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High order finite volume methods for singular perturbation problems

Science China Mathematics 2008年第8期51卷 1391-1400页

作者： CHEN ZhongYing HE ChongNan WU Bin Department of Scientific Computing and Computer Applications Sun Yat-Sen UniversityGuangzhou 510275China College of Mathematics and Computer Science Guangxi University for NationalitiesNanning 530006China

In this paper we establish a high order finite volume method for the fourth order singular perturbation *** conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergenc... 详细信息

关键词： finite volume methods optimal meshes singular perturbation problems 65L10 65L12 65L60

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Fast collocation methods for high-dimensional weakly singular integral equations

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Journal of Integral Equations and applications 2008年第1期20卷 49-92页

作者： Chen, Zhongying Wu, Bin Xu, Yuesheng Department of Scientific Computing and Computer Applications Sun Yat-sen University Guangzhou 510275 China Department of Mathematics Syracuse University Syracuse NY 13244-1150 United States

We realize fast collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels on a polyhedral domain in Rd with d ≥ 3. A polyhedral domain is subdivided into a finite num...

We realize fast collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels on a polyhedral domain in R^d with d ≥ 3. A polyhedral domain is subdivided into a finite number of simplices. We construct a uniform self-similar partition of a simplex for the purpose of constructing multi-scale bases and their corresponding collocation functionals. The multi-scale bases and the collocation functionals lead to a compression of the matrix representation of the weakly singular integral operator and thus to a fast collocation scheme for solving the integral equation. We develop a quadrature rule for computing the weakly singular integrals appearing in the matrix. We propose an error control strategy for the numerical integration so that the nearly optimal convergence order for the discrete fast collocation method is obtained. Finally, a numerical experiment of solving the three-dimensional equation is presented to confirm the theoretical estimates. © 2008 Rocky Mountain Mathematics Consortium.

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A parameter choice strategy for a multi-level augmentation method solving ill-posed operator equations

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Journal of Integral Equations and applications 2008年第4期20卷 569-590页

作者： Chen, Zhongying Jiang, Ying Song, Lihong Yang, Hongqi Department of Scientific Computing and Computer Applications Sun Yat-sen University Guangzhou 510275 China Centre for Signal Processing School of Electrical and Electronic Engineering Nanyang Technological University 639798 Singapore Singapore

We apply the multi-level augmentation method for solving operator equations of the first kind via the Tikhonov regularization method. We present a new a posteriori parameter choice strategy which leads to optimal convergence rates. Numerical experiments illustrate the efficiency of the method. © 2008 Rocky Mountain Mathematics Consortium.

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Broadband waveform modeling of moderate earthquakes in the San Francisco Bay Area and preliminary assessment of the USGS 3D seismic velocity model

Broadband waveform modeling of moderate earthquakes in the S...

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作者： Rodgers, Arthur Petersson, N. Anders Nilsson, Stefan Sjögreen, Björn McCandless, Kathleen Atmospheric Earth and Energy Division Chemistry Materials Earth and Life Sciences Directorate Lawrence Livermore National Laboratory 7000 East Avenue L-205 Livermore CA 94551 United States Center for Applied Scientific Computing Computations Directorate Lawrence Livermore National Laboratory 7000 East Avenue L-550 Livermore CA 94551 United States Computer Applications and Research Department Computations Directorate Lawrence Livermore National Laboratory 7000 East Avenue L-463 Livermore CA 94551 United States

Recently, the United States Geologic Survey Earthquake Hazards Program developed a 3D seismic velocity model of Northern California based on geology, including a detailed model of the urbanized San Francisco Bay Area. In this study, we report comparisons of observed three-component broadband (0.03-0.25-Hz) wave-forms with synthetic seismograms computed with the new 3D model using an elastic finite difference method. We selected a set of 12 moderate earthquakes (Mw 4.0-5.1) that occurred within the greater San Francisco Bay Area, having well-constrained source parameters and broadband recordings with high signal-to-noise ratios. The objective of this study was to investigate how well the 3D velocity model predicts observed waveforms and to identify features of the model that may require revision to improve the waveform fits and predictions of ground motions for future events. We show for the 3 September 2000 Yountville earthquake that reported source parameters accurately predict waveforms at two close strong-motion stations (approximately 10 km from the epicenter). By comparing synthetics for the average 1D model GIL7 (Stidham et al., 1999) and the 3D structures we show that the effects of seismic wave propagation in the 3D model become important for frequencies at and above 0.1 Hz (periods less than 10 see). Comparison of observed and synthetic seismograms for the 3D model consistently shows that the model predicts energy arriving earlier than is observed, particularly for the surface waves, indicating that the shear velocities in the upper crust must be reduced. We cross correlated the observed and synthetic waveforms and recorded the delay time and linear correlation for best alignment of the data and delayed synthetic. The results indicate that generally the 3D model predicts the observed waveforms well (mean linear correlations 0.41) and includes features that arise from the interaction of the wave field with 3D structure, especially the major sedimentary basin

关键词： Seismic waves

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A Stefan problem related to a non-equilibrium shrinking unreacted core model with fast reaction for the sphere

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PAMM 2008年第1期7卷

作者： Adrian Muntean CASA – Center for Analysis Scientific computing and Applications Department of Mathematics and Computer Science TU Eindhoven PO Box 513 5600 MB Eindhoven The Netherlands

The problem studied in this note refers to a substantial part of a larger system of partial differential equations modeling diffusion and fast reaction of a gaseous species A in a reactive spherical porous region. We report on the local existence and uniqueness of weak solutions to the corresponding moving-boundary system containing two coupled mass-balance equations in a moving annulus. Since the system incorporates an explicit description of the velocity of the moving boundary, our formulation resembles to the one-phase Stefan-like problem with kinetic condition. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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A complete flux scheme for the stationary advection-diffusion-reaction equation

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PAMM 2008年第1期7卷

作者： J.H.M. ten Thije Boonkkamp Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology PO Box 513 5600 MB Eindhoven The Netherlands

Expressions for the numerical flux of a conservation law of advection-diffusion-reaction type are derived from a local solution of the entire conservation law, including the source term. The resulting complete flux scheme is given for one-dimensional (in Cartesian and spherical coordinates) and two-dimensional model equations. Combined with a finite volume method, the numerical scheme is second order accurate, uniformly in the Peclet numbers. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Ground-motion modeling of the 1906 San Francisco Earthquake, part II: Ground-motion estimates for the 1906 earthquake and scenario events

Ground-motion modeling of the 1906 San Francisco Earthquake,...

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作者： Aagaard, Brad T. Brocher, Thomas M. Dolenc, David Dreger, Douglas Graves, Robert W. Harmsen, Stephen Hartzell, Stephen Larsen, Shawn McCandless, Kathleen Nilsson, Stefan Petersson, N. Anders Rodgers, Arthur Sjögreen, Björn Zoback, Mary Lou U.S. Geological Survey 345 Middlefield Rd. Menlo Park CA 94025 United States Seismological Laboratory University of California Berkeley 215 McCone Hall Berkeley CA 94720 United States URS Corporation 566 El Dorado St. Pasadena CA 91101 United States U.S. Geological Survey MS966 P.O. Box 25046 Golden CO 80225 United States Lawrence Livermore National Laboratory Box 808 L-103 Livermore CA 94551-0808 United States Computer Applications and Research Department Computations Directorate Lawrence Livermore National Laboratory Box 808 L-550 Livermore CA 94551-0808 United States Center for Applied Scientific Computing Computations Directorate Lawrence Livermore National Laboratory Box 808 L-550 Livermore CA 94551-0808 United States Atmospheric Earth and Energy Department Energy and Environment Directorate Lawrence Livermore National Laboratory Box 808 L-205 Livermore CA 94551-0808 United States

We estimate the ground motions produce by the 1906 San Francisco earthquake making use of the recently developed Song et al. (2008) source model that combines the available geodetic and seismic observations and recently constructed 3D geologic and seismic velocity models. Our estimates of the ground motions for the 1906 earthquake are consistent across five ground-motion modeling groups employing different wave propagation codes and simulation domains. The simulations successfully reproduce the main features of the Boatwright and Bundock (2005) ShakeMap, but tend to over predict the intensity of shaking by 0.1-0.5 modified Mercalli intensity (MMI) units. Velocity waveforms at sites throughout the San Francisco Bay Area exhibit characteristics consistent with rupture directivity, local geologic conditions (e.g., sedimentary basins), and the large size of the event (e.g., durations of strong shaking lasting tens of seconds). We also compute ground motions for seven hypothetical scenarios rupturing the same extent of the northern San Andreas fault, considering three additional hypocenters and an additional, random distribution of slip. Rupture directivity exerts the strongest influence on the variations in shaking, although sedimentary basins do consistently contribute to the response in some locations, such as Santa Rosa, Livermore, and San Jose. These scenarios suggest that future large earthquakes on the northern San Andreas fault may subject the current San Francisco Bay urban area to stronger shaking than a repeat of the 1906 earthquake. Ruptures propagating southward towards San Francisco appear to expose more of the urban area to a given intensity level than do ruptures propagating northward.

关键词： Earthquakes

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The discrete multi-projection method for fredholm integral equations of the second kind

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Journal of Integral Equations and applications 2007年第2期19卷 143-162页

作者： Chen, Zhongying Long, Guangqing Nelakanti, Gnaneshwar Department of Scientific Computing and Computer Applications Sun Yat-Sen University Guangzhou 510275 China Department of Mathematics Guangxi Normal College Nanning 530001 China Department of Mathematics Indian Institute of Technology Kharagpur-721302 India

In this paper, discrete multi-projection methods are developed for solving the second kind Fredholm integral equations. We propose a theoretical framework for analysis of the convergence of these methods. The theory is then applied to establish super-convergence results for the corresponding discrete Galerkin method, collocation method and their iterated solutions. Numerical examples are presented to illustrate the theoretical estimates for the error of these methods. © 2007 Rocky Mountain Mathematics Consortium.

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Some properties on multivariate filter banks with a matrix factorization

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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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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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