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ETNA - Electronic Transactions on Numerical Analysis最新文献

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Additive Schwarz preconditioners for the obstacle problem of clamped Kirchhoff plates 夹紧基尔霍夫板障碍问题的加性Schwarz预调节器
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2018-09-17 DOI: 10.1553/etna_vol49s274
S. C. Brenner, C. B. Davis, L. Sung
{"title":"Additive Schwarz preconditioners for the obstacle problem of clamped Kirchhoff plates","authors":"S. C. Brenner, C. B. Davis, L. Sung","doi":"10.1553/etna_vol49s274","DOIUrl":"https://doi.org/10.1553/etna_vol49s274","url":null,"abstract":"When the obstacle problem of clamped Kirchhoff plates is discretized by a partition of unity method, the resulting discrete variational inequalities can be solved by a primal-dual active set algorithm. In this paper we develop and analyze additive Schwarz preconditioners for the systems that appear in each iteration of the primal-dual active set algorithm. Numerical results that corroborate the theoretical estimates are also presented.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132034229","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
Transformed rank-1 lattices for high-dimensional approximation 变换秩1格用于高维近似
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2018-05-23 DOI: 10.1553/etna_vol53s239
Robert Nasdala, D. Potts
{"title":"Transformed rank-1 lattices for high-dimensional approximation","authors":"Robert Nasdala, D. Potts","doi":"10.1553/etna_vol53s239","DOIUrl":"https://doi.org/10.1553/etna_vol53s239","url":null,"abstract":"This paper describes an extension of Fourier approximation methods for multivariate functions defined on the torus $mathbb{T}^d$ to functions in a weighted Hilbert space $L_{2}(mathbb{R}^d, omega)$ via a multivariate change of variables $psi:left(-frac{1}{2},frac{1}{2}right)^dtomathbb{R}^d$. We establish sufficient conditions on $psi$ and $omega$ such that the composition of a function in such a weighted Hilbert space with $psi$ yields a function in the Sobolev space $H_{mathrm{mix}}^{m}(mathbb{T}^d)$ of functions on the torus with mixed smoothness of natural order $m in mathbb{N}_{0}$. In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials on the torus $mathbb{T}^d$ based on single and multiple reconstructing rank-$1$ lattices. Since in applications it may be difficult to choose a related function space, we make use of dimension incremental construction methods for sparse frequency sets. Various numerical tests confirm obtained theoretical results for the transformed methods.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124053885","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
A randomized multivariate matrix pencil method for superresolution microscopy 超分辨显微镜的随机多元矩阵铅笔法
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2018-05-07 DOI: 10.1553/ETNA_VOL51S63
M. Ehler, Stefan Kunis, T. Peter, C. Richter
{"title":"A randomized multivariate matrix pencil method for superresolution microscopy","authors":"M. Ehler, Stefan Kunis, T. Peter, C. Richter","doi":"10.1553/ETNA_VOL51S63","DOIUrl":"https://doi.org/10.1553/ETNA_VOL51S63","url":null,"abstract":"The matrix pencil method is an eigenvalue based approach for the parameter identification of sparse exponential sums. We derive a reconstruction algorithm for multivariate exponential sums that is based on simultaneous diagonalization. Randomization is used and quantified to reduce the simultaneous diagonalization to the eigendecomposition of a single random matrix. To verify feasibility, the algorithm is applied to synthetic and experimental fluorescence microscopy data.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126618720","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: 11
Flip-flop spectrum-revealing QR factorization and its applications to singular value decomposition 触发器揭示谱的QR分解及其在奇异值分解中的应用
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2018-03-06 DOI: 10.1553/ETNA_VOL51S469
Yuehua Feng, Jianwei Xiao, M. Gu
{"title":"Flip-flop spectrum-revealing QR factorization and its applications to singular value decomposition","authors":"Yuehua Feng, Jianwei Xiao, M. Gu","doi":"10.1553/ETNA_VOL51S469","DOIUrl":"https://doi.org/10.1553/ETNA_VOL51S469","url":null,"abstract":"We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to initialize a partial column pivoted QR factorization and then compute a partial LQ factorization. As observed by Stewart in his original QLP work, Flip-Flop SRQR tracks the exact singular values with \"considerable fidelity\". We develop singular value lower bounds and residual error upper bounds for Flip-Flop SRQR factorization. In situations where singular values of the input matrix decay relatively quickly, the low-rank approximation computed by SRQR is guaranteed to be as accurate as truncated SVD. We also perform a complexity analysis to show that for the same accuracy, Flip-Flop SRQR is faster than randomized subspace iteration for approximating the SVD, the standard method used in Matlab tensor toolbox. We also compare Flip-Flop SRQR with alternatives on two applications, tensor approximation and nuclear norm minimization, to demonstrate its efficiency and effectiveness.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115093363","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 unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid 弹性膜与不可压缩流体相互作用问题的无条件稳定半隐式CutFEM
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2018-01-17 DOI: 10.1553/ETNA_VOL54S296
Kyle G. Dunn, R. Lui, M. Sarkis
{"title":"An unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid","authors":"Kyle G. Dunn, R. Lui, M. Sarkis","doi":"10.1553/ETNA_VOL54S296","DOIUrl":"https://doi.org/10.1553/ETNA_VOL54S296","url":null,"abstract":"In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points representing this membrane move with the local fluid velocity. We design and implement a high-accuracy cut finite element method (CutFEM) which enables the use of a structured mesh that is not aligned with the immersed membrane and then we formulate a time discretization that yields an unconditionally energy stable scheme. We prove that the stability is not restricted by the parameter choices that constrained previous finite element immersed boundary methods and illustrate the theoretical results with numerical simulations.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115964093","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: 0
Efficient cubature rules 高效培养规则
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2017-12-20 DOI: 10.1553/etna_vol51s219
J. V. Zandt
{"title":"Efficient cubature rules","authors":"J. V. Zandt","doi":"10.1553/etna_vol51s219","DOIUrl":"https://doi.org/10.1553/etna_vol51s219","url":null,"abstract":"73 new cubature rules are found for three standard multidimensional integrals with spherically symmetric regions and weights, using direct search with a numerical zero-finder. All but four of the new rules have fewer integration points than known rules of the same degree, and twenty are within three points of M{\"o}ller's lower bound. Most have all positive coefficients and most have some symmetry, including some supported by one or two concentric spheres. They include degree 7 formulas for integration over the sphere and Gaussian-weighted integrals over all space, each in 6 and 7 dimensions, with 127 and 183 points, respectively.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129146518","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: 4
Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology 心脏电生理僵硬问题的高阶Rush-Larsen时间步进方法
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2017-07-06 DOI: 10.1553/etna_vol52s342
Y. Coudière, C. D. Lontsi, C. Pierre, Yvescoudì Ere, Charlie Douanla-Lontsi
{"title":"Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology","authors":"Y. Coudière, C. D. Lontsi, C. Pierre, Yvescoudì Ere, Charlie Douanla-Lontsi","doi":"10.1553/etna_vol52s342","DOIUrl":"https://doi.org/10.1553/etna_vol52s342","url":null,"abstract":"The development of efficient solvers in cardiac electrophysiology requires high order (semi) explicit and stable time stepping methods. In this paper are introduced two new exponential integrators of orders 3 and 4. They generalize the order 2 Rush Larsen scheme derived by Perego and Veneziani [24] in 2009. They have been named Rush Larsen of order k, shortly RL k. The RL k schemes are explicit exponential multistep integrators. They display a simple general formulation and an easy implementation. The RL k schemes are shown to be stable under perturbation (or 0-stable) and con-vergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in cardiac electrophysiology.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121113112","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
Modified Filon-Clenshaw-Curtis rules for oscillatory integrals with a nonlinear oscillator 非线性振子振荡积分的修正Filon-Clenshaw-Curtis规则
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2016-04-18 DOI: 10.1553/ETNA_VOL54S276
H. Majidian
{"title":"Modified Filon-Clenshaw-Curtis rules for oscillatory integrals with a nonlinear oscillator","authors":"H. Majidian","doi":"10.1553/ETNA_VOL54S276","DOIUrl":"https://doi.org/10.1553/ETNA_VOL54S276","url":null,"abstract":"Filon-Clenshaw-Curtis rules are among rapid and accurate quadrature rules for computing highly oscillatory integrals. In the implementation of the Filon-Clenshaw-Curtis rules in the case when the oscillator function is not linear, its inverse should be evaluated at some points. In this paper, we solve this problem by introducing an approach based on the interpolation, which leads to a class of modifications of the original Filon-Clenshaw-Curtis rules. In the absence of stationary points, two kinds of modified Filon-Clenshaw-Curtis rules are introduced. For each kind, an error estimate is given theoretically, and then illustrated by some numerical experiments. Also, some numerical experiments are carried out for a comparison of the accuracy and the efficiency of the two rules. In the presence of stationary points, the idea is applied to the composite Filon-Clenshaw-Curtis rules on graded meshes. An error estimate is given theoretically, and then illustrated by some numerical experiments.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"31 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126125392","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
On the composite discontinuous Galerkin method for simulations of electric properties of semiconductor devices 半导体器件电性能模拟的复合不连续伽辽金法
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 2016-03-03 DOI: 10.1553/etna_vol51s75
K. Sakowski, L. Marcinkowski, P. Strak, P. Kempisty, S. Krukowski
{"title":"On the composite discontinuous Galerkin method for simulations of electric properties of semiconductor devices","authors":"K. Sakowski, L. Marcinkowski, P. Strak, P. Kempisty, S. Krukowski","doi":"10.1553/etna_vol51s75","DOIUrl":"https://doi.org/10.1553/etna_vol51s75","url":null,"abstract":"In this paper, a variant of discretization of the van Roosbroeck equations in the equilibrium state with the Composite Discontinuous Galerkin Method for the rectangular domain is discussed. It is based on Symmetric Interior Penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution on the interfaces of devices' layers. It is shown that the discrete problem is well-defined and that discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129903535","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
Revisiting aggregation-based multigrid for edge elements 重访基于聚合的多网格边缘元素
ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL51S118
Artem Napov, R. Perrussel
{"title":"Revisiting aggregation-based multigrid for edge elements","authors":"Artem Napov, R. Perrussel","doi":"10.1553/ETNA_VOL51S118","DOIUrl":"https://doi.org/10.1553/ETNA_VOL51S118","url":null,"abstract":"We consider a modification of the Reitzinger-Schoberl algebraic multigrid method for the iterative solution of the curl-curl boundary value problem discretized with edge elements. The Reitzinger-Schoberl method is attractive for its low memory requirements and moderate cost per iteration, but the number of iterations typically tends to increase with the problem size. Here we propose several modifications to the method that aim at curing the size-dependent convergence behavior without significantly affecting the attractive features of the original method. The comparison with an auxiliary space preconditioner, a state-of-the-art solver for the considered problems, further indicates that both methods typically require a comparable amount of work to solve a given discretized problem but that the proposed approach requires less memory.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"127 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":"115642448","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
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