The Experts below are selected from a list of 30381 Experts worldwide ranked by ideXlab platform
Chung-kuan Cheng - One of the best experts on this subject based on the ideXlab platform.
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stability and convergency exploration of Matrix Exponential integration on power delivery network transient simulation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2020Co-Authors: Xinyuan Wang, Pengwen Chen, Chung-kuan ChengAbstract:We propose a stability preserved Arnoldi algorithm for Matrix Exponential in the time domain simulation of large-scale power delivery networks (PDNs), which are formulated as semi-explicit differential-algebraic equations (DAEs). The Matrix Exponential and vector products (MEVPs) compose the solution of DAEs in multistep integration methods and can be efficiently approximated with the rational Krylov subspace. To produce stable simulation results for the ill-conditioned system from semi-explicit DAEs, the revised Arnoldi algorithm introduces a new structured orthogonalization process to construct the Krylov subspace. We demonstrate the performance of the new algorithm with theoretical proof and experiments. In the computation of MEVPs, we utilize the Exponential related $\varphi $ functions to improve the numerical accuracy. We further explore the optimal ratio to confine the spectrum in the rational Krylov subspace. Finally, the transient framework is tested on a group of system-level PDNs, showing that Matrix Exponential-based algorithms could achieve high efficiency and accuracy.
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transient circuit simulation for differential algebraic systems using Matrix Exponential
International Conference on Computer Aided Design, 2018Co-Authors: Pengwen Chen, Chung-kuan Cheng, Dongwon Park, Xinyuan WangAbstract:Transient simulation becomes a bottleneck for modern IC designs due to large numbers of transistors, interconnects and tight design margins. For modified nodal analysis (MNA) formulation, we could have differential algebraic equations (DAEs) which consist ordinary differential equations (ODEs) and algebraic equations. Study of solving DAEs with conventional multi-step integration methods has been a research topic in the last few decades. We adopt Matrix Exponential based integration method for circuit transient analysis, its stability and accuracy with DAEs remain an open problem. We identify that potential stability issues in the calculation of Matrix Exponential and vector product (MEVP) with rational Krylov method are originated from the singular system Matrix in DAEs. We then devise a robust algorithm to implicitly regularize the system Matrix while maintaining its sparsity. With the new approach, $\varphi$ functions are applied for MEVP to improve the accuracy of results. Moreover our framework no longer suffers from the limitation on step sizes thus a large leap step is adopted to skip many simulation steps in between. Features of the algorithm are validated on large-scale power delivery networks which achieve high efficiency and accuracy.
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circuit simulation via Matrix Exponential method for stiffness handling and parallel processing
International Conference on Computer Aided Design, 2012Co-Authors: Shih-hung Weng, Quan Chen, Ngai Wong, Chung-kuan ChengAbstract:We propose an advanced Matrix Exponential method (MEXP) to handle the transient simulation of stiff circuits and enable parallel simulation. We analyze the rapid decaying of fast transition elements in Krylov subspace approximation of Matrix Exponential and leverage such scaling effect to leap larger steps in the later stage of time marching. Moreover, Matrix-vector multiplication and restarting scheme in our method provide better scalability and parallelizability than implicit methods. The performance of ordinary MEXP can be improved up to 4.8 times for stiff cases, and the parallel implementation leads to another 11 times speedup. Our approach is demonstrated to be a viable tool for ultra-large circuit simulations (with 1.6M ~ 12M nodes) that are not feasible with existing implicit methods.
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Time-Domain Analysis of Large-Scale Circuits by Matrix Exponential Method With Adaptive Control
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2012Co-Authors: Shih-hung Weng, Quan Chen, Chung-kuan ChengAbstract:We propose an explicit numerical integration method based on Matrix Exponential operator for transient analysis of large-scale circuits. Solving the differential equation analytically, the limiting factor of maximum time step changes largely from the stability and Taylor truncation error to the error in computing the Matrix Exponential operator. We utilize Krylov subspace projection to reduce the computation complexity of Matrix Exponential operator. We also devise a prediction-correction scheme tailored for the Matrix Exponential approach to dynamically adjust the step size and the order of Krylov subspace approximation. Numerical experiments show the advantages of the proposed method compared with the implicit trapezoidal method.
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circuit simulation using Matrix Exponential method
International Conference on ASIC, 2011Co-Authors: Shih-hung Weng, Quan Chen, Chung-kuan ChengAbstract:We propose a stable explicit numerical integration method based on Matrix Exponential operator that enables accurate large time stepping for transient analysis. We utilize Krylov subspace projection to reduce the computational complexity of Matrix Exponential. Numerical experiments show the advantages of the proposed method over backward Euler in terms of accuracy and performance.
Pedro A. Ruiz - One of the best experts on this subject based on the ideXlab platform.
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high performance computing of the Matrix Exponential
Journal of Computational and Applied Mathematics, 2016Co-Authors: Pedro A. Ruiz, Jacinto Javier Ibáñez, Jorge Sastre, Emilio DefezAbstract:This work presents a new algorithm for Matrix Exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but reducing processing time. It has also been compared with two state-of-the-art implementations based on Pade approximations, one commercial and the other implemented in Matlab, getting better accuracy and processing time results in the majority of cases.
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new scaling squaring taylor algorithms for computing the Matrix Exponential
SIAM Journal on Scientific Computing, 2015Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the Matrix Exponential is a combination of “scaling and squaring” with a Pade approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of Matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided.
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NEW SCALING-SQUARING TAYLOR ALGORITHMS FOR COMPUTING THE Matrix Exponential ∗
SIAM Journal on Scientific Computing, 2015Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the Matrix Exponential is a combination of “scaling and squaring” with a Pade approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of Matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided.
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Accurate and efficient Matrix Exponential computation
International Journal of Computer Mathematics, 2013Co-Authors: Jorge Sastre, Jacinto Javier Ibáñez, Pedro A. Ruiz, Emilio DefezAbstract:This work gives a new formula for the forward relative error of Matrix Exponential Taylor approximation and proposes new bounds for it depending on the Matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the Matrix Exponential. A Matlab version of the new algorithm is provided and compared with Pade state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.
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accurate Matrix Exponential computation to solve coupled differential models in engineering
Mathematical and Computer Modelling, 2011Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for Matrix Exponential computation. It uses forward and backward error analysis with improved bounds for normal and nonnormal matrices. Applied to the Taylor method, it has presented a lower or similar cost compared to the state-of-the-art Pade algorithms with better accuracy results in the majority of test matrices, avoiding Pade's denominator condition problems.
Emilio Defez - One of the best experts on this subject based on the ideXlab platform.
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On the Inverse of the Caputo Matrix Exponential
Mathematics, 2019Co-Authors: Emilio Defez, Michael M. Tung, Benito M. Chen-charpentier, Jose M. AlonsoAbstract:Matrix Exponentials are widely used to efficiently tackle systems of linear differential equations. To be able to solve systems of fractional differential equations, the Caputo Matrix Exponential of the index α > 0 was introduced. It generalizes and adapts the conventional Matrix Exponential to systems of fractional differential equations with constant coefficients. This paper analyzes the most significant properties of the Caputo Matrix Exponential, in particular those related to its inverse. Several numerical test examples are discussed throughout this exposition in order to outline our approach. Moreover, we demonstrate that the inverse of a Caputo Matrix Exponential in general is not another Caputo Matrix Exponential.
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Boosting the computation of the Matrix Exponential
Applied Mathematics and Computation, 2019Co-Authors: Jorge Sastre, Jacinto Javier Ibáñez, Emilio DefezAbstract:Abstract This paper presents new Taylor algorithms for the computation of the Matrix Exponential based on recent new Matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Pade algorithm for the computation of the Matrix Exponential, providing higher accuracy and cost performances.
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A new efficient and accurate spline algorithm for the Matrix Exponential computation
Journal of Computational and Applied Mathematics, 2018Co-Authors: Emilio Defez, Jorge Sastre, Javier Ibáñez, Jesús Peinado, Pedro AlonsoAbstract:Abstract In this work an accurate and efficient method based on Matrix splines for computing Matrix Exponential is given. An algorithm and a MATLAB implementation have been developed and compared with the state-of-the-art algorithms for computing the Matrix Exponential. We also developed a parallel implementation for large scale problems. This implementation allowed us to get a much better performance when working with this kind of problems.
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high performance computing of the Matrix Exponential
Journal of Computational and Applied Mathematics, 2016Co-Authors: Pedro A. Ruiz, Jacinto Javier Ibáñez, Jorge Sastre, Emilio DefezAbstract:This work presents a new algorithm for Matrix Exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but reducing processing time. It has also been compared with two state-of-the-art implementations based on Pade approximations, one commercial and the other implemented in Matlab, getting better accuracy and processing time results in the majority of cases.
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new scaling squaring taylor algorithms for computing the Matrix Exponential
SIAM Journal on Scientific Computing, 2015Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the Matrix Exponential is a combination of “scaling and squaring” with a Pade approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of Matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided.
Adrian Doicu - One of the best experts on this subject based on the ideXlab platform.
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A review of the Matrix-Exponential formalism in radiative transfer
Journal of Quantitative Spectroscopy and Radiative Transfer, 2017Co-Authors: Dmitry S. Efremenko, Víctor Molina García, Sebastián Gimeno García, Adrian DoicuAbstract:This paper outlines the Matrix Exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the Matrix Exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the Matrix operator method, and the Matrix Riccati equations method is proved rigorously by means of the Matrix Exponential formalism. For optically thin layers, approximate solution methods relying on the Pade and Taylor series approximations to the Matrix Exponential, as well as on the Matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.
Jorge Sastre - One of the best experts on this subject based on the ideXlab platform.
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Boosting the computation of the Matrix Exponential
Applied Mathematics and Computation, 2019Co-Authors: Jorge Sastre, Jacinto Javier Ibáñez, Emilio DefezAbstract:Abstract This paper presents new Taylor algorithms for the computation of the Matrix Exponential based on recent new Matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Pade algorithm for the computation of the Matrix Exponential, providing higher accuracy and cost performances.
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A new efficient and accurate spline algorithm for the Matrix Exponential computation
Journal of Computational and Applied Mathematics, 2018Co-Authors: Emilio Defez, Jorge Sastre, Javier Ibáñez, Jesús Peinado, Pedro AlonsoAbstract:Abstract In this work an accurate and efficient method based on Matrix splines for computing Matrix Exponential is given. An algorithm and a MATLAB implementation have been developed and compared with the state-of-the-art algorithms for computing the Matrix Exponential. We also developed a parallel implementation for large scale problems. This implementation allowed us to get a much better performance when working with this kind of problems.
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high performance computing of the Matrix Exponential
Journal of Computational and Applied Mathematics, 2016Co-Authors: Pedro A. Ruiz, Jacinto Javier Ibáñez, Jorge Sastre, Emilio DefezAbstract:This work presents a new algorithm for Matrix Exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but reducing processing time. It has also been compared with two state-of-the-art implementations based on Pade approximations, one commercial and the other implemented in Matlab, getting better accuracy and processing time results in the majority of cases.
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new scaling squaring taylor algorithms for computing the Matrix Exponential
SIAM Journal on Scientific Computing, 2015Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the Matrix Exponential is a combination of “scaling and squaring” with a Pade approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of Matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided.
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NEW SCALING-SQUARING TAYLOR ALGORITHMS FOR COMPUTING THE Matrix Exponential ∗
SIAM Journal on Scientific Computing, 2015Co-Authors: Jorge Sastre, Emilio Defez, Jacinto Javier Ibáñez, Pedro A. RuizAbstract:The Matrix Exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the Matrix Exponential is a combination of “scaling and squaring” with a Pade approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of Matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided.
