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MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems

JOURNAL OF GLOBAL OPTIMIZATION 2015年第2期62卷 205-227页

作者： Liu, Qunfeng Zeng, Jinping Yang, Gang Dongguan Univ Technol Sch Comp Dongguan 523808 Peoples R China

Although DIRECT global optimization algorithm quickly gets close to the basin of the optimum, it often takes much longer to refine the solution to a high degree of accuracy. This behavior of DIRECT is similar to the "smooth mode phenomenon" encountered when solving linear systems discretized from partial differential equation (PDE). In the case of PDE, this smooth mode phenomenon can be eliminated efficiently by the multigrid algorithm in which the PDE solver is applied at different levels of discretization. In this paper we adapt the multigrid approach to a robust version of DIRECT algorithm, obtaining a "multilevel" robust DIRECT (MrDIRECT) algorithm. Although additional parameters are needed, our numerical results show that MrDIRECT is insensitive to the parameters, and the parameters setting proposed in this paper performs very well on the tested sets of benchmark problems, in terms of the speed with which the global optimum is found to a high degree of accuracy.

关键词： Global optimization multilevel algorithm Multigrid algorithm DIRECT algorithm multilevel partition

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Fast MAP-based super-resolution algorithm using multilevel interpolation and reconstruction

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2012年第6期35卷 711-722页

作者： Wu, Jiunn-Lin Hung, Meng-Han Natl Chung Hsing Univ Inst Networking & Multimedia Dept Comp Sci & Engn Taichung 402 Taiwan

Super-resolution (SR) image reconstruction can produce a high-resolution (HR) digital image from multiple low-resolution (LR) photographs. Many applications require HR images, including medical imaging, satellite imaging, and video applications. Recovering lost details from down-sampled images is the main challenge of SR techniques. However, most studies have not taken computational complexity into consideration. Therefore, this article presents a new fast maximum a posteriori (MAP)-based SR image reconstruction method based on a multilevel algorithm. In particular, this work focuses on the case of input LR images that do not meet the requirements for the analysis. A two-step interpolation process is proposed to increase the quality of the constructed SR image. Experimental results show that the proposed algorithm reduces the blocking artifacts in the reconstruct SR image caused by a lack of LR images. Compared to the conventional MAP-based method, the proposed method also achieves up to 60% reduction in computational complexity with comparable peak signal-to-noise ratio and visual quality.

关键词： super-resolution maximum a posteriori method multilevel algorithm multiframe image reconstruction

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multilevel fast multipole algorithm for analysis of large-scale microstrip structures

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IEEE MICROWAVE AND GUIDED WAVE LETTERS 1999年第12期9卷 508-510页

作者： Ling, F Song, JM Jin, JM Univ Illinois Dept Elect & Comp Engn Ctr Comp Electromagnet Urbana IL 61801 USA

An efficient algorithm combining multilevel fast multipole method and the discrete complex image method is presented for analyzing large-scale microstrip structures. The resulting algorithm has the memory requirement and the CPU time per iteration proportional to O(N log N). where N denotes the number of unknowns. Numerical results for microstrip antennas are presented to demonstrate the efficiency and accuracy of this method.

关键词： Green's function fast multipole method of moments microstrip multilevel algorithm

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Simulation of radiation from an antenna mounted on a vehicle by a multilevel QR compression algorithm

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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 2005年第3期15卷 177-179页

作者： Bunlon, X Borderies, P Poirier, JR Paletta, L Gobin, V Div Res F-78288 Guyancourt France DEMR ONERA F-31055 Toulouse France ENSEIGHT LEN7 F-31071 Toulouse France

We describe here a real case application of a formerly presented compression technique for the method of moments. This method is based on a QR compression of the impedance matrix off-diagonals blocks. In this letter, it is extended to the multilevel three-dimensional case, and applied to the radiation of an antenna mounted on a car model. The ability of this technique to treat antenna radiation on a large complex structure is demonstrated, as well as the improvement in memory storage and computation time when. compared with the conventional method.

关键词： antenna placement compression methods method of moments (MoM) multilevel algorithm QR decomposition

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Analysis of the RATAN-600 radiotelescope antenna with a multilevel Physical Optics algorithm

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COMPTES RENDUS PHYSIQUE 2012年第1期13卷 38-45页

作者： Letrou, Christine Khaikin, Vladimir Boag, Amir TELECOM SudParis Lab SAMOVAR UMR CNRS 5157 F-91011 Evry France RAS Special Astrophys Observ Moscow Russia Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

The RATAN-600 antenna is a flexible multireflector system composed of reflectors of very large dimensions. An extended system, with improved performance in the millimetric range, includes a focal receiver array. Accurate electromagnetic analysis of such a system, and simulation of three-dimensional (3D) patterns, represents a substantial computational challenge. A fast Physical Optics method based on a multilevel subdivision of the surfaces of integration is proposed to address this problem. This method allows to perform Physical Optics integrals with a computational complexity comparable to that of the Fast Fourier Transform. The algorithm and initial numerical results of its application to the RATAN-600 antenna system are presented. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

关键词： Radiotelescope Multireflector antenna Physical Optics multilevel algorithm

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A multilevel Non-uniform Grid algorithm for Acceleration of Volumetric Integral Equation Based Solvers for Analysis of Arbitrarily Shaped Dielectric Radomes

A Multilevel Non-uniform Grid Algorithm for Acceleration of ...

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IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS)

作者： Rotbart, Asaf Boag, Amir Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

ISBN: (纸本)9781457716928

A fast algorithm combined with the volume integral equation (VIE) is proposed for analyzing antenna radiation properties in the presence of an arbitrary shaped dielectric radome. The discrete form of the VIE is obtained using the method of moments (MOM). Evaluation of electromagnetic fields is accelerated using the multilevel volumetric non-uniform grid algorithm (MLVNG). The algorithm is based on phase and amplitude compensation of fields which are produced by a bounded volume of source distribution. The compensated field is band-limited function of its coordinates, which allows sampling it on a sparse non-uniform spherical grid at rates proportional to the source volume. Tight sampling rules are suggested in order to reduce the computational complexity of the field evaluation. The computational complexity of the MLVNG algorithm is demonstrated on representative example.

关键词： Fast algorithm Hierarchical decomposition Iterative solver Method of moments multilevel algorithm Radome Scattering Volumetric integral equation

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A multilevel tabu search algorithm for balanced partitioning of unstructured grids

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2016年第9期105卷 678-692页

作者： Mehrdoost, Zahra Bahrainian, Seyed Saied Shahid Chamran Univ Ahvaz Dept Mech Engn Ahvaz *** Iran

This paper presents a multilevel algorithm for balanced partitioning of unstructured grids. The grid is partitioned such that the number of interface elements is minimized and each partition contains an equal number of grid elements. The partition refinement of the proposed multilevel algorithm is based on iterative tabu search procedure. In iterative partition refinement algorithms, tie-breaking in selection of maximum gain vertices affects the performance considerably. A new tie-breaking strategy in the iterative tabu search algorithm is proposed that leads to improved partitioning quality. Numerical experiments are carried out on various unstructured grids in order to evaluate the performance of the proposed algorithm. The partition results are compared with those produced by the well-known partitioning package Metis and k-means clustering algorithm and shown to be superior in terms of edge cut, partition balance, and partition connectivity. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： grid partitioning multilevel algorithm tabu search unstructured grid

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multilevel FAST-MULTIPOLE algorithm FOR SOLVING COMBINED FIELD INTEGRAL-EQUATIONS OF ELECTROMAGNETIC SCATTERING

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 1995年第1期10卷 14-19页

作者： SONG, JM CHEW, WC Electromagnetics Laboratory Department of Electrical and Computer Engineering University of Illinois Urbana Illinois 61801

The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N-2) to O(N-1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592-unknown problem can be solved within 24 h on a SUN Sparc10. (C) 1995 John Wiley & Sons, Inc.

关键词： FAST MULTIPOLE multilevel algorithm INTEGRAL EQUATION METHOD OF MOMENTS ELECTROMAGNETIC SCATTERING

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TOTALLY PARALLEL multilevel algorithmS

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International Journal of High Speed Computing 1989年第2期1卷 233-245页

作者： PAUL O. FREDERICKSON RIACS Ames Research Center Moffett Field CA 94035

Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four algorithms are Parallel Superconvergent Multigrid (PSMG) of Frederickson and McBryan, Robust Multigrid (RMG) of Hackbusch, the FFT based Spectral algorithm, and Parallel Cyclic Reduction. In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which we will refer to as TPMA. In certain cases the spectral radius of TPMA is zero, and it is recognized to be a direct algorithm. In many other cases the spectral radius, although not zero, is small enough that a single iteration per timestep keeps the local error within the required tolerance.

关键词： multilevel algorithm multigrid cyclic reduction spectral method

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Complexity of Banach space valued and parametric stochastic Ito integration

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JOURNAL OF COMPLEXITY 2017年 40卷 100-122页

作者： Daun, Thomas Heinrich, Stefan Univ Kaiserslautern Dept Comp Sci D-67653 Kaiserslautern Germany

We present a complexity analysis for strong approximation of Banach space valued and parameter dependent scalar stochastic Ito integration, driven by a Wiener process. Both definite and indefinite integration are considered. We analyze the Banach space valued version of the Euler-Maruyama scheme. Based on these results, we define a multilevel algorithm for the parameter dependent stochastic integration problem and show its order optimality for various input classes. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Stochastic integral Banach space Parametric problem multilevel algorithm Lower bounds

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