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

Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration 利用皮卡尔迭代的局部径向基函数近似对小应变弹塑性变形进行数值分析

arXiv - CS - Numerical Analysis Pub Date : 2024-05-08 DOI: arxiv-2405.04970

Filip Strniša, Mitja Jančič, Gregor Kosec

{"title":"Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration","authors":"Filip Strniša, Mitja Jančič, Gregor Kosec","doi":"arxiv-2405.04970","DOIUrl":"https://doi.org/arxiv-2405.04970","url":null,"abstract":"This paper deals with a numerical analysis of plastic deformation under\u0000various conditions, utilizing Radial Basis Function (RBF) approximation. The\u0000focus is on the elasto-plastic von Mises problem under plane-strain assumption.\u0000Elastic deformation is modelled using the Navier-Cauchy equation. In regions\u0000where the von Mises stress surpasses the yield stress, corrections are applied\u0000locally through a return mapping algorithm. The non-linear deformation problem\u0000in the plastic domain is solved using the Picard iteration. The solutions for the Navier-Cauchy equation are computed using the Radial\u0000Basis Function-Generated Finite Differences (RBF-FD) meshless method using only\u0000scattered nodes in a strong form. Verification of the method is performed\u0000through the analysis of an internally pressurized thick-walled cylinder\u0000subjected to varying loading conditions. These conditions induce states of\u0000elastic expansion, perfectly-plastic yielding, and plastic yielding with linear\u0000hardening. The results are benchmarked against analytical solutions and\u0000traditional Finite Element Method (FEM) solutions. The paper also showcases the\u0000robustness of this approach by solving case of thick-walled cylinder with\u0000cut-outs. The results affirm that the RBF-FD method produces results comparable\u0000to those obtained through FEM, while offering substantial benefits in managing\u0000complex geometries without the necessity for conventional meshing, along with\u0000other benefits of meshless methods.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"2016 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942454","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

Unique continuation for the wave equation based on a discontinuous Galerkin time discretization 基于非连续伽勒金时间离散化的波方程唯一续集

arXiv - CS - Numerical Analysis Pub Date : 2024-05-07 DOI: arxiv-2405.04615

Erik Burman, Janosch Preuss

引用次数: 0

Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems 非连续伽勒金谱元近似超双曲系统已决过网格问题的能量边界

arXiv - CS - Numerical Analysis Pub Date : 2024-05-07 DOI: arxiv-2405.04668

David A. Kopriva, Andrew R. Winters, Jan Nordström

引用次数: 0

An adaptive heavy ball method for ill-posed inverse problems 一种自适应重球方法，用于处理问题严重的逆问题

arXiv - CS - Numerical Analysis Pub Date : 2024-04-04 DOI: arxiv-2404.03218

Qinian Jin, Qin Huang

引用次数: 0

Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation 量化不确定性传播中代用模型的条件伪可逆归一化流程

arXiv - CS - Numerical Analysis Pub Date : 2024-03-31 DOI: arxiv-2404.00502

Minglei Yang, Pengjun Wang, Ming Fan, Dan Lu, Yanzhao Cao, Guannan Zhang

{"title":"Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation","authors":"Minglei Yang, Pengjun Wang, Ming Fan, Dan Lu, Yanzhao Cao, Guannan Zhang","doi":"arxiv-2404.00502","DOIUrl":"https://doi.org/arxiv-2404.00502","url":null,"abstract":"We introduce a conditional pseudo-reversible normalizing flow for\u0000constructing surrogate models of a physical model polluted by additive noise to\u0000efficiently quantify forward and inverse uncertainty propagation. Existing\u0000surrogate modeling approaches usually focus on approximating the deterministic\u0000component of physical model. However, this strategy necessitates knowledge of\u0000noise and resorts to auxiliary sampling methods for quantifying inverse\u0000uncertainty propagation. In this work, we develop the conditional\u0000pseudo-reversible normalizing flow model to directly learn and efficiently\u0000generate samples from the conditional probability density functions. The\u0000training process utilizes dataset consisting of input-output pairs without\u0000requiring prior knowledge about the noise and the function. Our model, once\u0000trained, can generate samples from any conditional probability density\u0000functions whose high probability regions are covered by the training set.\u0000Moreover, the pseudo-reversibility feature allows for the use of\u0000fully-connected neural network architectures, which simplifies the\u0000implementation and enables theoretical analysis. We provide a rigorous\u0000convergence analysis of the conditional pseudo-reversible normalizing flow\u0000model, showing its ability to converge to the target conditional probability\u0000density function using the Kullback-Leibler divergence. To demonstrate the\u0000effectiveness of our method, we apply it to several benchmark tests and a\u0000real-world geologic carbon storage problem.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"116 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571802","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

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