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Some properties on multivariate filter banks with a matrix factorization

Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2* and CHEN Qiuhui3(1. department of Mathematics, Beijing Jiaotong University, Beijing 100044, China 2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 3. department of scientific computing and computer applications, Zhongshan University, Guangzhou 510275, China) Department of Mathematics Beijing Jiaotong University Beijing 100044 China. Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

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Efficient estimation of the friction factor for forced laminar flow in axially symmetric corrugated pipes

Efficient estimation of the friction factor for forced lamin...

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ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting, FEDSM 2010 Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels

作者： Rosen Esquivel, Patricio I. Ten Thije Boonkkamp, Jan H.M. Dam, Jacques A.M. Mattheij, Robert M.M. Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Stork FDO Inoteq Amsterdam Netherlands

ISBN: (纸本)9780791849484

In this paper we present an efficient method for calculating the friction factor for forced laminar flow in arbitrary axially symmetric pipes. The approach is based on an analytic expression for the friction factor, obtained after integrating the Navier- Stokes equations over a segment of the pipe. The friction factor is expressed in terms of surface integrals over the pipe wall, these integrals are then estimated by means of approximate velocity and pressure profiles computed via the method of slow variations. Our method for computing the friction factor is validated by comparing the results, to those obtained using CFD techniques for a set of examples featuring pipes with sinusoidal walls. The amplitude and wavelength parameters are used for describing their influence on the flow, as well as for characterizing the cases in which the method is applicable. Since the approach requires only numerical integration in one dimension, the method proves to be much faster than general CFD simulations, while predicting the friction factor with adequate accuracy. Copyright © 2010 by ASME.

关键词： Laminar flow

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Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition

Fast Fourier-Galerkin methods for solving singular boundary ...

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作者： Jiang, Ying Xu, Yuesheng Department of Scientific Computing and Computer Applications Sun Yat-sen University Guangzhou 510275 China Department of Mathematics Syracuse University Syracuse NY 13244 United States

We develop a fast fully discrete FourierGalerkin method for solving a class of singular boundary integral equations. We prove that the number of multiplications used in generating the compressed matrix is O(n log3 n), and the solution of the proposed method preserves the optimal convergence order O(n-t), where n is the order of the Fourier basis functions used in the method and t denotes the degree of regularity of the exact solution. Moreover, we propose a preconditioning which ensures the numerical stability when solving the preconditioned linear system. Numerical examples are presented to confirm the theoretical estimates and to demonstrate the approximation accuracy and computational efficiency of the proposed algorithm. © 2010 Elsevier B.V. All rights reserved.

关键词： Computational efficiency

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MULTILEVEL ITERATION METHODS FOR SOLVING LINEAR ILL-POSED PROBLEMS

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2005年第3期14卷 244-251页

作者：罗兴钧陈仲英 Department of Mathematics and Computer Gannan Teachers College Ganzhou 341000 China Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 PRC Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 PRC

In this paper we develop multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for ill-posed problems. The algorithm and its convergence analysis are pr... 详细信息

关键词：多级迭代法病态问题 Tikhonov调整线性系统收敛性

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Towards detailed material deformation patterns in the hypervelocity impacts of laminated plates with smoothed particle hydrodynamics

Towards detailed material deformation patterns in the hyperv...

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ASME 2016 Pressure Vessels and Piping Conference, PVP 2016

作者： Zisis, Iason Van Der Linden, Bas Giannopapa, Christina Koren, Barry Dam, Jacques Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science TU Eindhoven Eindhoven Netherlands Energy Technology Department of Mechanical Engineering TU Eindhoven Eindhoven Netherlands

ISBN: (纸本)9780791850404

Hypervelocity impacts onto the outer structure of spacecraft induce shock waves, which in case of multimaterial structures interact with the material interfaces. This interaction is expected to produce different deformation patterns for laminates compared to the patterns appearing for materials with homogeneous density. In order to exhibit these different features and to show that the Smoothed Particle Hydrodynamics computational method is capable of describing them, a numerical hypervelocity impact experiment is performed for three plates. The first one is a laminate, with discontinuous density and material parameters, the second is a simple homogenized version of the laminate and the last is a monolithic metal plate. Copyright © 2016 by ASME.

关键词： Shock waves

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MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS

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Numerical Mathematics(Theory,Methods and applications) 2005年第1期 31-55页

作者：陈仲英巫斌许跃生 Academy of Mathematics and System Sciences Beijing 100080 Chinese Academy of Sciences Department of Mathematics Department of Scientific Computing and Computer Applications Department of Scientific Computing and computer Applications Guangzhou 510275 NY 13244-1150 PRC. Syracuse University USA/ Institute of Mathematics Zhongshan University

We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstra

关键词： Multilevel augmentation methods operator equations Predholm integral equations of the second kind.

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An algebraic Method to Compute Generators of Finite Reflection Groups in 3-D Euclidean space

An algebraic Method to Compute Generators of Finite Reflecti...

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作者： Peichang Ouyang Dongsheng Cheng School of Mathematics & Physics Jinggangshan University Department of Scientific Computing and Computer Applications SunYat-Sen University

the generators of reflection groups in 3-D Euclidean space were obtained by observing geometrical models. However, this method is difficult to ascertain the generators of regular polytopes in higher dimension space for there are no visible *** an abstract presentation of a regular polyhedral group, this paper proposes a pure algebraic method to determine its generators. The method can be similarly extended to deal with the regular polytopes in arbitrary dimension space.

关键词： regular polyhedra generator finite reflection group spherical geometry

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Dynamical reduced basis methods for hamiltonian systems

arXiv

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arXiv 2020年

作者： Pagliantini, Cecilia Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the rich geometric structure encoding the physical and stability properties of the dynamics and its local low-rank nature. To address these aspects, we propose a nonlinear structure-preserving model reduction where the reduced phase space evolves in time. In the spirit of dynamical low-rank approximation, the reduced dynamics is obtained by a symplectic projection of the Hamiltonian vector field onto the tangent space of the approximation manifold at each reduced state. A priori error estimates are established in terms of the projection error of the full model solution onto the reduced manifold. For the temporal discretization of the reduced dynamics we employ splitting techniques. The reduced basis satisfies an evolution equation on the manifold of symplectic and orthogonal rectangular matrices having one dimension equal to the size of the full model. We recast the problem on the tangent space of the matrix manifold and develop intrinsic temporal integrators based on Lie group techniques together with explicit Runge-Kutta (RK) schemes. The resulting methods are shown to converge with the order of the RK integrator and their computational complexity depends only linearly on the dimension of the full model, provided the evaluation of the reduced flow velocity has a comparable cost. Copyright © 2020, The Authors. All rights reserved.

关键词： Phase space methods

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Fluid structure interaction in HPC multi-code coupling

Fluid structure interaction in HPC multi-code coupling

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作者： Cajas, J.C. Zavala, M. Houzeaux, G. Casoni, E. Vázquez, M. Moulinec, C. Fournier, Y. Computer Applications for Science and Engineering Barcelona Supercomputing Center Spain Scientific Computing Department Science and Technology Facilities Council Daresbury Laboratory Warrington United Kingdom Research and Development Électricité de France Chatou France

Fluid structure interaction (FSI) problems are of great interest in many applied fields such as aerodynamics, renewable energy generation, nuclear energy generation, vehicles design and biophysical systems research. This kind of problems can be addressed using a monolithic or a staggered approach. The monolithic scheme usually provides robustness and stability in the simulation process but involves extensive code rewriting and is usually less flexible than the staggered approach. The later usually suffers instability in the coupling algorithm but it allows to reuse previously existing code for the physical components of the problem. Extreme-scaling codes for computational fluid dynamics (CFD) and computational solid dynamics (CSD) have been developed for high end machines through the years, and have proven to run efficiently on the most powerful supercomputing infrastructure available. This makes the staggered multi-code coupling approach particularly attractive for FSI simulations on high performance computing (HPC) systems. However, besides the physical difficulties belonging to the FSI simulations, multi-code coupling poses its own computational challenges, as it involves extra communication between two a priori independent parallel applications. This creates an extra level of load imbalance and synchronization points that have to be carefully considered in order to maintain the efficiency of the separated codes, as well as of the whole coupling. In this paper, a staggered approach for FSI problems is presented. Two instances of the same extreme-scale code are used, Alya-Nastin for the CFD simulation and Alya-solidz for the CSD simulation. Characteristics of the parallel code coupling are presented and a validation test case is considered. © Civil-Comp Press, 2015.

关键词： Computational fluid dynamics

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Rate scalable video compression based on flexible block wavelet coding technique

Rate scalable video compression based on flexible block wave...

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Data Compression Conference (DCC)

作者： Ming Wei Hongyang Chao Department of Computer Sciences University of North Texas Denton TX USA Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou China

ISBN: (纸本)0769514774

Summary form only given. We present a new wavelet coding technique, flexible block wavelet coding (FBWC). It is specially designed for delta frame compression. FBWC not only makes delta frame compression more efficient but also keeps the rate scalability and other scalabilities of wavelet based scalable video compression techniques. Based on this new delta frame compression technique, we have implemented a highly efficient rate scalable video codec. Its overall performance surpasses the video codec based on SPIHT and is comparable to that of H.263. Using FBWC, delta frames are compressed in three steps: First, we use motion compensation to eliminate the temporal redundancy between adjacent frames and the predicted error frames (PEF) are generated. Next, the PEF are transformed into the wavelet domain using the flexible block wavelet transform (FBWT). Finally, the zerotree coding mechanism and entropy coder are used to actually compress the FBWT transformed wavelet coefficients to the target data rate.

关键词： Video compression Wavelet transforms Scalability Motion compensation Chaos Video codecs Wavelet domain PSNR scientific computing computer applications

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