Electronic Transactions on Numerical Analysis最新文献_第2页

Optimized surface parameterizations with applications to Chinese virtual broadcasting 优化表面参数化及其在中文虚拟广播中的应用

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2020-01-01 DOI: 10.1553/etna_vol53s383

M. Yueh, H. Huang, Tie-xiang Li, Wen-Wei Lin, S. Yau

引用次数: 4

Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions 具有动力学边界条件的半线性声波方程的有限元离散化

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2020-01-01 DOI: 10.1553/ETNA_VOL53S522

M. Hochbruck, Jan Leibold

引用次数: 9

A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations 混合公式中热方程空时域分解的后验停止准则

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2018-06-18 DOI: 10.1553/ETNA_VOL49S151

S. Hassan, C. Japhet, M. Vohralík

{"title":"A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations","authors":"S. Hassan, C. Japhet, M. Vohralík","doi":"10.1553/ETNA_VOL49S151","DOIUrl":"https://doi.org/10.1553/ETNA_VOL49S151","url":null,"abstract":"We propose and analyse a posteriori estimates for global-in-time, nonoverlapping domain decomposition methods for heterogeneous and anisotropic porous media diffusion problems. We consider mixed formulations, with a lowest-order Raviart–Thomas–Nedelec discretization, often used for such problems. Optimized Robin transmission conditions are employed on the space-time interface between subdomains, and different time grids are used to adapt to different time scales in the subdomains. Our estimators allow to distinguish the spatial discretization, the temporal discretization, and the domain decomposition error components. We design an adaptive space-time domain decomposition algorithm, wherein the iterations are stopped when the domain decomposition error does not affect significantly the global error. Thus, a guaranteed bound on the overall error is obtained on each iteration of the space-time domain decomposition algorithm, and simultaneously important savings in terms of the number of domain decomposition iterations can be achieved. Numerical results for two-dimensional problems with strong heterogeneities and local time stepping are presented to illustrate the performance of our adaptive domain decomposition algorithm.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Asymptotic consistent exponential-type integrators for Klein-Gordon-Schrödinger systems from relativistic to non-relativistic regimes 从相对论到非相对论的Klein-Gordon-Schrödinger系统的渐近一致指数型积分器

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2018-03-26 DOI: 10.1553/ETNA_VOL48S63

Simon Baumstark, Georgia Kokkala, Katharina Schratz

引用次数: 5

Varying the s in Your s-step GMRES 改变你的s步GMRES中的s

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2018-01-01 DOI: 10.1553/ETNA_VOL47S206

David Imberti, J. Erhel

引用次数: 0

On generalized iterated Tikhonov regularization with operator-dependent seminorms 算子相关半模的广义迭代Tikhonov正则化

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2018-01-01 DOI: 10.1553/ETNA_VOL47S73

D. Bianchi, M. Donatelli

引用次数: 14

Low-Rank Solvers for Fractional Differential Equations 分数阶微分方程的低秩解

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2016-01-01 DOI: 10.17617/2.2270973

T. Breiten, V. Simoncini, M. Stoll

引用次数: 47

A MATRIX-FREE LEGENDRE SPECTRAL METHOD FOR INITIAL-BOUNDARY VALUE PROBLEMS 初边值问题的无矩阵Legendre谱法

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2016-01-01 DOI: 10.15496/PUBLIKATION-27275

Bernd Brumm, Emil Kieri

{"title":"A MATRIX-FREE LEGENDRE SPECTRAL METHOD FOR INITIAL-BOUNDARY VALUE PROBLEMS","authors":"Bernd Brumm, Emil Kieri","doi":"10.15496/PUBLIKATION-27275","DOIUrl":"https://doi.org/10.15496/PUBLIKATION-27275","url":null,"abstract":"We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrodinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable.The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67154485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations 大型Lyapunov和Sylvester方程的自生成和有效移位参数的ADI方法

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2014-01-01 DOI: 10.17617/2.2071065

P. Benner, P. Kürschner, J. Saak

{"title":"Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations","authors":"P. Benner, P. Kürschner, J. Saak","doi":"10.17617/2.2071065","DOIUrl":"https://doi.org/10.17617/2.2071065","url":null,"abstract":"Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well estab- lished methods for the numerical solution of large-scale Sylvester and Lyapunov equations. Probably the biggest disadvantage of these methods is their dependence on a set of shift parameters that are crucial for fast convergence. Here we firstly review existing shift generation strategies that compute a number of shifts before the actual itera- tion. These approaches come with several disadvantages such as, e.g., expensive numerical computations and the difficulty to obtain necessary spectral information or data n eeded to initially setup their generation. Secondly, we propose two novel shift selection strategies with the motivation to resolve these issues at least partially. Both ap- proaches generate shifts automatically in the course of the ADI iterations. Extensive numerical tests show that one of these new approaches, based on a Galerkin projection onto the space spanned by the current ADI data, is superior to other approaches in the majority of cases both in terms of convergence speed and required execution time.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67654632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 73

Rational Interpolation Methods for Symmetric Sylvester Equations 对称Sylvester方程的有理插值方法

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2014-01-01 DOI: 10.17617/2.2060858

P. Benner, T. Breiten

引用次数: 3