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 ...
详细信息
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.
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 hig...
详细信息
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'.
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 m...
详细信息
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.
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 ...
详细信息
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.
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 a...
详细信息
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.
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 au...
详细信息
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.
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 a...
详细信息
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.
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 ...
详细信息
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.
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 receive...
详细信息
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).
Current laboratory prediction systems in nephrology face challenges such as handling non-stationary datasets, limited accuracy, and insufficient personalization. To address these issues, this study introduces three ma...
详细信息
Current laboratory prediction systems in nephrology face challenges such as handling non-stationary datasets, limited accuracy, and insufficient personalization. To address these issues, this study introduces three machine learning-based models: the Adaptive Predictive Model for Laboratory Results with Patient-specific Adaptation (APMLR), the Adaptive Input-Output Model for eGFR Prediction based on Other Results (AIOM), and the Intelligent Assessment Model for Renal Function (IAMRF). These models leverage advanced algorithms to improve the accuracy and reliability of predictions for critical parameters such as eGFR, creatinine, and urea levels. The APMLR system achieved superior performance with Linear SVR, reaching a prediction accuracy of up to 96.97%, while Gradient Boosting emerged as the most effective method for both AIOM and IAMRF systems (approx. 95%). These findings highlight the potential of machine learning to enhance nephrology patient care by automating diagnoses, improving operational workflows, and setting anew standard for renal function assessment in clinical practice.
暂无评论