Comput. Math. Appl.最新文献_第4页

Unconditional energy stability and temporal convergence of first-order numerical scheme for the square phase-field crystal model 方相场晶体模型一阶数值格式的无条件能量稳定性和时间收敛性

Comput. Math. Appl. Pub Date : 2023-01-01 DOI: 10.2139/ssrn.4359797

Guomei Zhao, Shuaifei Hu, P. Zhu

引用次数: 0

Hankel tensor-based model and $$L_1$$-Tucker decomposition-based frequency recovery method for harmonic retrieval problem 基于Hankel张量模型和$$L_1$$ -Tucker分解的频率恢复方法求解谐波恢复问题

Comput. Math. Appl. Pub Date : 2022-12-19 DOI: 10.1007/s40314-022-02151-3

Zhenting Luan, Zhenyu Ming, Yuchi Wu, Wei Han, Xiang Chen, Bo Bai, Liping Zhang

引用次数: 1

Operator inference with roll outs for learning reduced models from scarce and low-quality data 从稀缺和低质量的数据中学习简化模型的算子推理

Comput. Math. Appl. Pub Date : 2022-12-02 DOI: 10.48550/arXiv.2212.01418

W. I. Uy, D. Hartmann, B. Peherstorfer

引用次数: 4

A simplified lattice Boltzmann implementation of the quasi-static approximation in pipe flows under the presence of non-uniform magnetic fields 非均匀磁场作用下管道流动准静态近似的简化晶格玻尔兹曼实现

Comput. Math. Appl. Pub Date : 2022-11-17 DOI: 10.2139/ssrn.4368194

Hugo S. Tavares, B. Magacho, L. Moriconi, J. Loureiro

{"title":"A simplified lattice Boltzmann implementation of the quasi-static approximation in pipe flows under the presence of non-uniform magnetic fields","authors":"Hugo S. Tavares, B. Magacho, L. Moriconi, J. Loureiro","doi":"10.2139/ssrn.4368194","DOIUrl":"https://doi.org/10.2139/ssrn.4368194","url":null,"abstract":"We propose a single-step simplified lattice Boltzmann algorithm capable of performing magnetohydrodynamic (MHD) flow simulations in pipes for very small values of magnetic Reynolds numbers $R_m$. In some previous works, most lattice Boltzmann simulations are performed with values of $R_m$ close to the Reynolds numbers for flows in simplified rectangular geometries. One of the reasons is the limitation of some traditional lattice Boltzmann algorithms in dealing with situations involving very small magnetic diffusion time scales associated with most industrial applications in MHD, which require the use of the so-called quasi-static (QS) approximation. Another reason is related to the significant dependence that many boundary conditions methods for lattice Boltzmann have on the relaxation time parameter. In this work, to overcome the mentioned limitations, we introduce an improved simplified algorithm for velocity and magnetic fields which is able to directly solve the equations of the QS approximation, among other systems, without preconditioning procedures. In these algorithms, the effects of solid insulating boundaries are included by using an improved explicit immersed boundary algorithm, whose accuracy is not affected by the values of $R_m$. Some validations with classic benchmarks and the analysis of the energy balance in examples including uniform and non-uniform magnetic fields are shown in this work. Furthermore, a progressive transition between the scenario described by the QS approximation and the MHD canonical equations in pipe flows is visualized by studying the evolution of the magnetic energy balance in examples with unsteady flows.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78481699","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

The symmetric solution of the matrix equation $$AXB=D$$ on subspace 子空间上矩阵方程$$AXB=D$$的对称解

Comput. Math. Appl. Pub Date : 2022-11-03 DOI: 10.1007/s40314-022-02093-w

Shanshan Hu, Yongxin Yuan

引用次数: 0

A new variable shape parameter strategy for RBF approximation using neural networks 一种基于神经网络的变形状参数RBF逼近策略

Comput. Math. Appl. Pub Date : 2022-10-30 DOI: 10.48550/arXiv.2210.16945

F. Mojarrad, M. H. Veiga, J. Hesthaven, Philipp Öffner

引用次数: 4

A modified weak Galerkin method for H(curl)-elliptic problem H(旋度)-椭圆问题的修正弱Galerkin方法

Comput. Math. Appl. Pub Date : 2022-10-01 DOI: 10.48550/arXiv.2203.01568

Ming Tang, L. Zhong, Yingying Xie

引用次数: 1

Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction 基于深度神经网络预测的准最优hp有限元奇异点优化

Comput. Math. Appl. Pub Date : 2022-09-13 DOI: 10.48550/arXiv.2209.05844

Tomasz Sluzalec, R. Grzeszczuk, Sergio Rojas, W. Dzwinel, M. Paszyński

{"title":"Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction","authors":"Tomasz Sluzalec, R. Grzeszczuk, Sergio Rojas, W. Dzwinel, M. Paszyński","doi":"10.48550/arXiv.2209.05844","DOIUrl":"https://doi.org/10.48550/arXiv.2209.05844","url":null,"abstract":"We show how to construct the deep neural network (DNN) expert to predict quasi-optimal $hp$-refinements for a given computational problem. The main idea is to train the DNN expert during executing the self-adaptive $hp$-finite element method ($hp$-FEM) algorithm and use it later to predict further $hp$ refinements. For the training, we use a two-grid paradigm self-adaptive $hp$-FEM algorithm. It employs the fine mesh to provide the optimal $hp$ refinements for coarse mesh elements. We aim to construct the DNN expert to identify quasi-optimal $hp$ refinements of the coarse mesh elements. During the training phase, we use the direct solver to obtain the solution for the fine mesh to guide the optimal refinements over the coarse mesh element. After training, we turn off the self-adaptive $hp$-FEM algorithm and continue with quasi-optimal refinements as proposed by the DNN expert trained. We test our method on three-dimensional Fichera and two-dimensional L-shaped domain problems. We verify the convergence of the numerical accuracy with respect to the mesh size. We show that the exponential convergence delivered by the self-adaptive $hp$-FEM can be preserved if we continue refinements with a properly trained DNN expert. Thus, in this paper, we show that from the self-adaptive $hp$-FEM it is possible to train the DNN expert the location of the singularities, and continue with the selection of the quasi-optimal $hp$ refinements, preserving the exponential convergence of the method.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80819358","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

Hybrid mixed discontinuous Galerkin finite element method for incompressible wormhole propagation problem 不可压缩虫洞传播问题的混合不连续Galerkin有限元法

Comput. Math. Appl. Pub Date : 2022-09-04 DOI: 10.48550/arXiv.2209.01528

Jiansong Zhang, Yun-Wey Yu, Jiang Zhu, Yue Yu, R. Qin

引用次数: 2

Plain convergence of goal-oriented adaptive FEM 面向目标的自适应有限元法的平面收敛性

Comput. Math. Appl. Pub Date : 2022-08-22 DOI: 10.48550/arXiv.2208.10143

Valentin Helml, M. Innerberger, D. Praetorius

引用次数: 0