arXiv - CS - Numerical Analysis最新文献_第2页

Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity 粘性可变的奥森方程优化控制的发散符合 DG 方法

arXiv - CS - Numerical Analysis Pub Date : 2024-03-23 DOI: arxiv-2403.15783

Harpal Singh, Arbaz Khan

引用次数: 0

Cross Algorithms for Cost-Effective Time Integration of Nonlinear Tensor Differential Equations on Low-Rank Tucker Tensor and Tensor Train Manifolds 低张量塔克张量和张量列车漫域上成本效益型非线性张量微分方程时间积分交叉算法

arXiv - CS - Numerical Analysis Pub Date : 2024-03-19 DOI: arxiv-2403.12826

Behzad Ghahremani, Hessam Babaee

{"title":"Cross Algorithms for Cost-Effective Time Integration of Nonlinear Tensor Differential Equations on Low-Rank Tucker Tensor and Tensor Train Manifolds","authors":"Behzad Ghahremani, Hessam Babaee","doi":"arxiv-2403.12826","DOIUrl":"https://doi.org/arxiv-2403.12826","url":null,"abstract":"Dynamical low-rank approximation (DLRA) provides a rigorous, cost-effective\u0000mathematical framework for solving high-dimensional tensor differential\u0000equations (TDEs) on low-rank tensor manifolds. Despite their effectiveness,\u0000DLRA-based low-rank approximations lose their computational efficiency when\u0000applied to nonlinear TDEs, particularly those exhibiting non-polynomial\u0000nonlinearity. In this paper, we present a novel algorithm for the time\u0000integration of TDEs on the tensor train and Tucker tensor low-rank manifolds,\u0000which are the building blocks of many tensor network decompositions. This paper\u0000builds on our previous work (Donello et al., Proceedings of the Royal Society\u0000A, Vol. 479, 2023) on solving nonlinear matrix differential equations on\u0000low-rank matrix manifolds using CUR decompositions. The methodology we present\u0000offers multiple advantages: (i) it leverages cross algorithms based on the\u0000discrete empirical interpolation method to strategically sample sparse entries\u0000of the time-discrete TDEs to advance the solution in low-rank form. As a\u0000result, it offers near-optimal computational savings both in terms of memory\u0000and floating-point operations. (ii) The time integration is robust in the\u0000presence of small or zero singular values. (iii) The algorithm is remarkably\u0000easy to implement, as it requires the evaluation of the full-order model TDE at\u0000strategically selected entries and it does not use tangent space projections,\u0000whose efficient implementation is intrusive and time-consuming. (iv) We develop\u0000high-order explicit Runge-Kutta schemes for the time integration of TDEs on\u0000low-rank manifolds. We demonstrate the efficiency of the presented algorithm\u0000for several test cases, including a 100-dimensional TDE with non-polynomial\u0000nonlinearity.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168638","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

A better compression driver? CutFEM 3D shape optimization taking viscothermal losses into account 更好的压缩驱动器？考虑粘热损失的 CutFEM 3D 形状优化

arXiv - CS - Numerical Analysis Pub Date : 2024-03-14 DOI: arxiv-2403.17963

Martin Berggren, Anders Bernland, André Massing, Daniel Noreland, Eddie Wadbro

{"title":"A better compression driver? CutFEM 3D shape optimization taking viscothermal losses into account","authors":"Martin Berggren, Anders Bernland, André Massing, Daniel Noreland, Eddie Wadbro","doi":"arxiv-2403.17963","DOIUrl":"https://doi.org/arxiv-2403.17963","url":null,"abstract":"The compression driver, the standard sound source for midrange acoustic\u0000horns, contains a cylindrical compression chamber connected to the horn throat\u0000through a system of channels known as a phase plug. The main challenge in the\u0000design of the phase plug is to avoid resonance and interference phenomena. The\u0000complexity of these phenomena makes it difficult to carry out this design task\u0000manually, particularly when the phase-plug channels are radially oriented.\u0000Therefore, we employ an algorithmic technique that combines numerical solutions\u0000of the governing equations with a gradient-based optimization algorithm that\u0000can deform the walls of the phase plug. A particular modeling challenge here is\u0000that viscothermal losses cannot be ignored, due to narrow chambers and slits in\u0000the device. Fortunately, a recently developed, accurate, but computationally\u0000inexpensive boundary-layer model is applicable. We use this model, a level-set\u0000geometry description, and the Cut Finite Element technique to avoid mesh\u0000changes when the geometry is modified by the optimization algorithm. Moreover,\u0000the shape calculus needed to compute derivatives for the optimization algorithm\u0000is carried out in the fully discrete case. Applying these techniques, the\u0000algorithm was able to successfully design the shape of a set of\u0000radially-directed phase plugs so that the final frequency response surprisingly\u0000closely matches the ideal response, derived by a lumped circuit model where\u0000wave interference effects are not accounted for. This result may serve to\u0000resuscitate the radial phase plug design, rarely used in today's commercial\u0000compression drivers.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140324991","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

Gradient-free neural topology optimization 无梯度神经拓扑优化

arXiv - CS - Numerical Analysis Pub Date : 2024-03-07 DOI: arxiv-2403.04937

Gawel Kus, Miguel A. Bessa

引用次数: 0

Helmholtz preconditioning for the compressible Euler equations using mixed finite elements with Lorenz staggering 使用带洛伦兹交错的混合有限元对可压缩欧拉方程进行亥姆霍兹预处理

arXiv - CS - Numerical Analysis Pub Date : 2024-03-06 DOI: arxiv-2403.04095

David Lee, Alberto Martin, Kieran Ricardo

{"title":"Helmholtz preconditioning for the compressible Euler equations using mixed finite elements with Lorenz staggering","authors":"David Lee, Alberto Martin, Kieran Ricardo","doi":"arxiv-2403.04095","DOIUrl":"https://doi.org/arxiv-2403.04095","url":null,"abstract":"Implicit solvers for atmospheric models are often accelerated via the\u0000solution of a preconditioned system. For block preconditioners this typically\u0000involves the factorisation of the (approximate) Jacobian for the coupled system\u0000into a Helmholtz equation for some function of the pressure. Here we present a\u0000preconditioner for the compressible Euler equations with a flux form\u0000representation of the potential temperature on the Lorenz grid using mixed\u0000finite elements. This formulation allows for spatial discretisations that\u0000conserve both energy and potential temperature variance. By introducing the dry\u0000thermodynamic entropy as an auxiliary variable for the solution of the\u0000algebraic system, the resulting preconditioner is shown to have a similar block\u0000structure to an existing preconditioner for the material form transport of\u0000potential temperature on the Charney-Phillips grid, and to be more efficient\u0000and stable than either this or a previous Helmholtz preconditioner for the flux\u0000form transport of density weighted potential temperature on the Lorenz grid for\u0000a one dimensional thermal bubble configuration. The new preconditioner is\u0000further verified against standard two dimensional test cases in a vertical\u0000slice geometry.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140070847","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

Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with Caputo fractional Laplacian and variable coefficient wave number $μ$ 具有卡普托分数拉普拉奇和可变系数波数 $μ$ 的近似非局部赫尔姆霍兹方程的渐近谱特性和预处理

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10569

Andrea Adriani, Rosita Luisa Sormani, Cristina Tablino-Possio, Rolf Krause, Stefano Serra-Capizzano

引用次数: 0

A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy 斯托克斯-达西耦合问题的灰泥法，使用斯托克斯的 MAC 方案和达西的混合有限元方案

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10615

Wietse M. Boon, Dennis Gläser, Rainer Helmig, Kilian Weishaupt, Ivan Yotov

引用次数: 0

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics 成分孔力学的压力稳定定应力迭代解法

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10469

Ryan M. Aronson, Nicola Castelletto, François P. Hamon, J. A. White, Hamdi A. Tchelepi

引用次数: 0

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks 通过物理信息神经网络识别生物组织的异质微机械特性

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10741

Wensi Wu, Mitchell Daneker, Kevin T. Turner, Matthew A. Jolley, Lu Lu

{"title":"Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks","authors":"Wensi Wu, Mitchell Daneker, Kevin T. Turner, Matthew A. Jolley, Lu Lu","doi":"arxiv-2402.10741","DOIUrl":"https://doi.org/arxiv-2402.10741","url":null,"abstract":"The heterogeneous micromechanical properties of biological tissues have\u0000profound implications across diverse medical and engineering domains. However,\u0000identifying the full-field heterogeneous elastic properties of soft materials\u0000using traditional computational and engineering approaches is fundamentally\u0000challenging due to difficulties in estimating local stress fields. Recently,\u0000there has been a growing interest in using data-driven models to learn\u0000full-field mechanical responses such as displacement and strain from\u0000experimental or synthetic data. However, research studies on inferring the\u0000full-field elastic properties of materials, a more challenging problem, are\u0000scarce, particularly for large deformation, hyperelastic materials. Here, we\u0000propose a novel approach to identify the elastic modulus distribution in\u0000nonlinear, large deformation hyperelastic materials utilizing physics-informed\u0000neural networks (PINNs). We evaluate the prediction accuracies and\u0000computational efficiency of PINNs, informed by mechanic features and\u0000principles, across three synthetic materials with structural complexity that\u0000closely resemble real tissue patterns, such as brain tissue and tricuspid valve\u0000tissue. Our improved PINN architecture accurately estimates the full-field\u0000elastic properties, with relative errors of less than 5% across all examples.\u0000This research has significant potential for advancing our understanding of\u0000micromechanical behaviors in biological materials, impacting future innovations\u0000in engineering and medicine.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"220 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139902603","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

Reduced Order Model Enhanced Source Iteration with Synthetic Acceleration for Parametric Radiative Transfer Equation 参数辐射传输方程的减阶模型增强源迭代与合成加速度

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10488

Zhichao Peng

{"title":"Reduced Order Model Enhanced Source Iteration with Synthetic Acceleration for Parametric Radiative Transfer Equation","authors":"Zhichao Peng","doi":"arxiv-2402.10488","DOIUrl":"https://doi.org/arxiv-2402.10488","url":null,"abstract":"Applications such as uncertainty quantification and optical tomography,\u0000require solving the radiative transfer equation (RTE) many times for various\u0000parameters. Efficient solvers for RTE are highly desired. Source Iteration with Synthetic Acceleration (SISA) is one of the most\u0000popular and successful iterative solvers for RTE. Synthetic Acceleration (SA)\u0000acts as a preconditioning step to accelerate the convergence of Source\u0000Iteration (SI). After each source iteration, classical SA strategies introduce\u0000a correction to the macroscopic particle density by solving a low order\u0000approximation to a kinetic correction equation. For example, Diffusion\u0000Synthetic Acceleration (DSA) uses the diffusion limit. However, these\u0000strategies may become less effective when the underlying low order\u0000approximations are not accurate enough. Furthermore, they do not exploit low\u0000rank structures concerning the parameters of parametric problems. To address these issues, we propose enhancing SISA with data-driven ROMs for\u0000the parametric problem and the corresponding kinetic correction equation.\u0000First, the ROM for the parametric problem can be utilized to obtain an improved\u0000initial guess. Second, the ROM for the kinetic correction equation can be\u0000utilized to design a low rank approximation to it. Unlike the diffusion limit,\u0000this ROM-based approximation builds on the kinetic description of the\u0000correction equation and leverages low rank structures concerning the\u0000parameters. We further introduce a novel SA strategy called ROMSAD. ROMSAD\u0000initially adopts our ROM-based approximation to exploit its greater efficiency\u0000in the early stage, and then automatically switches to DSA to leverage its\u0000robustness in the later stage. Additionally, we propose an approach to\u0000construct the ROM for the kinetic correction equation without directly solving\u0000it.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"184 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139902420","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