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Dan Jiao - One of the best experts on this subject based on the ideXlab platform.

  • Fast Algorithms for Converting an FMM-Based Representation of Electrically Large Integral Operators to a Minimal-Rank ℋ 2 -Matrix
    2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, 2019
    Co-Authors: Chang Yang, Dan Jiao
    Abstract:

    In this paper, we develop fast algorithms to convert an FMM-based representation to a new ℋ2-matrix whose rank is minimized based on Accuracy. We then apply these algorithms to solve electrically large surface electric field integral equations for scattering analysis. The resultant new ℋ2-matrix is found to have a much reduced rank without sacrificing Prescribed Accuracy.

  • Method for Generating a Minimal-Rank $\mathcal{H}^{2}$ -Matrix from FMM for Electrically Large Analysis
    2018 IEEE International Symposium on Antennas and Propagation & USNC URSI National Radio Science Meeting, 2018
    Co-Authors: Chang Yang, Dan Jiao
    Abstract:

    In this work, we develop an efficient method to generate a rank-minimized $\mathcal{H}^{2}$ -matrix to represent electrically large integral operators for a Prescribed Accuracy. We first generate an $\mathcal{H}^{2}$ -matrix using the Fast Multipole Method (FMM), and hence the complexity for $\mathcal{H}^{2}$ -construction is as low as $O ({NlogN})$ for solving electrically large surface integral equations. We then convert the FMM-based $\mathcal{H}^{2}$ -matrix whose rank is full asymptotically to a new $\mathcal{H}^{2}$ -representation, whose rank is minimized based on Accuracy. Numerical experiments demonstrate a significantly reduced rank with Prescribed Accuracy satisfied.

  • Direct finite element solver of linear complexity for analyzing electrically large problems
    2015
    Co-Authors: Bangda Zhou, Dan Jiao
    Abstract:

    In this paper, we develop a fast direct finite element solver of linear (optimal) complexity for the electromagnetic analysis of electrically large problems. Both theoretical analysis and numerical experiments have demonstrated the solver's linear complexity in CPU time and memory consumption with Prescribed Accuracy satisfied.

  • Fast ${\cal H}$ -Matrix-Based Direct Integral Equation Solver With Reduced Computational Cost for Large-Scale Interconnect Extraction
    IEEE Transactions on Components Packaging and Manufacturing Technology, 2013
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    In this paper, we propose a fast H-matrix-based direct solution with a significantly reduced computational cost for an integral-equation-based capacitance extraction of large-scale 3-D interconnects in multiple dielectrics. We reduce the computational cost of an H-matrix-based computation by simultaneously optimizing the H-matrix partition to minimize the number of matrix blocks and minimizing the rank of each matrix block based on a Prescribed Accuracy. With the proposed cost-reduction method, we develop a fast LU-based direct solver. This solver possesses a complexity of kCspO (NlogN) in storage, a complexity of k2Csp2O(Nlog2N) in LU factorization, and a complexity of kCspO(NlogN) in LU solution, where k is the maximal rank, Csp is a constant dependent on matrix partition, and the constant kCsp is minimized based on Accuracy by the proposed cost-reduction method. The proposed solver successfully factorizes dense matrices that involve millions of unknowns in fast CPU time and modest memory consumption, and with the Prescribed Accuracy satisfied. As an algebraic method, the underlying fast technique is kernel independent.

  • A linear-complexity direct integral equation solver accelerated by a new rank-minimized H 2 -representation for large-scale 3-D interconnect extraction
    2012 IEEE MTT-S International Microwave Symposium Digest, 2012
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    We develop a new ℌ2-matrix-based representation of the dense system matrix arising from an integral-equation based analysis of large-scale 3D interconnects. The new ℌ2-representation possesses a minimized rank in both nested cluster bases and coupling matrices for a Prescribed Accuracy. It is applicable to both scalar and vector based integral equation formulations, and real- and complex-valued system matrices. In addition, the new ℌ2-representation is constructed in linear time, and hence the computational overhead is small. Based on the proposed new ℌ2-representation, we develop a linear-complexity direct integral equation solver for 3-D impedance extraction and capacitance extraction of on-chip and package interconnects. The proposed solver is shown to outperform the state-of-the-art linear-complexity direct solver in both memory and CPU consumption. A dense matrix resulting from the capacitance extraction of large-scale 3-D interconnects having 3.71 million unknowns and 576 conductors is inverted in fast CPU time (1.6 hours), modest memory consumption (4.4 GB), and with Prescribed Accuracy satisfied on a single core running at 3 GHz.

O. C. Zienkiewicz - One of the best experts on this subject based on the ideXlab platform.

  • Chapter 16 – Adaptive Finite Element Refinement
    The Finite Element Method: its Basis and Fundamentals, 2013
    Co-Authors: O. C. Zienkiewicz, Robert L. Taylor, J.z. Zhu
    Abstract:

    In this chapter, we discuss adaptive finite element refinement methods that are used to reduce the approximation error. We describe strategies to achieve Prescribed Accuracy on an optimal mesh by using a posteriori error estimators. We also demonstrate how element size distribution of the optimal mesh can be accurately predicted. The use of such refinement strategies in the adaptive h-refinement and adaptive hp-refinement always leads to the optimal rate of convergence of the finite element approximation. When integrated with automatic mesh generators, the Prescribed Accuracy can be achieved with minimum computational cost.

  • Adaptive finite element analysis with quadrilaterals
    Computers & Structures, 2003
    Co-Authors: J.z. Zhu, E. Hinton, O. C. Zienkiewicz
    Abstract:

    Abstract A new development in the automatic mesh generation of quadrilateral elements is described and nearly optimal mesh design using this type of mesh generator in adaptive FE (finite element) analysis is presented. Numerical experiments show that the Prescribed Accuracy is achieved with the optimal rate of convergence obtained. A preliminary comparison is made on the performance of linear triangular and bilinear quadrilateral elements in the adaptive FE stress analysis.

  • a simple error estimator and adaptive time stepping procedure for dynamic analysis
    Earthquake Engineering & Structural Dynamics, 1991
    Co-Authors: O. C. Zienkiewicz
    Abstract:

    A simple local error estimator is presented for time integration schemes in dynamic analysis. This error estimator involves only a small computational cost. The time step size is adaptively adjusted so that the local error at each time step is within a Prescribed Accuracy. It is found that the estimator performs well under various circumstances and provides an economical adaptive process. Attempts to estimate the global time integration error are also reported.

Wenwen Chai - One of the best experts on this subject based on the ideXlab platform.

  • Fast ${\cal H}$ -Matrix-Based Direct Integral Equation Solver With Reduced Computational Cost for Large-Scale Interconnect Extraction
    IEEE Transactions on Components Packaging and Manufacturing Technology, 2013
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    In this paper, we propose a fast H-matrix-based direct solution with a significantly reduced computational cost for an integral-equation-based capacitance extraction of large-scale 3-D interconnects in multiple dielectrics. We reduce the computational cost of an H-matrix-based computation by simultaneously optimizing the H-matrix partition to minimize the number of matrix blocks and minimizing the rank of each matrix block based on a Prescribed Accuracy. With the proposed cost-reduction method, we develop a fast LU-based direct solver. This solver possesses a complexity of kCspO (NlogN) in storage, a complexity of k2Csp2O(Nlog2N) in LU factorization, and a complexity of kCspO(NlogN) in LU solution, where k is the maximal rank, Csp is a constant dependent on matrix partition, and the constant kCsp is minimized based on Accuracy by the proposed cost-reduction method. The proposed solver successfully factorizes dense matrices that involve millions of unknowns in fast CPU time and modest memory consumption, and with the Prescribed Accuracy satisfied. As an algebraic method, the underlying fast technique is kernel independent.

  • A linear-complexity direct integral equation solver accelerated by a new rank-minimized H 2 -representation for large-scale 3-D interconnect extraction
    2012 IEEE MTT-S International Microwave Symposium Digest, 2012
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    We develop a new ℌ2-matrix-based representation of the dense system matrix arising from an integral-equation based analysis of large-scale 3D interconnects. The new ℌ2-representation possesses a minimized rank in both nested cluster bases and coupling matrices for a Prescribed Accuracy. It is applicable to both scalar and vector based integral equation formulations, and real- and complex-valued system matrices. In addition, the new ℌ2-representation is constructed in linear time, and hence the computational overhead is small. Based on the proposed new ℌ2-representation, we develop a linear-complexity direct integral equation solver for 3-D impedance extraction and capacitance extraction of on-chip and package interconnects. The proposed solver is shown to outperform the state-of-the-art linear-complexity direct solver in both memory and CPU consumption. A dense matrix resulting from the capacitance extraction of large-scale 3-D interconnects having 3.71 million unknowns and 576 conductors is inverted in fast CPU time (1.6 hours), modest memory consumption (4.4 GB), and with Prescribed Accuracy satisfied on a single core running at 3 GHz.

  • A Theoretical Study on the Rank of the Integral Operators for Large-­‐Scale Electrodynamic Analysis
    2011
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    We theoretically prove that the minimal rank of the interaction between two separated geometry blocks in an integral-equation based analysis of general threedimensional objects, for a Prescribed error bound, scales linearly with the electric size of the block diameter. We thus prove the existence of the error-bounded lowrank representation of both surface and volume based integral operators for electrodynamic analysis, irrespective of electric size and scatterer shape. The theoretical analysis developed in this work permits an analytical study of the minimal rank for a Prescribed Accuracy, for arbitrarily shaped objects with arbitrary electric sizes. Numerical experiments have verified its validity. This work provides a theoretical proof on why the low-rank matrix algebra can be employed to accelerate the computation of large-scale electrodynamic problems. The rank studied in this paper is based on a singular value decomposition based minimal rank approximation of integral operators, which does not rely on the separation of observation and source coordinates. Methods that do not generate a minimal rank approximation for a Prescribed Accuracy can result in a rank that scales with electric size at a much higher rate.

  • A new H 2 -matrix-based representation of electrodynamic systems with minimized rank and Prescribed Accuracy
    2010 IEEE Antennas and Propagation Society International Symposium, 2010
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    In recent years, fast solvers [1] such as fast multiple based methods, fast low-rank compression methods, and FFT-based methods have been developed, which dramatically reduce the memory complexity of the iterative integral equation (IE) solvers to O(N), and the CPU time to O(N log N) for electrodynamic problems. The H2-matrix based mathematical framework has also been introduced and further developed to reduce the computational complexity of IE-based solutions of electrodynamic problems [2]. It is shown that given a wide range of electric sizes which lead to a wide range of N, the dense system of O(N2) parameters can be compactly stored in O(N) units, and the dense matrix-vector multiplication can be performed in O(N) operations. Moreover, the same order of Accuracy can be kept across this range. The H2-matrix-based representation of the electrodynamic kernels in [2] is generated by an interpolation based scheme. The rank of each admissible block is determined by the number of interpolation points, which varies with the tree level based on a rank function. Such a rank function can be used to maintain the same order of Accuracy in a wide range of electric sizes without compromising the linear computational cost. However, restricted by the interpolation based H2-representation, the resultant rank for each admissible block and for each electric size is often much larger than the minimal one that is required to satisfy a Prescribed Accuracy. This can greatly slow down the computation.

  • a complexity reduced h matrix based direct integral equation solver with Prescribed Accuracy for large scale electrodynamic analysis
    IEEE Antennas and Propagation Society International Symposium, 2010
    Co-Authors: Wenwen Chai, Dan Jiao
    Abstract:

    The Integral equation (IE) based computational electromagnetic methods generally lead to a dense system of linear equations, the solution of which could be very expensive. Recently, fast solvers [1–3] such as FMM-based methods, fast low-rank compression methods, FFT-based methods, and H2-matrix based methods have been developed, which dramatically reduce the memory and CPU time of iterative IE solvers for electrodynamic problems. Fast direct solvers have also been developed. LU factorization of O(N2) time complexity and O(N1.5) memory complexity was reported [4]. Compared to iterative solvers, direct solvers have advantages when the number of iterations or the number of right hand sides is large.

Jung-hoon Lee - One of the best experts on this subject based on the ideXlab platform.

  • A New Integral Variable Structure Regulation Controller for Robot Manipulators with Accurately Predetermined Output Performance
    2004
    Co-Authors: Jung-hoon Lee
    Abstract:

    In this paper, a new integral variable structure regulation controller(IVSRC) is designed by using a special integral sliding surface and a disturbance observer for the improved regulation control of highly nonlinear robot manipulators with Prescribed output performance. The sliding surface having the integral state with a special initial condition is employed in this paper to exactly predetermine the ideal sliding trajectory from a given initial condition to origin without any reaching phase. And a continuous sliding mode input using the disturbance observer is also introduced in oder to effectively follow the predetermined sliding trajectory within the Prescribed Accuracy without large computation burden. The performance of the Prescribed tracking Accuracy to the predetermined sliding trajectory is clearly investigated in detail through the two theorems together with the closed loop stability. The design of the proposed IVSRC is separated into the performance design and robustness design in each independent link. The usefulness of the algorithm has been demonstrated through simulation studies on the regulation control of a two link manipulator under parameter uncertainties and payload variations, in view of no reaching phase, no overshoot, predetermined response with Prescribed Accuracy, easy change of output performance, separation of design phase, and so on.

  • A new integral variable structure regulation controller for robot manipulators with accurately predetermined output
    ISIE '99. Proceedings of the IEEE International Symposium on Industrial Electronics (Cat. No.99TH8465), 1999
    Co-Authors: Jung-hoon Lee, Myoung-joong Youn
    Abstract:

    In this paper, a new Prescribed variable structure regulation controller is designed for highly nonlinear robot manipulators using an integral sliding surface and disturbance observer. With the sliding mode control algorithm, it is possible to guarantee the predetermined output within the Prescribed Accuracy based on the integral sliding surface especially for removing the reaching phase and the disturbance observer for efficient compensation. In regulation, the desired transient and steady state output is Prescribed by means of the sliding dynamics, and the real output with the Prescribed Accuracy is controlled by the continuous input based on the sliding mode control with the disturbance observer, which are investigated through the two theorems together with the closed loop stability of the algorithm. The usefulness of the algorithm has been demonstrated by simulations about regulation controls of a two-link robot under parameter and payload uncertainties.

Paluri S. V. Nataraj - One of the best experts on this subject based on the ideXlab platform.

  • Reliable Computation of Rectangular System Templates to Prescribed Accuracy
    Iete Technical Review, 2015
    Co-Authors: Paluri S. V. Nataraj
    Abstract:

    An algorithm is proposed for reliable computation of rectangular template enclosures for transfer functions of linear systems with uncertain parameters. The algorithm is developed using tools of interval mathematics. The main feature of the algorithm is its applicability to any transfer function whose magnitude and phase values over the given parameter ranges are (i) bounded, and (ii) can be found using a digital computer. It is shown that a machine interval arithmetic implementation of the algorithm accounts for all kinds of computational errors, and generates reliable values for the magnitude and phase intervals of the template. The algorithm is demonstrated on a seven parameter non-rational nuclear reactor example having multiple transport lags and highly correlated nonlinear parameter dependencies.

  • Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties
    International Journal of Robust and Nonlinear Control, 2005
    Co-Authors: Paluri S. V. Nataraj, J. J. Barve
    Abstract:

    We propose an algorithm to compute the limit cycle set of uncertain non-rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a Prescribed Accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the Prescribed Accuracy. Moreover, for a Prescribed Accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non-rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd.

  • Reliable computation of frequency response plots for nonrational transfer functions to Prescribed Accuracy
    Reliable Computing, 2003
    Co-Authors: Paluri S. V. Nataraj, Jayesh Barve
    Abstract:

    We propose algorithms to compute the well known Bode, Nyquist, and Nichols frequency response plots for nonrational transfer functions. The proposed algorithms are very widely applicable—the magnitude and phase functions need to be only bounded and continuous in frequency. The proposed algorithms guarantee that the magnitude and phase plots are reliably computed to a Prescribed Accuracy, in a finite number of iterations. Through several practical nonrational examples, we demonstrate the superior performance of the proposed algorithm over the widely used routines in MATLAB's control system toolbox and over the conventional gridding method.