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numerical algorithms for solutions of large eigenvalue problems in piezoelectric resonators.

INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 1996年第6期39卷 909-922页

作者： Yong, YK Cho, Y Department of Civil and Environmental Engineering Rutgers University P.O. Box 909 Piscataway NJ 08855-0909 U.S.A.

Two algorithms for eigenvalue problems in piezoelectric finite element analyses are introduced. The first algorithm involves the use of Lanczos method with a new matrix storage scheme, while the second algorithm uses a Rayleigh quotient iteration scheme. In both solution methods, schemes are implemented to reduce storage requirements and solution time. Both solution methods also seek to preserve the sparsity structure of the stiffness matrix to realize major savings in memory. In the Lanczos method with the new storage scheme, the bandwidth of the stiffness matrix is optimized by mixing the electrical degree of freedom with the mechanical degrees of freedom. The unique structural pattern of the consistent mass matrix is exploited to reduce storage requirements. These major reductions in memory requirements for both the;stiffness and mass matrices also provided large savings in computational time. In the Rayleigh quotient iteration method, an algorithm for generating good initial eigenpairs is employed to improve its overall convergence rate, and its convergence stability in the regions of closely spaced eigenvalues and repeated eigenvalues. The initial eigenvectors are obtained by interpolation from a coarse mesh. In order for this multi-mesh iterative method to be effective, an eigenvector of interest in the fine mesh must resemble an eigenvector in the coarse mesh. Hence, the method is effective for finding the set of eigenpairs in the low-frequency range, while the Lanczos method with a-mixed electromechanical matrix can be used for any frequency range. Results of example problems are presented to show the savings in solution time and storage requirements of the proposed algorithms when compared with the existing algorithms in the literature.

关键词： piezoelectric resonators numerical algorithms large scale eigenvalue problems

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numerical algorithms for high-performance computational science

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2020年第2166期378卷 20190066-20190066页

作者： Dongarra, Jack Grigori, Laura Higham, Nicholas J. Univ Tennessee ICL Knoxville TN USA Oak Ridge Natl Lab Oak Ridge TN USA Univ Manchester Dept Math Manchester M13 9PL Lancs England Univ Paris Sorbonne Univ CNRS AlpinesInria ParisLab Jacques Louis Lions F-75012 Paris France

A number of features of today's high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies;the high cost of data movement;use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous;and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue 'numerical algorithms for high-performance computational science'.

关键词： numerical algorithms numerical linear algebra rounding errors floating-point arithmetic high-performance computing exascale computer

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Reliability Model for Load-Sharing k-out-of-n System and its numerical algorithms 11

Reliability Model for Load-Sharing k-out-of-n System and its...

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11th International Conference on Reliability, Maintainability and Safety (ICRMS) - Integrating Big Data, Improving Reliability & Serving Personalization

作者： Cai, Mingxi Zhao, Guangyan Sun, Yufeng BeiHang Univ Sch Reliabil & Syst Engn Beijing Peoples R China

ISBN: (纸本)9781509027149

Dependent failure is a difficult problem, which is not easily solved by traditional reliability models. With an increase in system complexity, dependent failure becomes more and more common. So a special reliability model is needed to describe this kind of problem. A load-sharing system is a typical dependent system. The merits of reliability block diagrams (RBD) include simplicity, intuition and ease of use. This paper builds an extendable RBD model to describe k-out-of-n load-sharing systems. A mathematical reliability model is also set up. A mathematical model with exponential and other distributions is discussed. Then the general mathematic description of the model is provided. On this basis, numerical algorithms for the model are studied. The improved GAUSS quadrature method is then adopted to solve the problem of multiple indefinite integral calculations, solving the general model. Finally, a typical case is used for verifying the correctness and veracity of the model and its algorithms.

关键词： load-sharing system reliability model numerical algorithms

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Diffraction effects, scattering effects, analytical problems, numerical algorithms and program packages 5

Diffraction effects, scattering effects, analytical problems...

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5th Congress on Modern Optics

作者： Sreckovic, M Ostojic, S Mircevski, J Bundaleski, N Univ Belgrade Fac Elect Engn YU-11001 Belgrade Yugoslavia

ISBN: (纸本)0819430382

Diffraction problems in analytical treatments and numeric have been constant topics for a very long time and there are a lot of different analytical expressions as well as numerical algorithms. The modern approaches are concentrated in the area of particle sizing, fibber optical sizing and loss evaluation in laser physics and techniques. Some problems between the fibber optics dimensioning and particles of cylindrical shape dimensioning are chosen and based on literature;some ameliorations in numerical approaches are made. The evolved expressions can be used for different laser wavelengths, different dimensions of disturbance objects tin scattering and diffraction phenomena) as well as different indices of refractions where the particles tin a very general way) are stratified. Some existing programs for scattering are discussed and the new computer architecture is presented here.

关键词： diffraction scattering laser computer simulation Bessel functions numerical algorithms

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HighPerMeshes - A Domain-Specific Language for numerical algorithms on Unstructured Grids

HighPerMeshes - A Domain-Specific Language for Numerical Alg...

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26th International Conference on Parallel and Distributed Computing (Euro-Par)

作者： Alhaddad, Samer Foerstner, Jens Groth, Stefan Gruenewald, Daniel Grynko, Yevgen Hannig, Frank Kenter, Tobias Pfreundt, Franz-Josef Plessl, Christian Schotte, Merlind Steinke, Thomas Teich, Juergen Weiser, Martin Wende, Florian Paderborn Univ Paderborn Ctr Parallel Comp Paderborn Germany Paderborn Univ Dept Comp Sci Paderborn Germany Paderborn Univ Dept Elect Engn Paderborn Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Hardware Software Codesign Dept Comp Sci Erlangen Germany Fraunhofer Inst Techno & Wirtschaftsmath Kaiserslautern Germany Zuse Inst Berlin Berlin Germany

ISBN: (纸本)9783030715939;9783030715922

Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPerMeshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell's equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.

关键词： Domain-specific language numerical algorithms Unstructured grids Parallel computing

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Mutant Accuracy Testing for Assessing the Implementation of numerical algorithms 12th

Mutant Accuracy Testing for Assessing the Implementation of ...

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12th International Workshop on numerical Software Verification (NSV)

作者： Wu, Ruining (Ray) Mitchell, Ian M. Univ British Columbia Dept Comp Sci Vancouver BC Canada Univ Toronto Dept Comp Sci Toronto ON Canada

ISBN: (纸本)9783030284237;9783030284220

Despite their widespread use, implementations of numerical computing algorithms are generally tested manually with fuzzily defined thresholds determining success or failure. Modern software testing methods, such as automated regression testing, are difficult to apply because both test oracles and algorithm output are approximate. Based on the observation that high accuracy numerical algorithms appear to be fragile by design to errors in their parameters, we propose to compare the error of target implementations to mutated versions of themselves with the expectation that the mutants will suffer degraded accuracy. We test the idea on Matlab implementations of some basic numerical algorithms, and find that most mutants are worse while the few which are better show a distinctive pattern of mutation.

关键词： Mutation testing numerical algorithms Oracle problem Hypothesis testing

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numerical computation algorithms for sequential checkpoint placement

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PERFORMANCE EVALUATION 2009年第6期66卷 311-326页

作者： Ozaki, Tatsuya Dohi, Tadashi Kaio, Naoto Hiroshima Univ Dept Informat Engn Higashihiroshima 7398527 Japan Hiroshima Shudo Univ Dept Econ Informat Asaminami Ku Hiroshima 7313195 Japan

This paper concerns sequential checkpoint placement problems under two dependability measures: steady-state system availability and expected reward per unit time in the steady state. We develop numerical computation algorithms to determine the optimal checkpoint sequence, based on the classical Brender's fixed point algorithm and further give three simple approximation methods. numerical examples with the Weibull failure time distribution are devoted to illustrate quantitatively the overestimation and underestimation of the sub-optimal checkpoint sequences based on the approximation methods. (C) 2008 Elsevier B.V. All rights reserved.

关键词： File systems Checkpointing Sequential checkpoints Availability Expected reward numerical algorithms

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The HighPerMeshes framework for numerical algorithms on unstructured grids

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2022年第14期34卷 e6616-e6616页

作者： Alhaddad, Samer Foerstner, Jens Groth, Stefan Gruenewald, Daniel Grynko, Yevgen Hannig, Frank Kenter, Tobias Pfreundt, Franz-Josef Plessl, Christian Schotte, Merlind Steinke, Thomas Teich, Jurgen Weiser, Martin Wende, Florian Paderborn Univ Paderborn Ctr Parallel Comp Paderborn Germany Paderborn Univ Dept Comp Sci Paderborn Germany Paderborn Univ Dept Elect Engn Paderborn Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Hardware Software Codesign Dept Comp Sci Erlangen Germany Fraunhofer Inst Techno & Wirtschaftsmath Kaiserslautern Germany Zuse Inst Berlin Germany

Solving partial differential equations (PDEs) on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HighPerMeshes C++-embedded domain-specific language (DSL) that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPerMeshes DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HighPerMeshes code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems.

关键词： code generation distributed computing domain-specific languages numerical algorithms

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Performance Comparison of numerical Optimization algorithms for RSS-TOA-Based Target Localization 97

Performance Comparison of Numerical Optimization Algorithms ...

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97th IEEE Vehicular Technology Conference (VTC-Spring)

作者： Lee, Halim Seo, Jiwon Yonsei Univ Sch Integrated Technol Incheon South Korea

ISBN: (纸本)9798350311143

In the literature, a hyper-enhanced local positioning system (HELPS) was developed to locate a target mobile device in an emergency. HELPS finds the target mobile device (i.e., emergency caller) using multiple receivers (i.e., signal measurement equipment of first responders) that measure the received signal strength (RSS) and time of arrival (TOA) of the long-term evolution (LTE) uplink signal from the target mobile device. The maximum likelihood (ML) estimator can be applied to localize a target mobile device using the RSS and TOA. However, the ML estimator for the RSS-TOA-based target localization problem is nonconvex and nonlinear, having no analytical solution. Therefore, the ML estimator should be solved numerically, unless it is relaxed into a convex or linear form. This study investigates the target localization performance and computational complexity of numerical methods for solving an ML estimator. The three widely used numerical methods are: grid search, gradient descent, and particle swarm optimization. In the experimental evaluation, the grid search yielded the lowest target localization root-mean-squared error;however, the 95th percentile error of the grid search was larger than those of the other two algorithms. The average code computation time of the grid search was extremely large compared with those of the other two algorithms, and gradient descent exhibited the lowest computation time. HELPS can select numerical algorithms by considering their constraints (e.g., the computational resources of the localization server or target accuracy).

关键词： Target Localization numerical algorithms Emergency Response E911 Positioning

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Coupling fluid plasma and kinetic neutral models using correlated Monte Carlo methods

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NUCLEAR MATERIALS AND ENERGY 2025年 42卷

作者： Parker, G. J. Umansky, M. V. Dudson, B. D. Stanford Univ Dept Math Stanford CA 94305 USA Lawrence Livermore Natl Lab Livermore CA 94550 USA

boundary plasmas present-day generally regime, species boundary often require kinetic models due to long mean-free-paths compared to characteristic spatial scales in the region. Monte-Carlo (MC) methods provide a complete, high-fidelity approach to solving kinetic models, and must be coupled to fluid plasma models to simulate the full plasma-neutrals system. The statistical nature of MC methods, however, prevents the convergence of coupled fluid-kinetic simulations to an exact self-consistent steady-state. Moreover, this forces the use of explicit methods that can suffer from numerical errors and require huge computational resources. Correlated Monte-Carlo (CMC) methods are expected to alleviate these issues but have historically enjoyed only mixed success. Here, a fully implicit method for coupled plasma-neutral systems is demonstrated in 1D using the UEDGE plasma code and a homemade CMC code. In particular, it is shown that ensuring the CMC method is a differentiable function of the background plasma is sufficient to employ a Jacobian-Free Newton-Krylov solver for implicit time steps. The convergence of the implicit coupling method is explored and compared with explicit coupling and uncorrelated methods. It is shown that ensuring differentiability by controlling random seeds in the MC is sufficient to achieve convergence, and that the use of implicit time-stepping methods has the potential for improved stability and runtimes over explicit coupling methods.

关键词： Fusion Boundary plasma numerical algorithms Monte-Carlo methods

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