ACM Transactions on Mathematical Software (TOMS)最新文献_第4页

Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes 多边形和多面体单元网格上任意阶有限元自由度映射的构造

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-02-23 DOI: 10.1145/3524456

Matthew W. Scroggs, Jørgen S. Dokken, C. Richardson, G. N. Wells

{"title":"Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes","authors":"Matthew W. Scroggs, Jørgen S. Dokken, C. Richardson, G. N. Wells","doi":"10.1145/3524456","DOIUrl":"https://doi.org/10.1145/3524456","url":null,"abstract":"We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and, in the case of hexahedral cells, not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including arbitrary degree Lagrange, serendipity, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in open-source libraries.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"32 1","pages":"1 - 23"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87908668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 54

Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines 算法1020:多次tchbycheffian b样条的计算

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-01-31 DOI: 10.1145/3478686

H. Speleers

引用次数: 6

Robust level-3 BLAS Inverse Iteration from the Hessenberg Matrix 基于Hessenberg矩阵的鲁棒3级BLAS逆迭代

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-01-13 DOI: 10.1145/3544789

A. Schwarz

引用次数: 0

H2Pack

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-15 DOI: 10.1145/3412850

Hua Huang, Xin Xing, Edmond Chow

{"title":"H2Pack","authors":"Hua Huang, Xin Xing, Edmond Chow","doi":"10.1145/3412850","DOIUrl":"https://doi.org/10.1145/3412850","url":null,"abstract":"Dense kernel matrices represented in H2 matrix format typically require less storage and have faster matrix-vector multiplications than when these matrices are represented in the standard dense format. In this article, we present H2Pack, a high-performance, shared-memory library for constructing and operating with H2 matrix representations for kernel matrices defined by non-oscillatory, translationally invariant kernel functions. Using a hybrid analytic-algebraic compression method called the proxy point method, H2Pack can efficiently construct an H2 matrix representation with linear computational complexity. Storage and matrix-vector multiplication also have linear complexity. H2Pack also introduces the concept of “partially admissible blocks” for H2 matrices to make H2 matrix-vector multiplication mathematically identical to the fast multipole method (FMM) if analytic expansions are used. We optimize H2Pack from both the algorithm and software perspectives. Compared to existing FMM libraries, H2Pack generally has much faster H2 matrix-vector multiplications, since the proxy point method is more effective at producing block low-rank approximations than the analytic methods used in FMM. As a tradeoff, H2 matrix construction in H2Pack is typically more expensive than the setup cost in FMM libraries. Thus, H2Pack is ideal for applications that need a large number of matrix-vector multiplications for a given configuration of data points.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"5 1","pages":"1 - 29"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74250654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Strengths and Limitations of Stretching for Least-squares Problems with Some Dense Rows 具有密集行的最小二乘问题的拉伸的优点和局限性

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-06 DOI: 10.1145/3412559

J. Scott, M. Tuma

引用次数: 6

Algorithm 1013 算法1013

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-06 DOI: 10.1145/3421316

Daisy Arroyo, X. Emery

{"title":"Algorithm 1013","authors":"Daisy Arroyo, X. Emery","doi":"10.1145/3421316","DOIUrl":"https://doi.org/10.1145/3421316","url":null,"abstract":"A continuous spectral algorithm and computer routines in the R programming environment that enable the simulation of second-order stationary and intrinsic (i.e., with second-order stationary increments or generalized increments) vector Gaussian random fields in Euclidean spaces are presented. The simulation is obtained by computing a weighted sum of cosine and sine waves, with weights that depend on the matrix-valued spectral density associated with the spatial correlation structure of the random field to simulate. The computational cost is proportional to the number of locations targeted for simulation, below that of sequential, matrix decomposition and discrete spectral algorithms. Also, the implementation is versatile, as there is no restriction on the number of vector components, workspace dimension, number and geometrical configuration of the target locations. The computer routines are illustrated with synthetic examples and statistical testing is proposed to check the normality of the distribution of the simulated random field or of its generalized increments. A by-product of this work is a spectral representation of spherical, cubic, penta, Askey, J-Bessel, Cauchy, Laguerre, hypergeometric, iterated exponential, gamma, and stable covariance models in the d-dimensional Euclidean space.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"44 1","pages":"1 - 25"},"PeriodicalIF":0.0,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90171710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

An Enhancement of the Bisection Method Average Performance Preserving Minmax Optimality 一种保持最小最大最优性的对分法平均性能的改进

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-06 DOI: 10.1145/3423597

I. F. D. Oliveira, R. Takahashi

{"title":"An Enhancement of the Bisection Method Average Performance Preserving Minmax Optimality","authors":"I. F. D. Oliveira, R. Takahashi","doi":"10.1145/3423597","DOIUrl":"https://doi.org/10.1145/3423597","url":null,"abstract":"We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also pinpoint one specific method within the class and show that under mild initial conditions it can attain an order of convergence of up to 1.618, i.e., the same as the secant method. Hence, we attain both an improved average performance and an improved order of convergence with no cost on the minmax optimality of the bisection method. Numerical experiments show that, on regular functions, the proposed method requires a number of function evaluations similar to current state-of-the-art methods, about 24% to 37% of the evaluations required by the bisection procedure. In problems with non-regular functions, the proposed method performs significantly better than the state-of-the-art, requiring on average 82% of the total evaluations required for the bisection method, while the other methods were outperformed by bisection. In the worst case, while current state-of-the-art commercial solvers required two to three times the number of function evaluations of bisection, our proposed method remained within the minmax bounds of the bisection method.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"29 1","pages":"1 - 24"},"PeriodicalIF":0.0,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79317303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 19

GetFEM

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-06 DOI: 10.1145/3412849

Y. Renard, K. Poulios

引用次数: 9

Algorithm 1014 算法1014

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-12-06 DOI: 10.1145/3428446

C. F. Borges

引用次数: 0

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers 在SUNDIALS非线性和微分/代数方程求解器套件中实现新的灵活性

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-11-19 DOI: 10.1145/3539801

D. J. Gardner, D. Reynolds, C. Woodward, C. Balos

引用次数: 1526