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Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization 基于改进离散边界型形状梯度的pde约束形状优化
SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/21m1457400
W. Gong, Jiajie Li, Shengfeng Zhu
{"title":"Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization","authors":"W. Gong, Jiajie Li, Shengfeng Zhu","doi":"10.1137/21m1457400","DOIUrl":"https://doi.org/10.1137/21m1457400","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91453903","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
A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations 基于小波的非局部算子方程仿真与最优控制方法
SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/20m1350790
S. Dahlke, H. Harbrecht, T. Surowiec
{"title":"A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations","authors":"S. Dahlke, H. Harbrecht, T. Surowiec","doi":"10.1137/20m1350790","DOIUrl":"https://doi.org/10.1137/20m1350790","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90446743","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
BDDC Deluxe Algorithms for Two-Dimensional H($curl$) Isogeometric Analysis 二维H($curl$)等几何分析的BDDC高级算法
SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/21m1438839
O. Widlund, S. Scacchi, L. Pavarino
{"title":"BDDC Deluxe Algorithms for Two-Dimensional H($curl$) Isogeometric Analysis","authors":"O. Widlund, S. Scacchi, L. Pavarino","doi":"10.1137/21m1438839","DOIUrl":"https://doi.org/10.1137/21m1438839","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73363566","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: 2
Piecewise-Global Nonlinear Model Order Reduction for PDE-Constrained Optimization in High-Dimensional Parameter Spaces 高维参数空间中pde约束优化的分段全局非线性模型降阶
SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/21m1435343
Gabriele Boncoraglio, C. Farhat
{"title":"Piecewise-Global Nonlinear Model Order Reduction for PDE-Constrained Optimization in High-Dimensional Parameter Spaces","authors":"Gabriele Boncoraglio, C. Farhat","doi":"10.1137/21m1435343","DOIUrl":"https://doi.org/10.1137/21m1435343","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79793453","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: 2
Linearly Implicit Invariant-Preserving Decoupled Difference Scheme For The Rotation-Two-Component Camassa-Holm System 旋转-双分量Camassa-Holm系统的线性隐式不变解耦差分格式
SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/21m1452020
Qifeng Zhang, Lingling Liu, Zhimin Zhang
{"title":"Linearly Implicit Invariant-Preserving Decoupled Difference Scheme For The Rotation-Two-Component Camassa-Holm System","authors":"Qifeng Zhang, Lingling Liu, Zhimin Zhang","doi":"10.1137/21m1452020","DOIUrl":"https://doi.org/10.1137/21m1452020","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81320037","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: 2
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions 快速扩展到磁盘上的谐波:具有快速径向旋转的可操纵基础
SIAM J. Sci. Comput. Pub Date : 2022-07-27 DOI: 10.48550/arXiv.2207.13674
Nicholas F. Marshall, Oscar Mickelin, A. Singer
{"title":"Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions","authors":"Nicholas F. Marshall, Oscar Mickelin, A. Singer","doi":"10.48550/arXiv.2207.13674","DOIUrl":"https://doi.org/10.48550/arXiv.2207.13674","url":null,"abstract":"We present a fast and numerically accurate method for expanding digitized $L times L$ images representing functions on $[-1,1]^2$ supported on the disk ${x in mathbb{R}^2 : |x|<1}$ in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we refer to as the Fast Disk Harmonics Transform (FDHT), runs in $O(L^2 log L)$ operations. This basis is also known as the Fourier-Bessel basis, and it has several computational advantages: it is orthogonal, ordered by frequency, and steerable in the sense that images expanded in the basis can be rotated by applying a diagonal transform to the coefficients. Moreover, we show that convolution with radial functions can also be efficiently computed by applying a diagonal transform to the coefficients.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90718936","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
Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes 非结构网格输运模拟的欧拉-拉格朗日龙格-库塔不连续伽辽金方法
SIAM J. Sci. Comput. Pub Date : 2022-07-26 DOI: 10.1137/21m1456753
Xiaofeng Cai, Jing-Mei Qiu
{"title":"Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes","authors":"Xiaofeng Cai, Jing-Mei Qiu","doi":"10.1137/21m1456753","DOIUrl":"https://doi.org/10.1137/21m1456753","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75739700","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
Proper Orthogonal Decomposition-Lattice Boltzmann Method: Simulating the Air Pollutant Problem in Street Canyon Areas 适当正交分解-晶格玻尔兹曼方法:模拟街道峡谷地区空气污染问题
SIAM J. Sci. Comput. Pub Date : 2022-07-26 DOI: 10.1137/21m1405733
Reza MohammadiArani, M. Dehghan, Mostafa Abbaszadeh
{"title":"Proper Orthogonal Decomposition-Lattice Boltzmann Method: Simulating the Air Pollutant Problem in Street Canyon Areas","authors":"Reza MohammadiArani, M. Dehghan, Mostafa Abbaszadeh","doi":"10.1137/21m1405733","DOIUrl":"https://doi.org/10.1137/21m1405733","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79345844","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
Stochastic rounding variance and probabilistic bounds: A new approach 随机舍入方差和概率界:一种新方法
SIAM J. Sci. Comput. Pub Date : 2022-07-21 DOI: 10.48550/arXiv.2207.10321
E. E. Arar, D. Sohier, P. D. O. Castro, E. Petit
{"title":"Stochastic rounding variance and probabilistic bounds: A new approach","authors":"E. E. Arar, D. Sohier, P. D. O. Castro, E. Petit","doi":"10.48550/arXiv.2207.10321","DOIUrl":"https://doi.org/10.48550/arXiv.2207.10321","url":null,"abstract":"Stochastic rounding (SR) offers an alternative to the deterministic IEEE-754 floating-point rounding modes. In some applications such as PDEs, ODEs and neural networks, SR empirically improves the numerical behavior and convergence to accurate solutions while no sound theoretical background has been provided. Recent works by Ipsen, Zhou, Higham, and Mary have computed SR probabilistic error bounds for basic linear algebra kernels. For example, the inner product SR probabilistic bound of the forward error is proportional to $sqrt$ nu instead of nu for the default rounding mode. To compute the bounds, these works show that the errors accumulated in computation form a martingale. This paper proposes an alternative framework to characterize SR errors based on the computation of the variance. We pinpoint common error patterns in numerical algorithms and propose a lemma that bounds their variance. For each probability and through Bienaym{'e}-Chebyshev inequality, this bound leads to better probabilistic error bound in several situations. Our method has the advantage of providing a tight probabilistic bound for all algorithms fitting our model. We show how the method can be applied to give SR error bounds for the inner product and Horner polynomial evaluation.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85732749","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
PLSS: A Projected Linear Systems Solver PLSS:一个投影线性系统求解器
SIAM J. Sci. Comput. Pub Date : 2022-07-15 DOI: 10.48550/arXiv.2207.07615
J. Brust, M. Saunders
{"title":"PLSS: A Projected Linear Systems Solver","authors":"J. Brust, M. Saunders","doi":"10.48550/arXiv.2207.07615","DOIUrl":"https://doi.org/10.48550/arXiv.2207.07615","url":null,"abstract":"We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but even the smaller systems can be costly. We develop a process that appends one column to the sketching matrix each iteration and converges in a finite number of iterations whether the sketch is random or deterministic. In general, our process generates orthogonal updates to the approximate solution xk. By choosing the sketch to be the set of all previous residuals, we obtain a simple recursive update and convergence in at most rank(A) iterations (in exact arithmetic). By choosing a sequence of identity columns for the sketch, we develop a generalization of the Kaczmarz method. In experiments on large sparse systems, our method (PLSS) with residual sketches is competitive with LSQR and LSMR, and with residual and identity sketches compares favorably with state-of-the-art randomized methods.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89821924","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
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