ETNA - Electronic Transactions on Numerical Analysis最新文献_第5页

A block Toeplitz preconditioner for all-at-once systems from linear wave equations 线性波动方程一次性系统的块Toeplitz预条件

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s177

S. Hon, S. Serra-Capizzano

{"title":"A block Toeplitz preconditioner for all-at-once systems from linear wave equations","authors":"S. Hon, S. Serra-Capizzano","doi":"10.1553/etna_vol58s177","DOIUrl":"https://doi.org/10.1553/etna_vol58s177","url":null,"abstract":". In this work, we propose a novel parallel-in-time preconditioner for an all-at-once system, arising from the numerical solution of linear wave equations. Namely, our main result concerns a block tridiagonal Toeplitz preconditioner that can be diagonalized via fast sine transforms, whose effectiveness is theoretically shown for the nonsymmetric block Toeplitz system resulting from discretizing the concerned wave equation. Our approach is to ﬁrst transform the original linear system into a symmetric one and subsequently develop the desired preconditioning strategy based on the spectral symbol of the modiﬁed matrix. Various Krylov subspace methods are considered. That is, we show that the minimal polynomial of the preconditioned matrix is of low degree, which leads to fast convergence when the generalized minimal residual method is used. To fully utilize the symmetry of the modiﬁed matrix, we additionally construct an absolute-value preconditioner which is symmetric positive deﬁnite. Then, we show that the eigenvalues of the preconditioned matrix are clustered around ± 1 , which gives a convergence guarantee when the minimal residual method is employed. Numerical examples are given to support the effectiveness of our preconditioner. Our block Toeplitz preconditioner provides an alternative to the existing block circulant preconditioner proposed by McDonald, Pestana, and Wathen in [SIAM J. Sci. Comput., 40 (2018), pp. A1012–A1033], advancing the symmetrization preconditioning theory that originated from the same work.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115244648","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: 3

${}_{delta}^{gamma}!mathbf{Phi}$-type inclusion set for eigenvalues of a tensor ${}_{delta}^{gamma}!mathbf{Phi}$张量特征值的型包含集

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol51s262

Xiaoqiang Lei

引用次数: 0

The bisection eigenvalue method for unitary Hessenberg matrices via their quasiseparable structure 基于准可分结构的幺正Hessenberg矩阵的二分本征值方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol59s60

Y. Eidelman, I. Haimovici

引用次数: 0

A numerical method for solving systems of hypersingular integro-differential equations 求解超奇异积分-微分方程组的数值方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s378

M. C. De Bonis, A. Mennouni, D. Occorsio

引用次数: 1

Preconditioned gradient iterations for the eigenproblem of definite matrix pairs 定矩阵对特征问题的预条件梯度迭代

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol51s331

Marija Miloloza Pandur

{"title":"Preconditioned gradient iterations for the eigenproblem of definite matrix pairs","authors":"Marija Miloloza Pandur","doi":"10.1553/etna_vol51s331","DOIUrl":"https://doi.org/10.1553/etna_vol51s331","url":null,"abstract":"Preconditioned gradient iterations for large and sparse Hermitian generalized eigenvalue problems Ax = λBx, with positive definite B, are efficient methods for computing a few extremal eigenpairs. In this paper we give a unifying framework of preconditioned gradient iterations for definite generalized eigenvalue problems with indefinite B. More precisely, these iterations compute a few eigenvalues closest to the definiteness interval, which can be in the middle of the spectrum, and the corresponding eigenvectors of definite matrix pairs (A,B), that is, pairs having a positive definite linear combination. Sharp convergence theorems for the simplest variants are given. This framework includes an indefinite locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm derived by Kressner, Miloloža Pandur, and Shao [Numer. Algorithms, 66 (2014), pp. 681–703]. We also give a generic algorithm for constructing new “indefinite extensions” of standard (with positive definite B) eigensolvers. Numerical experiments demonstrate the use of our algorithm for solving a product and a hyperbolic quadratic eigenvalue problem. With excellent preconditioners, the indefinite variant of LOBPCG is the most efficient method. Finally, we derive some ideas on how to use our indefinite eigensolver to compute a few eigenvalues around any spectral gap and the corresponding eigenvectors of definite matrix pairs.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133431607","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: 3

A combined finite element and machine learning approach for the prediction of specific cutting forces and maximum tool temperatures in machining 一种结合有限元和机器学习的方法，用于预测加工中的特定切削力和最高刀具温度

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol56s66

Sai Manish Reddy Mekarthy, M. Hashemitaheri, H. Cherukuri

引用次数: 0

Additive Schwarz preconditioners for a localized orthogonal decomposition method 加性Schwarz预调节器的局部正交分解方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL54S234

S. C. Brenner, J. C. Garay, L. Sung

引用次数: 6

A time-stepping finite element method for a time-fractional partial differential equation of hidden-memory space-time variable order 隐记忆时空变阶时间分数阶偏微分方程的时间步进有限元法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s652

Xiangcheng Zheng, Hong Wang

引用次数: 1

Adaptive Multilevel Krylov Methods 自适应多级Krylov方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol51s512

René Kehl, R. Nabben, D. Szyld

引用次数: 4

Robust BDDC algorithms for finite volume element methods 有限体积元鲁棒BDDC算法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s66

Ya Su, Xuemin Tu, Yingxiang Xu

引用次数: 0