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Boundary Integral Equations and A Posteriori Error Estimates

Tsinghua Science and Technology 2005年第1期10卷 35-42页

作者：余德浩赵龙花 Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science Chinese Academy of Sciences P. O. Box 2719 Beijing 100080 China

Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations.

关键词： boundary integral equation natural boundary reduction a posteriori error estimate hyper- singular residual pseudo-differential operator

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STUDIES ON STRUCTURAL AND MECHANICAL PROPERTIES UNDER ISOSTATIC COMPRESSION WITH LARGE-SCALE DISCRETE ELEMENT SIMULATIONS

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Acta Mechanica Solida Sinica 2014年第2期27卷 129-136页

作者： Jianguo Liu Qicheng Sun Feng Jin Qingkai Liu State Key Laboratory of Hydroscience and Engineering Tsinghua University High Performance Computing Center Institute of Applied Physics and Computational Mathematics

Granular systems undergo a jamming transition at point J simply by increasing the packing fraction. A large-scale parallel discrete element code （THDEM： TsingHua Discrete Element Method） was used to obtain a satisfying statistical description of the structural and me- chanical properties near point J. The isostatic compressions of 100,000 polydispersed frictionless particles were simulated on high performance computers to clearly observe the sophisticated con- figurations of force chains. The first peak of the pair correlation function, coordination number, spatial distribution of the packing fraction, and stress were calculated to analyze their variations with increasing packing fraction. The critical packing fraction at point J is determined to be 0.62. The incremental stress and coordination number from point J scale well with the power law, and coincide with previous theoretical predications. The distribution of the packing frac- tion is a normal distribution around the average value. The standard deviation decreases with increasing packing fraction, indicating the system is more uniform with a denser packing.

关键词： granular matter jamming transition force chains parallel computing

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Feasible Barzilai-Borwein-like methods for extreme symmetric eigenvalue problems

Feasible Barzilai-Borwein-like methods for extreme symmetric...

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作者： Jiang, Bo Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100190 China

This paper aims to study feasible Barzilai-Borwein (BB)-like methods for extreme symmetric eigenvalue problems. For the two-dimensional case, we establish the local superlinear convergence result of FLBB, FSBB, FABB, and FADBB algorithms. A counter-example is also given, showing that the algorithms may cycle or stop at a non-stationary point. In order to circumvent the difficulty, we propose a safeguard in choosing the stepsize. We also adopt an adaptive non-monotone line search with an improved line search to ensure the global convergence of AFBB-like methods. Numerical experiments on a set of test problems from UF Sparse Matrix Collection demonstrate that, comparing several available codes including eigs, irbleigs and jdcg, AFBB-like methods are very useful for large-scale sparse extreme symmetric eigenvalue problems. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Eigenvalues and eigenfunctions

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A NONMONOTONE CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2002年第2期15卷 139-145页

作者： Dai Yuhong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing 北京 100080

Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.

关键词： Unconstrained optimization conjugate gradient nonmonotone line search global convergence.

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A new trust region algorithm for image restoration

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Science China mathematics 2005年第2期48卷 169-184页

作者： WEN Zaiwen & WANG Yanfei State Key Laboratory of scientific engineering computing, institute of computational mathematics and scientific/engineering computing, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China National Key Laboratory on Remote Sensing Science, institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing 100101, China 1. State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. National Key Laboratory on Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China

The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter a. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious finding the regularization parameters and truncation levels. Some numerical tests on remotely sensed images are given to show that the trust region method is promising.

关键词： trust region algorithm, image restoration, Lanczos method, Kronecker matrix-vector product, preconditioning.

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A novel deep high-level concept-mining jointing hashing model for unsupervised cross-modal retrieval

High-Confidence Computing

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High-Confidence computing 2025年第2期5卷

作者： Chun-Ru Dong Jun-Yan Zhang Feng Zhang Qiang Hua Dachuan Xu Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding 071002 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China

Unsupervised cross-modal hashing has achieved great success in various information retrieval applications owing to its efficient storage usage and fast retrieval speed. Recent studies have primarily focused on training the hash-encoded networks by calculating a sample-based similarity matrix to improve the retrieval performance. However, there are two issues remain to solve: (1) The current sample-based similarity matrix only considers the similarity between image-text pairs, ignoring the different information densities of each modality, which may introduce additional noise and fail to mine key information for retrieval; (2) Most existing unsupervised cross-modal hashing methods only consider alignment between different modalities, while ignoring consistency between each modality, resulting in semantic conflicts. To tackle these challenges, a novel Deep High-level Concept-mining Jointing Hashing (DHCJH) model for unsupervised cross-modal retrieval is proposed in this study. DHCJH is able to capture the essential high-level semantic information from image modalities and integrate into the text modalities to improve the accuracy of guidance information. Additionally, a new hashing loss with a regularization term is introduced to avoid the cross-modal semantic collision and false positive pairs problems. To validate the proposed method, extensive comparison experiments on benchmark datasets are conducted. Experimental findings reveal that DHCJH achieves superior performance in both accuracy and efficiency. The code of DHCJH is available at Github.

关键词： Concept-mining Unsupervised learning Cross-modal Information retrieval

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Existence theorems of solution to variational inequality problems

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Science China mathematics 2001年第2期44卷 201-211页

作者：张立平韩继业徐大川 1. Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.

关键词： exceptional family variational inequality complementarity problem P0-function.

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A　CLASS　OF　FACTORIZATION　UPDATE　ALGORITHM　FOR　SOLVING　SYSTEMS　OF　SPARSE　NONLINEAR　EQUATIONS

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Acta Mathematicae Applicatae Sinica 1996年第2期12卷 188-200页

作者：白中治王德人 Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing China Shanghai University of Science & Technology Shanghai China

In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without introducing an m-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.

关键词： Quasi-Newton methods,matrix factorization,sparse update algorithm Qsuperlinear convergence

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The convergence of parallel iteration algorithms for linear complementarity problems

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COMPUTERS & mathematics WITH APPLICATIONS 1996年第9期32卷 1-17页

作者： Bai, ZZ Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 P.R. China

For the linear complementarity problem, we set up a class of parallel matrix multisplitting accelerated overrelaxation (AOR) algorithm suitable to multiprocessor systems (SIMD-systems). This new algorithm, when its relaxation parameters are suitably chosen, can not only afford extensive choices for parallely serving the linear complementarity problems, but also can greatly improve the convergence property of itself. When the system matrices of the problems are either H-matrices with positive diagonal elements or symmetric positive definite matrices, we establish convergence theories of the new algorithm in a detailed manner.

关键词： linear complementarity problem matrix multisplitting accelerated overrelaxation technique H-matrix symmetric positive definite matrix convergence theory

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Generalized pseudopolar format algorithm for radar imaging with highly suboptimal aperture length

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Science China(Information Sciences) 2015年第4期58卷 63-77页

作者： HAN KuoYe WANG YanPing CHANG XiangKe TAN WeiXian HONG Wen Science and Technology on Microwave Imaging Laboratory (MITL) Institute of ElectronicsChinese Academy of Sciences (IECAS) University of Chinese Academy of Sciences (UCAS) Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences (ICMSEC CAS)

Different from conventional spaceborne or airborne synthetic aperture radar(SAR) with optimal aperture length, an imaging radar with highly suboptimal aperture length acquires the data in short bursts by a geometry spreading over a large range. A polarlike or pseudopolar format grid is introduced to sample data close to the resolution, which presents the design of a separable kernel for efficient FFT *** proposed imaging algorithm formulates the reflectivity image of the target scene as an interpolation-free double image series expansion with two usual approximation-induced phase error terms being taken into account,whereby more generalized application scenarios with high frequency, large bandwidth or larger aperture length for imaging a target scene located within either the far-field or the near-field of the radar aperture are processable with high accuracy. In addition, convergence acceleration methods in computational mathematics are introduced to accelerate the convergence of the image series expansion, so as to make the algorithm more efficient. The proposed algorithm has been validated both qualitatively and quantitatively with an extensive collection of numerical simulations and field measurements of ground-based SAR(GB-SAR) data set.

关键词： pseudopolar format ε-algorithm convergence acceleration suboptimal imaging radar imaging synthetic aperture radar(SAR)

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