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American Control Conference (ACC)

作者： Xu, Bolun Korpas, Magnus Botterud, Audun O'Sullivan, Francis MIT Cambridge MA 02139 USA Norwegian Univ Sci & Technol Trondheim Norway

ISBN: (纸本)9781538682661

This paper presents a millisecond-level look-ahead control algorithm for energy storage. The algorithm connects the optimal control with the Lagrangian multiplier associated with the state-of-charge constraint. It is compared to solving look-ahead control using a state-of-the-art convex optimization solver. The paper include discussions on sufficient conditions for including the non-convex simultaneous charging and discharging constraint, and provide upper and lower bounds for the primal and dual results under such conditions. Simulation results show that both methods obtain the same control result, while the proposed algorithm runs up to 100,000 times faster and solves most problems within one millisecond. The theoretical results from developing this algorithm also provide key insights into designing optimal energy storage control schemes at the centralized system level as well as under distributed settings.

关键词： Energy systems numerical algorithm Predictive control for nonlinear systems

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Air Quality Dispersion Modeling in Spherical Coordinates 2nd

Air Quality Dispersion Modeling in Spherical Coordinates

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2nd International Conference on Advanced Technologies for Societal Applications (Techno-Societal)

作者： Rayshanov, Normakhmad Akhmedov, Dilshot Tashkent Univ Informat Technol Tashkent Uzbekistan

ISBN: (纸本)9783030169626;9783030169619

The paper deals with the development of a mathematical model of aerosol fine particles transport and diffusion in the atmosphere in spherical coordinates. This approach allows us to shorten the calculation time and increase the order of approximation with respect to spatial variables. For the numerical solution of the problem, a computational algorithm based on the “straight-line method” was proposed. This algorithm allows us to reduce the multidimensional problem in the form of a partial differential equation to an ordinary differential equation with the corresponding initial and boundary conditions. Based on the developed mathematical support, the main parameters that significantly influenced the process of transporting aerosol fine particles, as well as the rate of their deposition, were investigated. The obtained results can be successfully used as software in the optimal allocation of newly designed facilities in industrial regions, as well as to assess the scale and geography of emissions spread to the environment, to estimate the concentration of harmful substances in the atmosphere and on the underlying surface with subsequent decision making to minimize ecological risks.

关键词： Mathematical model numerical algorithm Transport and diffusion Harmful substances Atmosphere Hydromechanics

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Generating Families of Practical Fast Matrix Multiplication algorithms 31

Generating Families of Practical Fast Matrix Multiplication ...

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31st IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Huang, Jianyu Rice, Leslie Matthews, Devin A. van de Geijnt, Robert A. Univ Texas Austin Dept Comp Sci Austin TX 78712 USA Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA

ISBN: (纸本)9781538639146

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due to the increased cost of memory movement, which is particularly noticeable for non-square matrices. Such implementations also require considerable workspace and modifications to the standard BLAS interface. We propose a code generator framework to automatically implement a large family of FMM algorithms suitable for multiplications of arbitrary matrix sizes and shapes. By representing FMM with a triple of matrices [U, V, W] that capture the linear combinations of submatrices that are formed, we can use the Kronecker product to define a multi-level representation of Strassen-like algorithms. Incorporating the matrix additions that must be performed for Strassen-like algorithms into the inherent packing and micro-kernel operations inside GEMM avoids extra workspace and reduces the cost of memory movement. Adopting the same loop structures as high-performance GEMM implementations allows parallelization of all FMM algorithms with simple but efficient data parallelism without the overhead of task parallelism. We present a simple performance model for general FMM algorithms and compare actual performance of 20+ FMM algorithms to modeled predictions. Our implementations demonstrate a performance benefit over conventional GEMM on single core and multi-core systems. This study shows that Strassen-like fast matrix multiplication can be incorporated into libraries for practical use.

关键词： BLAS fast matrix multiplication GEMM linear algebra library numerical algorithm performance model Strassen

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On the maximization of a certain nondifferentiable function

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Journal of Optimization Theory and Applications 1971年第2期7卷 75-89页

作者： Demyanov, V.F. Computing Center University of Leningrad Leningrad Russia

Let us consider a function {Mathematical expression} where the functions fij(z) are supposed to be continuously differentiable and real-valued on a set Ω of En, z∂En. The problem is to find maxze{open}Ωφ{symbol}(z)... 详细信息

Let us consider a function {Mathematical expression} where the functions f_ij(z) are supposed to be continuously differentiable and real-valued on a set Ω of E_n, z∂E_n. The problem is to find max_{ze{open}Ωφ{symbol}}(z). In this paper, it is proved that φ{symbol}(z) is directionally differentiable. A necessary condition for a maximum is derived, and some numerical algorithms for maximizing φ{symbol} are suggested. The results obtained can be applied for solving some problems in mathematical programming and control theory. © 1971 Plenum Publishing Corporation.

关键词： Control Theory Mathematical Programming numerical algorithm Nondifferentiable Function

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algorithm Study for Supersonic Steam Injection Process Simulation of The Pressurizer Relief Tank 10

Algorithm Study for Supersonic Steam Injection Process Simul...

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10th IEEE International Conference on Software Engineering and Service Science (ICSESS)

作者： Wang, Yi Guo, Xiao-Wei Li, Chao Chcn, Lijuan Zhao, Ran Yang, Canqun Natl Univ Def Technol Coll Comp Changsha 410073 Peoples R China

ISBN: (纸本)9781728109459

Simulating the steam Injection process of pressurized decompression tanks is a challenging engineering problem due to the large amount of computational resource requirements and its complex physical model. This study is a necessary algorithmic study to perform a 3D numerical simulation from the PRT (Pressurizer Relief Tank) to the transient dumping process in a chamber containing a tank. Parallel simulation was performed by the open source CFD tool OpenFOAM based on the numerical algorithm we discussed. The results show that the simulation results are in accordance with the basic physical laws, and the results reflect the pressure and temperature of the entire pressure relief tank in detail, which can provide guidance for the safe design of the reactor coolant system.

关键词： pressurizer relief tank steam Injection process OpenFOAM numerical algorithm

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A nonparametric method for term structure fitting with automatic smoothing

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APPLIED ECONOMICS 2016年第58期48卷 5654-5666页

作者： Kaushanskiy, Vadim Lapshin, Victor Natl Res Univ Higher Sch Econ Moscow Russia

We present a nonparametric method for fitting the term structure of interest rates from bond prices. Our method is a variant of the smoothing spline approach, but within our framework we are able to determine the smoothing coefficient automatically from data using the generalized cross-validation or maximum likelihood estimates. We present an effective numerical algorithm to simultaneously find the term structure and the optimal smoothing coefficient. Finally, we compare the proposed nonparametric fitting method with other parametric and nonparametric methods to find its superior performance. We find that existing term structure fitting methods perform well in liquid markets while illiquid markets present new challenges, which we address in this article.

关键词： Term structure of interest rates automatic smoothing numerical algorithm illiquid bond markets E43 C14

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CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions 17

CPA Lyapunov Functions: Switched Systems vs. Differential In...

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17th International Conference on Informatics in Control, Automation and Robotics (ICINCO)

作者： Hafstein, Sigurdur Univ Iceland Sci Inst Dunhagi 5 IS-107 Reykjavik Iceland Univ Iceland Fac Phys Sci Dunhagi 5 IS-107 Reykjavik Iceland

ISBN: (纸本)9789897584428

We present an algorithm that uses linear programming to parameterize continuous and piecewise affine Lyapunov functions for switched systems. The novel feature of the algorithm is, that it can compute Lyapunov functions for switched system with a strongly asymptotically stable equilibrium, for which the equilibrium of the corresponding differential inclusion is merely weakly asymptotically stable. For the differential inclusion no such Lyapunov function exists. This is achieved by removing constraints from a linear programming problem of an earlier algorithm to compute Lyapunov functions, that are not necessary to assert strong stability for the switched system. We demonstrate the benefits of this new algorithm sing Artstein's circles as an example.

关键词： Lyapunov Function Switched Systems Differential Inclusions numerical algorithm Artstein's Circles

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Multipole Expansion of the Fundamental Solution of a Fractional Degree of the Laplace Operator

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Journal of Mathematical Sciences (United States) 2023年第5期275卷 548-555页

作者： Belevtsov, N.S. Lukashchuk, S. Yu. Ufa State Aviation Technical University Ufa Russian Federation

A multipole expansion of the fundamental solution of the fractional power of the Laplace operator is constructed in terms of the Gegenbauer polynomials. Based on the decomposition constructed and the idea of the fast multipole method, we propose a numerical algorithm for solving the fractional differential generalization of the Poisson equation in the two-dimensional and three-dimensional spaces. © 2023, Springer Nature Switzerland AG.

关键词： 35J08 35J08 35R11 35R11 fast multipole method fractional Laplacian fundamental solution multipole expansion numerical algorithm

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Highly accurate calculation of radial spheroidal functions

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Computational Mathematics and Mathematical Physics 2006年第6期46卷 949-954页

作者： Abramov, A.A. Kurochkin, S.V. Dorodnicyn Computing Center Russian Academy of Sciences Moscow 119991 ul. Vavilova 40 Russian Federation

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters. © MAIK "Nauka/ Interperiodica" (Russia), 2006.

关键词： Eigenvalue problem numerical algorithm numerical stability Radial spheroidal functions Recurrences

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Cholesky Factorization on Heterogeneous CPU and GPU Systems 9

Cholesky Factorization on Heterogeneous CPU and GPU Systems

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9th International Conference on Frontier of Computer Science and Technology

作者： Chen, Jieyang Chen, Zizhong Univ Calif Riverside Dept Comp Sci Riverside CA 92521 USA

ISBN: (纸本)9781467392952

General-purpose graphics processing units (GPGPUs) could bring huge performance improvements in scientific and numerical fields. We presented two approaches utilizing hybrid CPU/GPU system in Cholesky factorization. First, we analyzed the implementation of Cholesky factorization in MAGMA and identified the bottleneck of the current implementation, which is the use of fixed block size without considering any factors in the computing environment. So, we designed an algorithm, which could determine the optimal block size of Cholesky factorization based on multiple factors (input matrix size, CPU/GPU performance, and CPU/GPU bandwidth, etc.). Then, we presented a new improvement on MAGMA's implementation utilize the algorithm. Test results showed that our approach is more efficient than MAGMA's fixed block size implementation under some circumstance. After combining our implementation with MAGMA's implementation, the new hybrid implementation could outperform the current MAGMA implementation. Second, we identified that all the implementations of Cholesky factorization, to our best knowledge, that utilized the GPU do not fully utilized the multicore CPU. So, after studied other researchers approaches, we designed a new algorithm that could utilize multicore CPU and GPU simultaneously in Cholesky factorization. Our approach could keep the block size and workload distribution between CPU and GPU dynamically. Testing results showed the optimal data distribution ratio for our current implementation.

关键词： numerical algorithm Parallel algorithm Multicore GPU Cholesky Factorization

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