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A Posteriori Estimates for a Natural Neumann-Neumann domain decomposition algorithm on a Unilateral Contact Problem

JOURNAL OF SCIENTIFIC COMPUTING 2015年第3期64卷 818-836页

作者： Choi, D. Gallimard, L. Sassi, T. Univ Caen Basse Normandie LMNO F-14032 Caen France Univ Paris Ouest Nanterre La Def LEME F-92410 Ville Davray France

In this paper we present an error estimator for unilateral contact problems solved by a Neumann-Neumann domain decomposition algorithm. This error estimator takes into account both the spatial error due to the finite element discretization and the algebraic error due to the domain decomposition algorithm. To differentiate specifically the contribution of these two error sources to the global error, two quantities are introduced: a discretization error indicator and an algebraic error indicator. The effectivity indices and the convergence of both the global error estimator and the error indicators are shown on several examples.

关键词： Error estimation domain decomposition algorithm Contact problem Discretization error Algebraic error

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A finite difference non-matching domain decomposition algorithm for the parabolic equation

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010年第11期87卷 2480-2492页

作者： Wang, Ting Rui, Hongxing Shandong Univ Sch Math Jinan 250100 Peoples R China Chinese Acad Sci Inst Software Parallel Comp Lab Beijing Peoples R China

A finite difference domain decomposition algorithm on a non-overlapping non-matching grid for the parabolic equation is discussed. The basic procedure is to define the explicit scheme at the interface points with a larger mesh spacing H, then the implicit schemes with different mesh spacings are applied on the non-matching subdomains, respectively. The stability bound is released both for the one-dimensional and two-dimensional parabolic problem. Finally, numerical experiments are also presented.

关键词： parabolic equation domain decomposition algorithm finite difference non-matching grid parallel

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An Improved domain decomposition algorithm for Modeling Dense Distribution of Bodies of Revolution

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IEEE ACCESS 2020年 8卷 15360-15368页

作者： Su, Ting Chen, Jin Wang, Jinlong Hu, Yunqin Hainan Univ Sch Informat & Commun Engn Haikou 570100 Hainan Peoples R China Army Engn Univ PLA Coll Commun Engn Nanjing 210007 Peoples R China Nanjing Univ Posts & Telecommun Coll Commun Engn Nanjing 210003 Peoples R China

An improved algorithm is presented to overcome the shortage of the domain decomposition algorithm based on equivalence principle for multiple bodies of revolutions (EPA-MBoR). In a dense distribution of non-coaxal bodies of revolution (BoRs) containing at least two very close BoRs, no matter how to establish sphere equivalence surfaces (ESs), they are intersecting. It violates the equivalence principle and causes error results. The improvement is introduced to overcome the defect. In the improved algorithm, a sphere ES cluster is built on each BoR instead of a single sphere ES. We can freely adjust the sphere ES clusters on each BoR to avoid the intersection among them. The numerical results verify the above improvement successfully overcomes the deficiency and show the improved algorithm inherits the high efficiency of the previous algorithm.

关键词： Body of revolution domain decomposition algorithm equivalence principle surface integral equation

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Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

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Applied Mathematics and Mechanics(English Edition) 2009年第9期30卷 1177-1182页

作者：尚月强何银年 Faculty of Science Xi'an Jiaotong University School of Mathematics and Computer Science Guizhou Normal University

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

关键词： domain decomposition algorithm Schwarz method Fourier transform biharmonic equation

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On the Parallelization of A New Three Dimensional Hyperbolic Group Solver by domain decomposition Strategy

On the Parallelization of A New Three Dimensional Hyperbolic...

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12th International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES)

作者： Ming, Kew Lee Ali, Norhashidah Hj. Mohd. Univ Sains Malaysia Sch Math Sci George Town 11800 Malaysia

ISBN: (纸本)9780769550602

In this paper, the parallel implementation of a new explicit group iterative scheme is proposed for the solution of a three dimensional second order telegraph partial differential equation. The explicit group (EG) method is derived from the standard centered seven-point finite difference discretisation formula. We utilize the domain decomposition technique on this group scheme to divide the tasks involved in solving the equation. The aim of this study is to describe the development of the parallel group iterative scheme under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multiple-core technologies. Numerical experiments are conducted together with their detailed performance analysis. The results will be reported and discussed.

关键词： Telegraph equation explicit group method domain decomposition algorithm parallelization multiple-core OpenMP

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Development of a parallel molecular dynamics code on SIMD computers: algorithm for use of pair list criterion

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JOURNAL OF COMPUTATIONAL CHEMISTRY 1998年第7期19卷 685-694页

作者： Roccatano, D Bizzarri, R Chillemi, G Sanna, N Di Nola, A Univ Roma La Sapienza Dipartimento Chim I-00185 Rome Italy Univ Roma La Sapienza CASPUR Rome Italy Univ Roma La Sapienza Dipartimento Fis I-00185 Rome Italy

In recent years several implementations of molecular dynamics (MD) codes have been reported on multiple instruction multiple data (MIMD) machines. However, very few implementations of MD codes on single instruction multiple data (SIMD) machines have been reported. The difficulty in using pair lists of nonbonded interactions is the major problem with MD codes for SIMD machines, such that, generally, the full connectivity computation has been used. We present an algorithm, the global cut-off algorithm (GCA), which permits the use of pair lists on SIMD machines. GCA is based on a probabilistic approach and requires the cut-off condition to be simultaneously verified on all nodes of the machine. The MD code used was taken from the GROMOS package;only the routines involved in the pair lists and in the computation of nonbonded interactions were rewritten for a parallel architecture. The remaining calculations were performed on the host computer. The algorithm has been tested on Quadrics computers for configurations of 32, 128, and 512 processors and for systems of 4000, 8000, 15,000, and 30,000 particles. Quadrics was developed by Istituto Nazionale di Fisica Nucleare (INFN) and marketed by Alenia Spazio. (C) 1998 John Wiley & Sons, Inc.

关键词： molecular dynamics domain decomposition algorithm parallel computers pair list for molecular dynamics code on SIMD machines array processor elaborator (APE)

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On the Parallelization of A New Three Dimensional Hyperbolic Group Solver by domain decomposition Strategy

On the Parallelization of A New Three Dimensional Hyperbolic...

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第12届分布式计算及其应用国际学术研讨会

作者： Kew Lee Ming Norhashidah Hj.Mohd.Ali School of Mathematical Sciences Universiti Sains Malaysia

In this paper, the parallel implementation of a new explicit group iterative scheme is proposed for the solution of a three dimensional second order telegraph partial differential equation. The explicit group(EG) method is derived from the standard centered seven-point finite difference discretisation formula. We utilize the domain decomposition technique on this group scheme to divide the tasks involved in solving the equation. The aim of this study is to describe the development of the parallel group iterative scheme under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multiplecore technologies. Numerical experiments are conducted together with their detailed performance analysis. The results will be reported and discussed.

关键词： Telegraph equation explicit group method domain decomposition algorithm parallelization multiple-core OpenMP

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On the Parallelization of A New Three Dimensional Hyperbolic Group Solver by domain decomposition Strategy

On the Parallelization of A New Three Dimensional Hyperbolic...

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The 12th International Symposium on Distributed Computing and Applications to Business,Engineering and Science(DCABES 2013)(第十二届分布式计算及其应用国际学术研讨会)

作者： Kew Lee Ming Norhashidah Hj.Mohd.Ali School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia

In this paper,the parallel implementation of a new explicit group iterative scheme is proposed for the solution of a three dimensional second order telegraph partial differential *** explicit group(EG)method is derived from the standard centered seven-point finite difference discretisation *** utilize the domain decomposition technique on this group scheme to divide the tasks involved in solving the *** aim of this study is to describe the development of the parallel group iterative scheme under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multiplecore *** experiments are conducted together with their detailed performance *** results will be reported and discussed.

关键词： Telegraph equation explicit group method domain decomposition algorithm parallelization multiple-core OpenMP

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THE ASPECTS OF MATHEMATICAL MODELLING OF WEIGHT-BEARING HUMAN JOINTS 6

THE ASPECTS OF MATHEMATICAL MODELLING OF WEIGHT-BEARING HUMA...

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6th International Conference on APLIMAT

作者： Danek, Josef Univ W Bohemia Dept Math Plzen 30614 Czech Republic

ISBN: (纸本)9788096956241

The aim of this paper is to show procedure of mathematical modelling of weight-bearing human joints and numerical simulation of mechanical processes taking place during static loadening. It is important to know stress and deformation distributions in lower limb for example for application of the total knee or the total hip replacements. Afinite element approximation and domain decomposition method are used.

关键词： Biomechanics joint joint replacement unilateral contact problem finite element method domain decomposition algorithm

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抛物型方程的一种高精度区域分解有限差分算法

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高等学校计算数学学报 2009年第2期31卷 109-118页

作者：王婷芮洪兴中国科学院软件研究所并行计算实验室山东大学数学学院

引言近年来,区域分解算法以可以将大型问题分解为一系列小型问题以减少计算规模及算法可高度并行实现等特点受到了人们的广泛关注。前人也做了很多很好的工作:参考文献[1]中***等人提出了显-隐格式的区域分解算法,在时间层不分层的内边... 详细信息

引言近年来,区域分解算法以可以将大型问题分解为一系列小型问题以减少计算规模及算法可高度并行实现等特点受到了人们的广泛关注。前人也做了很多很好的工作:参考文献[1]中***等人提出了显-隐格式的区域分解算法,在时间层不分层的内边界点采用大步长向前-中心差分显格式及在内点采用古典隐格式,取得的精度为O（△t+h;+H;）。参考文献[2]中给出了[1]中区域分解算法对于内边界点为等距分布的多子区域时的新的误差估计,使含H;误差项的系数比[1]中缩小了一倍。还将采用大步长H的Saul’yev的非对称差分格式应用于内边界点,并给出了两个子区域和多个子区域情形下差分解的

关键词： parabolic equation domain decomposition algorithm finite difference high-order accuracy parallel efficiency.

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