arXiv - CS - Numerical Analysis最新文献_第3页

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

A Predictive Surrogate Model for Heat Transfer of an Impinging Jet on a Concave Surface 凹面上喷射流传热的预测替代模型

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10641

Sajad Salavatidezfouli, Saeid Rakhsha, Armin Sheidani, Giovanni Stabile, Gianluigi Rozza

{"title":"A Predictive Surrogate Model for Heat Transfer of an Impinging Jet on a Concave Surface","authors":"Sajad Salavatidezfouli, Saeid Rakhsha, Armin Sheidani, Giovanni Stabile, Gianluigi Rozza","doi":"arxiv-2402.10641","DOIUrl":"https://doi.org/arxiv-2402.10641","url":null,"abstract":"This paper aims to comprehensively investigate the efficacy of various Model\u0000Order Reduction (MOR) and deep learning techniques in predicting heat transfer\u0000in a pulsed jet impinging on a concave surface. Expanding on the previous\u0000experimental and numerical research involving pulsed circular jets, this\u0000investigation extends to evaluate Predictive Surrogate Models (PSM) for heat\u0000transfer across various jet characteristics. To this end, this work introduces\u0000two predictive approaches, one employing a Fast Fourier Transformation\u0000augmented Artificial Neural Network (FFT-ANN) for predicting the average\u0000Nusselt number under constant-frequency scenarios. Moreover, the investigation\u0000introduces the Proper Orthogonal Decomposition and Long Short-Term Memory\u0000(POD-LSTM) approach for random-frequency impingement jets. The POD-LSTM method\u0000proves to be a robust solution for predicting the local heat transfer rate\u0000under random-frequency impingement scenarios, capturing both the trend and\u0000value of temporal modes. The comparison of these approaches highlights the\u0000versatility and efficacy of advanced machine learning techniques in modelling\u0000complex heat transfer phenomena.","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":"139902598","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

Optimisation--Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics 基于优化的有限元模型与计算流体力学降序模型耦合

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10570

Ivan Prusak, Davide Torlo, Monica Nonino, Gianluigi Rozza

{"title":"Optimisation--Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics","authors":"Ivan Prusak, Davide Torlo, Monica Nonino, Gianluigi Rozza","doi":"arxiv-2402.10570","DOIUrl":"https://doi.org/arxiv-2402.10570","url":null,"abstract":"With the increased interest in complex problems, such as multiphysics and\u0000multiscale models, as well as real-time computations, there is a strong need\u0000for domain-decomposition (DD) segregated solvers and reduced-order models\u0000(ROMs). Segregated models decouple the subcomponents of the problems at hand\u0000and use already existing state-of-the-art numerical codes in each component. In\u0000this manuscript, starting with a DD algorithm on non-overlapping domains, we\u0000aim at the comparison of couplings of different discretisation models, such as\u0000Finite Element (FEM) and ROM for separate subcomponents. In particular, we\u0000consider an optimisation-based DD model on two non-overlapping subdomains where\u0000the coupling on the common interface is performed by introducing a control\u0000variable representing a normal flux. Gradient-based optimisation algorithms are\u0000used to construct an iterative procedure to fully decouple the subdomain state\u0000solutions as well as to locally generate ROMs on each subdomain. Then, we\u0000consider FEM or ROM discretisation models for each of the DD problem\u0000components, namely, the triplet state1-state2-control. We perform numerical\u0000tests on the backward-facing step Navier-Stokes problem to investigate the\u0000efficacy of the presented couplings in terms of optimisation iterations and\u0000relative errors.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"255 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139904119","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

High-order reliable numerical methods for epidemic models with non-constant recruitment rate 非恒定招募率流行病模型的高阶可靠数值方法

arXiv - CS - Numerical Analysis Pub Date : 2024-02-16 DOI: arxiv-2402.10549

B. M. Takács, G. Svantnerné Sebestyén, I. Faragó

引用次数: 0

Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation 热方程时空离散化中的小波压缩修正希尔伯特变换

arXiv - CS - Numerical Analysis Pub Date : 2024-02-15 DOI: arxiv-2402.10346

Helmut Harbrecht, Christoph Schwab, Marco Zank

{"title":"Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation","authors":"Helmut Harbrecht, Christoph Schwab, Marco Zank","doi":"arxiv-2402.10346","DOIUrl":"https://doi.org/arxiv-2402.10346","url":null,"abstract":"On a finite time interval $(0,T)$, we consider the multiresolution Galerkin\u0000discretization of a modified Hilbert transform $mathcal H_T$ which arises in\u0000the space-time Galerkin discretization of the linear diffusion equation. To\u0000this end, we design spline-wavelet systems in $(0,T)$ consisting of piecewise\u0000polynomials of degree $geq 1$ with sufficiently many vanishing moments which\u0000constitute Riesz bases in the Sobolev spaces $ H^{s}_{0,}(0,T)$ and $\u0000H^{s}_{,0}(0,T)$. These bases provide multilevel splittings of the temporal\u0000discretization spaces into \"increment\" or \"detail\" spaces of direct sum type.\u0000Via algebraic tensor-products of these temporal multilevel discretizations with\u0000standard, hierarchic finite element spaces in the spatial domain (with standard\u0000Lagrangian FE bases), sparse space-time tensor-product spaces are obtained,\u0000which afford a substantial reduction in the number of the degrees of freedom as\u0000compared to time-marching discretizations. In addition, temporal spline-wavelet\u0000bases allow to compress certain nonlocal integrodifferential operators which\u0000appear in stable space-time variational formulations of initial-boundary value\u0000problems, such as the heat equation and the acoustic wave equation. An\u0000efficient preconditioner is proposed that affords linear complexity solves of\u0000the linear system of equations which results from the sparse space-time\u0000Galerkin discretization.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139902412","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

Comparison of variational discretizations for a convection-diffusion problem 对流扩散问题的变分离散法比较

arXiv - CS - Numerical Analysis Pub Date : 2024-02-15 DOI: arxiv-2402.10281

Constantin Bacuta, Cristina Bacuta, Daniel Hayes

引用次数: 0