Math. Comput. Model.最新文献_第3页

A distribution function from population genetics statistics using Stirling numbers of the first kind: Asymptotics, inversion and numerical evaluation 用第一类斯特林数的群体遗传统计分布函数:渐近、反演和数值计算

Math. Comput. Model. Pub Date : 2021-10-29 DOI: 10.1090/mcom/3711

S. Chen, N. Temme

引用次数: 0

Greenberg's conjecture for real quadratic fields and the cyclotomic Z2-extensions 实二次场的Greenberg猜想及分环z2扩展

Math. Comput. Model. Pub Date : 2021-10-28 DOI: 10.1090/mcom/3712

L. Pagani

引用次数: 5

Improved computation of fundamental domains for arithmetic Fuchsian groups 改进了算术Fuchsian群基本域的计算

Math. Comput. Model. Pub Date : 2021-10-21 DOI: 10.1090/mcom/3777

James Rickards

引用次数: 2

How well-conditioned can the eigenvector problem be? 特征向量问题的条件有多好?

Math. Comput. Model. Pub Date : 2021-10-21 DOI: 10.1090/mcom/3706

Carlos Beltrán, Laurent Bétermin, P. Grabner, S. Steinerberger

引用次数: 1

Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation Cahn-Hilliard方程隐显法的稳定性和收敛性分析

Math. Comput. Model. Pub Date : 2021-09-30 DOI: 10.1090/mcom/3704

Dong Li, Chaoyu Quan, T. Tang

引用次数: 11

The equilateral small octagon of maximal width 最大宽度的等边小八边形

Math. Comput. Model. Pub Date : 2021-09-30 DOI: 10.1090/mcom/3733

Christian Bingane, Charles Audet

引用次数: 4

Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate 逐层构建随机秩1格规则，实现了几乎最优的随机错误率

Math. Comput. Model. Pub Date : 2021-09-23 DOI: 10.1090/mcom/3769

J. Dick, T. Goda, Kosuke Suzuki

{"title":"Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate","authors":"J. Dick, T. Goda, Kosuke Suzuki","doi":"10.1090/mcom/3769","DOIUrl":"https://doi.org/10.1090/mcom/3769","url":null,"abstract":"We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ullrich (2019) shows that rank-1 lattice rules with a randomly chosen number of points and good generating vector achieve almost the optimal order of the randomized error in weighted Korobov spaces, and moreover, that the error is bounded independently of the dimension if the weight parameters, $gamma_j$, satisfy the summability condition $sum_{j=1}^{infty}gamma_j^{1/alpha}<infty$, where $alpha$ is a smoothness parameter. The argument is based on the existence result that at least half of the possible generating vectors yield almost the optimal order of the worst-case error in the same function spaces. In this paper we provide a component-by-component construction algorithm of such randomized rank-1 lattice rules, without any need to check whether the constructed generating vectors satisfy a desired worst-case error bound. Similarly to the above-mentioned work, we prove that our algorithm achieves almost the optimal order of the randomized error and that the error bound is independent of the dimension if the same condition $sum_{j=1}^{infty}gamma_j^{1/alpha}<infty$ holds. We also provide analogous results for tent-transformed lattice rules for weighted half-period cosine spaces and for polynomial lattice rules in weighted Walsh spaces, respectively.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"2005 1","pages":"2771-2801"},"PeriodicalIF":0.0,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88362704","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: 6

Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids 隐构非牛顿流体非等温流动的有限元逼近与预处理

Math. Comput. Model. Pub Date : 2021-09-23 DOI: 10.1090/mcom/3703

P. Farrell, P. A. Gazca-Orozco, E. Süli

引用次数: 7

A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence 不可压缩Navier-Stokes方程的不连续Galerkin压力校正格式:稳定性和收敛性

Math. Comput. Model. Pub Date : 2021-09-22 DOI: 10.1090/mcom/3731

R. Masri, Chen Liu, B. Rivière

{"title":"A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence","authors":"R. Masri, Chen Liu, B. Rivière","doi":"10.1090/mcom/3731","DOIUrl":"https://doi.org/10.1090/mcom/3731","url":null,"abstract":"The numerical simulation of the incompressible Navier-Stokes equations presents a challenging computational task primarily because of two reasons: (a) the coupling of the velocity and pressure by the incompressibility constraint and (b) the nonlinearity of the convection term [14, 18]. The development of splitting schemes aims to overcome these difficulties by decoupling the nonlinearity in the convection term from the pressure term. For an overview of such methods, we refer to the works of Glowinski [15] and of Guermond, Minev, and Shen [18]. In this paper, we will focus on pressure correction schemes. The basic idea of a non-incremental pressure correction scheme in time was first proposed by Chorin and Temam [5, 28]. This scheme was subsequently modified by several mathematicians leading to two major variations: (1) the incremental scheme where a previous value of the pressure gradient is added [16,30] and (2) the rotational scheme where the non-physical boundary condition for the pressure is corrected by using the rotational form of the Laplacian [29]. The main contribution of our work is the theoretical analysis of a discontinuous Galerkin (dG) discretization of the pressure correction approach. We derive stability and a priori error bounds on a family of regular meshes. The discrete velocities are approximated by discontinuous piecewise polynomials of degree k1 and the discrete potential and pressure by polynomials of degree k2. Stability of the solutions is obtained under the constraint k1−1 ≤ k2 ≤ k1+1 whereas the convergence of the scheme is obtained for the case k2 = k1 − 1 because of approximation properties. The proofs are technical and rely on several tools including special lift operators. The semi-discrete error analysis of pressure correction schemes has been extensively studied, see for example the work by Shen and Guermond [21, 27]. The use","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"56 1","pages":"1625-1654"},"PeriodicalIF":0.0,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80458661","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: 10

Spanning the isogeny class of a power of an elliptic curve 张成椭圆曲线幂次的等根类

Math. Comput. Model. Pub Date : 2021-09-16 DOI: 10.1090/MCOM/3672

M. Kirschmer, Fabien Narbonne, C. Ritzenthaler, Damien Robert

引用次数: 7