SIAM J. Sci. Comput.最新文献_第7页

A Parallel Iterative Probabilistic Method for Mixed Problems of Laplace Equations with the Feynman-Kac Formula of Killed Brownian Motions 具有非布朗运动Feynman-Kac公式的拉普拉斯方程混合问题的并行迭代概率方法

SIAM J. Sci. Comput. Pub Date : 2022-10-01 DOI: 10.1137/22m1478458

Cuiyang Ding, Changhao Yan, Xuan Zeng, W. Cai

引用次数: 2

Well-Balanced and Positivity-Preserving Surface Reconstruction Schemes Solving Ripa Systems With Nonflat Bottom Topography 求解具有非平坦底地形的Ripa系统的平衡和保正曲面重建方案

SIAM J. Sci. Comput. Pub Date : 2022-09-26 DOI: 10.1137/21m1450823

Jian Dong, Xu Qian

引用次数: 0

Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations 半线性抛物型方程的有效指数积分有限元法

SIAM J. Sci. Comput. Pub Date : 2022-09-24 DOI: 10.48550/arXiv.2209.11922

Jianguo Huang, L. Ju, Y. Xu

引用次数: 1

SuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured Matrices SuperDC:提高秩结构矩阵稳定性的超快速分治特征值分解

SIAM J. Sci. Comput. Pub Date : 2022-09-22 DOI: 10.1137/21m1438633

Xiaofeng Ou, J. Xia

{"title":"SuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured Matrices","authors":"Xiaofeng Ou, J. Xia","doi":"10.1137/21m1438633","DOIUrl":"https://doi.org/10.1137/21m1438633","url":null,"abstract":". For dense symmetric matrices with small oﬀ-diagonal (numerical) ranks and in a 5 hierarchically semiseparable form, we give a divide-and-conquer eigendecomposition method with 6 nearly linear complexity (called SuperDC) that signiﬁcantly improves an earlier basic algorithm in 7 [Vogel, Xia, et al., SIAM J. Sci. Comput., 38 (2016)]. Some stability risks in the original algorithm are 8 analyzed, including potential exponential norm growth, cancellations, loss of accuracy with clustered 9 eigenvalues or intermediate eigenvalues, etc. In the dividing stage, we give a new structured low-rank 10 updating strategy with balancing that eliminates the exponential norm growth and also minimizes 11 the ranks of low-rank updates. In the conquering stage with low-rank updated eigenvalue solution, 12 the original algorithm directly uses the standard fast multipole method (FMM) to accelerate function 13 evaluations, which has the risks of cancellation, division by zero, and slow convergence. Here, we 14 design a triangular FMM to avoid cancellation. Furthermore, when there are clustered intermediate 15 eigenvalues, we design a novel local shifting strategy to integrate FMM accelerations into the solution 16 of shifted secular equations. This helps achieve both the eﬃciency and the reliability. We also provide 17 a deﬂation strategy with a user-supplied tolerance and give a precise description of the structure of 18 the resulting eigenvector matrix. The SuperDC eigensolver has signiﬁcantly improved stability while 19 keeping the nearly linear complexity for ﬁnding the entire eigenvalue decomposition. Extensive 20 numerical tests are used to show the eﬃciency and accuracy of SuperDC.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90059527","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 fast front-tracking approach and its analysis for a temporal multiscale flow problem with a fractional-order boundary growth 具有分数阶边界增长的时间多尺度流动问题的快速前沿跟踪方法及其分析

SIAM J. Sci. Comput. Pub Date : 2022-09-19 DOI: 10.48550/arXiv.2209.09038

Zhaoyang Wang, P. Lin, Lei Zhang

{"title":"A fast front-tracking approach and its analysis for a temporal multiscale flow problem with a fractional-order boundary growth","authors":"Zhaoyang Wang, P. Lin, Lei Zhang","doi":"10.48550/arXiv.2209.09038","DOIUrl":"https://doi.org/10.48550/arXiv.2209.09038","url":null,"abstract":"This paper is concerned with a blood flow problem coupled with a slow plaque growth at the artery wall. In the model, the micro (fast) system is the Navier-Stokes equation with a periodically applied force and the macro (slow) system is a fractional reaction equation, which is used to describe the plaque growth with memory effect. We construct an auxiliary temporal periodic problem and an effective time-average equation to approximate the original problem and analyze the approximation error of the corresponding linearized PDE (Stokes) system, where the simple front-tracking technique is used to update the slow moving boundary. An effective multiscale method is then designed based on the approximate problem and the front tracking framework. We also present a temporal finite difference scheme with a spatial continuous finite element method and analyze its temporal discrete error. Furthermore, a fast iterative procedure is designed to find the initial value of the temporal periodic problem and its convergence is analyzed as well. Our designed front-tracking framework and the iterative procedure for solving the temporal periodic problem make it easy to implement the multiscale method on existing PDE solving software. The numerical method is implemented by a combination of the finite element platform COMSOL Multiphysics and the mainstream software MATLAB, which significantly reduce the programming effort and easily handle the fluid-structure interaction, especially moving boundaries with more complex geometries. We present some numerical examples of ODEs and 2-D Navier-Stokes system to demonstrate the effectiveness of the multiscale method. Finally, we have a numerical experiment on the plaque growth problem and discuss the physical implication of the fractional order parameter.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84223858","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

Numerical Solutions of Quasilinear Parabolic Problems by a Continuous Space-Time Finite Element Scheme 拟线性抛物型问题的连续时空有限元格式数值解

SIAM J. Sci. Comput. Pub Date : 2022-09-15 DOI: 10.1137/21m1403722

I. Toulopoulos

引用次数: 2

Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method 用奇异分裂深里兹方法求解奇异源椭圆型问题

SIAM J. Sci. Comput. Pub Date : 2022-09-07 DOI: 10.48550/arXiv.2209.02931

Tianhao Hu, Bangti Jin, Zhi Zhou

{"title":"Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method","authors":"Tianhao Hu, Bangti Jin, Zhi Zhou","doi":"10.48550/arXiv.2209.02931","DOIUrl":"https://doi.org/10.48550/arXiv.2209.02931","url":null,"abstract":"In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems covers general point sources, line sources and the combination of point-line sources, and has a broad range of practical applications. The proposed approach is based on decomposing the true solution into a singular part that is known analytically using the fundamental solution of the Laplace equation and a regular part that satisfies a suitable modified elliptic PDE with a smoother source, and then solving for the regular part using the deep Ritz method. A path-following strategy is suggested to select the penalty parameter for enforcing the Dirichlet boundary condition. Extensive numerical experiments in two- and multi-dimensional spaces with point sources, line sources or their combinations are presented to illustrate the efficiency of the proposed approach, and a comparative study with several existing approaches based on neural networks is also given, which shows clearly its competitiveness for the specific class of problems. In addition, we briefly discuss the error analysis of the approach.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89457152","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

Strongly imposing the free surface boundary condition for wave equations with finite difference operators 对具有有限差分算子的波动方程强施加自由表面边界条件

SIAM J. Sci. Comput. Pub Date : 2022-09-01 DOI: 10.48550/arXiv.2209.00713

Longfei Gao

{"title":"Strongly imposing the free surface boundary condition for wave equations with finite difference operators","authors":"Longfei Gao","doi":"10.48550/arXiv.2209.00713","DOIUrl":"https://doi.org/10.48550/arXiv.2209.00713","url":null,"abstract":"Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive structural evaluation, etc. Finite difference methods remain popular choices for these simulations due to their simplicity and efficiency. In particular, the family of finite difference methods based on the summation-by-parts operators and the simultaneous-approximation-terms technique have been proposed for these simulations, which offers great flexibility in addressing boundary and interface conditions. For the applications mentioned above, surface of the earth is usually associated with the free surface boundary condition. In this study, we demonstrate that the weakly imposed free surface boundary condition through the simultaneous-approximation-terms technique can have issue when the source terms, which introduces abrupt disturbances to the wave field, are placed too close to the surface. In response, we propose to build the free surface boundary condition into the summation-by-parts finite difference operators and hence strongly and automatically impose the free surface boundary condition to address this issue. The procedure is very simple for acoustic wave equation, requiring resetting a few rows and columns in the existing difference operators only. For the elastic wave equation, the procedure is more involved and requires special design of the grid layout and summation-by-parts operators that satisfy additional requirements, as revealed by the discrete energy analysis. In both cases, the energy conserving property is preserved. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85003687","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

Efficient Color Image Segmentation via Quaternion-based L1/L2 Regularization 基于四元数L1/L2正则化的高效彩色图像分割

SIAM J. Sci. Comput. Pub Date : 2022-08-22 DOI: 10.1007/s10915-022-01970-0

Tingting Wu, Zhihui Mao, Zeyu Li, Yonghua Zeng, T. Zeng

引用次数: 6

The Short-Term Rational Lanczos Method and Applications 短期理性Lanczos方法及其应用

SIAM J. Sci. Comput. Pub Date : 2022-08-01 DOI: 10.1137/21m1403254

D. Palitta, S. Pozza, Valeria Simoncini

引用次数: 0