of computations as compared to both the FMM and Appel\u27s algorithm resulting in enhanced performance. A set of requirements are imposed on the data structures which are applicable, to maintain O(N) computation. However, the algorithm is capable of handling a wide range of data structures beyond the FMM

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201