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作者： Liu, Yang University of Michigan

学位级别：Ph.D., Doctor of Philosophy

The marching-on-in-time (MOT)-based time domain integral equation solvers provide an appealing avenue for solving transient electromagnetic scattering/radiation problems. These state-of-the-art solvers are high-order accurate, rapidly converging and low-/high-frequency stable. Moreover, their computational efficiencies can be significantly improved by accelerators such as the multilevel plane-wave time-domain (PWTD) algorithm. However, practical transient electromagnetic problems involving millions of spatial unknowns and thousands of time steps were barely solved by PWTD-accelerated MOT solvers. This is due to the lack of (i) an efficient parallelization scheme for PWTD’s heterogeneous structure on modern computing platforms, and (ii) a temporal/angular/spatial adaptive PWTD that further improves the computational efficiency. The contributions of this work are as follows: First, a provably scalable parallelization scheme for the PWTD algorithm is developed. The proposed scheme scales well on thousands of CPU processors upon hierarchically partitioning the workloads in spatial, angular and temporal dimensions. The proposed scheme is adopted to time domain surface/volume integral equations (TD-SIE/TD-VIE) solvers for analyzing transient scattering from large and complex-shaped conducting/dielectric objects involving ten million/tens of millions of spatial unknowns. In addition, we developed a single/multiple graphics processing units (GPU) implementation of the PWTD algorithm that achieves at least one order of magnitude speedups compared to serial CPU implementations. Second, a wavelet compression scheme based on local cosine bases (LCBs) that exploits the sparsity in the temporal dimension is developed. All PWTD operations are performed in the wavelet domain with reduced computational complexity. The resultant wavelet-enhanced TD-SIE solver is capable of analyzing transient scattering from smooth quasi-planar conducting objects spanning well over one hundred wavele

关键词： Computational electromagnetics Parallelization Plane-wave time-domain algorithm Time domain integral equation fast algorithms Transient scattering

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Recurrence relations and fast algorithms

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2010年第1期28卷 121-128页

作者： Tygert, Mark Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the values of these linear combinations at certain points, and. vice versa, for evaluating such linear combinations at those points, given the coefficients in the linear combinations;such procedures are also known as analysis and synthesis of series of certain special functions. The algorithms of the present paper are efficient in the sense that their computational costs are proportional to n Inn at any fixed precision of computations, where n is the amount of input and output data. Stated somewhat more precisely, we find a positive real number C such that, for any positive integer n >= 10 and positive real number epsilon <= 1/10, the algorithms require at most Cn(lnn)(ln(1/epsilon))(3) floating-point operations to evaluate at n appropriately chosen points any linear combination of n special functions. given the coefficients in the linear combination, where s is the precision of computations. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Recurrence fast algorithms Special functions Pseudospectral Transforms

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l₀ Sparsifying Transform Learning With Efficient Optimal Updates and Convergence Guarantees

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第9期63卷 2389-2404页

作者： Ravishankar, Saiprasad Bresler, Yoram Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, inpainting, and medical image reconstruction. In this paper, we focus instead on the sparsifying transform model, and study the learning of well-conditioned square sparsifying transforms. The proposed algorithms alternate between a "norm"-based sparse coding step, and a non-convex transform update step. We derive the exact analytical solution for each of these steps. The proposed solution for the transform update step achieves the global minimum in that step, and also provides speedups over iterative solutions involving conjugate gradients. We establish that our alternating algorithms are globally convergent to the set of local minimizers of the nonconvex transform learning problems. In practice, the algorithms are insensitive to initialization. We present results illustrating the promising performance and significant speed-ups of transform learning over synthesis K-SVD in image denoising.

关键词： Denoising dictionary learning fast algorithms image representation non-convex sparse representation transform model

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A fast SEMIDIRECT LEAST SQUARES ALGORITHM FOR HIERARCHICALLY BLOCK SEPARABLE MATRICES

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2014年第2期35卷 725-748页

作者： Ho, Kenneth L. Greengard, Leslie NYU Courant Inst Math Sci New York NY 10012 USA NYU Program Computat Biol New York NY 10012 USA

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data sparse and can describe many important operators including those derived from asymptotically smooth radial kernels that are not too oscillatory. The algorithm is based on a recursive skeletonization procedure that exposes this sparsity and solves the dense least squares problem as a larger, equality-constrained, sparse one. It relies on a sparse QR factorization coupled with iterative weighted least squares methods. In essence, our scheme consists of a direct component, comprised of matrix compression and factorization, followed by an iterative component to enforce certain equality constraints. At most two iterations are typically required for problems that are not too ill-conditioned. For an M x N HBS matrix with M >= N having bounded off-diagonal block rank, the algorithm has optimal O(M + N) complexity. If the rank increases with the spatial dimension as is common for operators that are singular at the origin, then this becomes O(M + N) in one dimension, O(M + N-3/2) in two dimensions, and O(M + N-2) in three dimensions. We illustrate the performance of the method on both overdetermined and underdetermined systems in a variety of settings, with an emphasis on radial basis function approximation and efficient updating and downdating.

关键词： fast algorithms matrix compression recursive skeletonization sparse QR decomposition weighted least squares deferred correction radial basis functions updating/downdating

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The Unified-FFT Algorithm for fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2014年第5期62卷 1112-1121页

作者： Rautio, Brian J. Okhmatovski, Vladimir I. Cangellaris, Andreas C. Rautio, James C. Lee, Jay Kyoon Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA Univ Manitoba Dept Elect & Comp Engn Winnipeg MB R3T 5V6 Canada Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Sonnet Software North Syracuse NY 13212 USA

The unified fast Fourier transform (UFFT) methodology is proposed for fast method of moments analysis of dense integrated circuits embedded in layered media inside perfectly electric conducting or perfectly magnetic conducting enclosures of rectangular cross section. The pre-corrected fast Fourier transform (FFT) method is modified to handle the dyadic Green's function (DGF) of shielded layered media through factorization of the DGF into four convolution/correlation terms enabling fast matrix solve operations (MSOs). Calculation of the impedance matrix elements in the form of an infinite series of waveguide modes is cast into the form of a 2-D discrete Fourier transform allowing for fast FFT-accelerated matrix fill operations (MFOs). fast FFT-enhanced MSOs and MFOs used in conjunction form the UFFT method. The computational complexity and memory requirements for the proposed UFFT solver scale as and, respectively, where is the number of unknowns in the discrete approximation of the governing integral equation. New criteria specific to shielded circuits for the projection of the current expansion functions on a uniform FFT grid are developed. The accuracy and efficiency of the solver is demonstrated through its application to multiple examples of full-wave analysis of large planar circuits.

关键词： Computer-aided design (CAD) CAD algorithms and techniques fast algorithms numerical analysis RF integrated circuit (RFIC) modeling

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fast Evaluation of Electromagnetic Fields Using a Parallelized Adaptive Cross Approximation

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2014年第5期62卷 2818-2822页

作者： Schroeder, Arne Bruens, Heinz-D. Schuster, Christian Tech Univ Hamburg Inst Theoret Elektrotech Hamburg Germany

This communication shows a novel application of the adaptive cross approximation (ACA). A hierarchical ACA is presented for accelerating the evaluation of electromagnetic fields from a known current distribution, as it is required in the post-processing stage of the method of moments. Furthermore, a parallelization which employs a master-worker scheme is outlined, resulting in a highly efficient parallel code. Numerical examples validate the accuracy and efficiency of the method for various electromagnetic problems such as field coupling and radiation problems. It is demonstrated that the proposed approach is applicable in a broad frequency range, where it provides a definable error bound. Moreover, an acceleration factor of more than 200 is achievable, making an extensive field analysis of electrically large objects feasible.

关键词： Adaptive cross approximation electromagnetic field computation fast algorithms method of moments post-processing

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A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年 258卷 227-245页

作者： Schmitz, Phillip G. Ying, Lexing Univ Texas Austin Dept Math Austin TX 78712 USA Stanford Univ Dept Math Stanford CA 94305 USA Stanford Univ ICME Stanford CA 94305 USA

We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining the nested dissection matrix factorization method with hierarchical matrices in two dimensions and extend it to the three dimensional case. A theoretical linear time complexity is derived and a more practical variant with slightly worse scaling is demonstrated. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Elliptic equations fast algorithms Nested dissection Hierarchical matrices Sparse matrix

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Low-Complexity Implementation of RAID Based on Reed-Solomon Codes

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ACM TRANSACTIONS ON STORAGE 2015年第1期11卷 1-1页

作者： Trifonov, P. St Petersburg State Polytech Univ St Petersburg 194021 Russia

fast algorithms are proposed for encoding and reconstructing data in RAID based on Reed-Solomon codes. The proposed approach is based on the cyclotomic fast Fourier transform algorithm and enables one to significantly reduce the number of expensive Galois field multiplications required. The complexity of the obtained algorithms is much lower than those for existing MDS array codes. Software implementation of the proposed algorithms is discussed. The performance results show that the new algorithms provide. substantially better performance compared with the standard algorithm.

关键词： Design algorithms Performance Reliability Reed-Solomon codes fast algorithms FFT RAID

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INTEGER COSINE TRANSFORMS: METHODS TO CONSTRUCT NEW ORDER 8, 16 fast TRANSFORMS AND THEIR APPLICATION

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CYBERNETICS AND SYSTEMS ANALYSIS 2014年第6期50卷 913-929页

作者： Hnativ, L. O. Natl Acad Sci Ukraine V M Glushkov Inst Cybernet Kiev Ukraine

Matrix methods to construct simple fast integer order 16 type I, II cosine transforms of low complexity are considered. A new approach and a generalized method are proposed to construct integer order 8 cosine transforms and their fast algorithms without multiplication. A new integer step transform with fast algorithm is introduced. Two transforms are proposed, whose speed is 1.7 to 2.9 times greater and which provide a higher quality of video coding than standard H. 265 does.

关键词： discrete cosine transform integer cosine transform integer step transform fast algorithms coding efficiency computational complexity video coding standards

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Tracking Entities in the Dynamic World: A fast Algorithm for Matching Temporal Records

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PROCEEDINGS OF THE VLDB ENDOWMENT 2014年第6期7卷 469-480页

作者： Chiang, Yueh-Hsuan Doan, Anhai Naughton, Jeffrey F. Univ Wisconsin 1210 Dayton St Madison WI 53706 USA

Identifying records referring to the same real world entity over time enables longitudinal data analysis. However, difficulties arise from the dynamic nature of the world: the entities described by a temporal data set often evolve their states over time. While the state of the art approach to temporal entity matching achieves high accuracy, this approach is computationally expensive and cannot handle large data sets. In this paper, we present an approach that achieves equivalent matching accuracy but takes far less time. Our key insight is "static first, dynamic second." Our approach first runs an evidence-collection pass, grouping records without considering the possibility of entity evolution, as if the world were "static." Then, it merges clusters from the initial grouping by determining whether an entity might evolve from the state described in one cluster to the state described in another cluster. This intuitively reduces a difficult problem, record matching with evolution, to two simpler problems: record matching without evolution, then "evolution detection" among the resulting clusters. Experimental results on several temporal data sets show that our approach provides an order of magnitude improvement in run time over the state-of-the-art approach while producing equivalent matching accuracy.

关键词： Entity matching Evidence collection fast algorithms Large datasets Longitudinal data Real world entities Record matching State of the art approach

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