International Journal for Numerical Methods in Engineering最新文献

{"title":"Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification","authors":"Xiaolong He,&nbsp;April Tran,&nbsp;David M. Bortz,&nbsp;Youngsoo Choi","doi":"10.1002/nme.7634","DOIUrl":"https://doi.org/10.1002/nme.7634","url":null,"abstract":"<div>\u0000 \u0000 <p>The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ % $$</annotation>\u0000 </semantics></math> Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ % $$</annotation>\u0000 </semantics></math> relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>×</mo>\u0000 </mrow>\u0000 <annotation>$$ times $$</annotation>\u0000 </semantics></math> speed-up.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strict Discretization Error Bounds on Quantities of Interest in Transient Dynamics","authors":"Qisheng Zheng,&nbsp;Jike Liu,&nbsp;Ludovic Chamoin,&nbsp;Li Wang","doi":"10.1002/nme.7622","DOIUrl":"https://doi.org/10.1002/nme.7622","url":null,"abstract":"<div>\u0000 \u0000 <p>This work proposes a guaranteed error estimator for linear transient elastodynamics, accounting for both time and space discretization errors. The key lies in the definition of a novel dynamic constitutive relation error formulation, which is proven to be a strict bound of the discretization error. Moreover, based on the established dynamic constitutive relation error and the goal-oriented error estimation framework, strict upper and lower bounds on quantities of interest are also obtained. Numerical examples are conducted to verify the proposed strict bounds and to explore the application of these bounds to adaptive time stepping and mesh refinement.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shape Optimization of Tunable Poisson's Ratio Metamaterials With Disk B-Splines","authors":"Yihui Ye,&nbsp;Nan Zheng,&nbsp;Xiaoya Zhai,&nbsp;Hongmei Kang,&nbsp;Falai Chen","doi":"10.1002/nme.7620","DOIUrl":"https://doi.org/10.1002/nme.7620","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose an explicit representation method using disk B-splines for Poisson's ratio metamaterial design. Disk B-spline representation generalizes the concept of the B-spline control point into a control disk, enhancing the ability to manipulate both the shape and thickness of the region. Therefore, this representation is frequently employed for shape optimization. The optimized metamaterials described by disk B-spline are decomposed into a sequence of circles constructing one implicit function. A novel optimization model based on disk B-spline representation is proposed, and the homogenization theory is used for calculating effective Poisson's ratio (PR). The numerical examples contained missing rib metamaterials, petal-like metamaterials, and extreme PR metamaterials, which are studies to illustrate the advantages and effectiveness. By explicitly manipulating the parameters of the disk's B-spline, a broad spectrum of unexpectedly negative Poisson's ratio from -0.1 to -0.9 sequences can be achieved, and arbitrary Poisson's ratios structures can be obtained through interpolating continuous parameters. It's also extended to encompass 3D structures. We validate the accuracy of our results by comparing them with simulations performed using commercial software.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Enhanced and Highly Efficient Semi-Implicit Combined Lagrange Multiplier Approach Preserving Original Energy Law for Dissipative Systems","authors":"Zhengguang Liu,&nbsp;Nan Zheng,&nbsp;Xiaoli Li","doi":"10.1002/nme.7619","DOIUrl":"https://doi.org/10.1002/nme.7619","url":null,"abstract":"<div>\u0000 \u0000 <p>Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu, and Shen, which has been broadly used to solve various challenging phase field problems. To design original energy-stable schemes, they have to solve a nonlinear algebraic equation to determine the introduced Lagrange multiplier, which can be computationally expensive, especially for large-scale and long-time simulations involving complex nonlinear terms. In this article, we propose an essential improved technique to modify this issue, which can be seen as a semi-implicit combined Lagrange multiplier approach. In general, the newly constructed schemes keep all the advantages of the Lagrange multiplier method and significantly reduce the computation costs. Besides, the new proposed second-order backward difference formula (BDF2) scheme dissipates the original energy, as opposed to a modified energy for the classic Lagrange multiplier approach. In addition, we establish a general framework for extending our constructed method to dissipative systems. Finally, several examples have been presented to demonstrate the effectiveness of the proposed approach.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Two-Stage Reliability Analysis Method Combining Improved Cross-Entropy Adaptive Sampling and Relevant Vector Machine","authors":"Xin Fan,&nbsp;Xufeng Yang,&nbsp;Yongshou Liu","doi":"10.1002/nme.7635","DOIUrl":"https://doi.org/10.1002/nme.7635","url":null,"abstract":"<div>\u0000 \u0000 <p>The computational burden becomes unbearable when reliability analysis involves time-consuming finite element analysis, especially for rare events. Therefore, reducing the number of performance function calls is the only way to improve computing efficiency. This paper proposes a novel reliability analysis method that combines relevant vector machine (RVM) and improved cross-entropy adaptive sampling (iCE). In this method, RVM is employed to approximate the limit state surface and iCE is performed based on the constructed RVM. To guarantee the precision of RVM, the first level samples and the last level samples of iCE are used as candidate samples and the last level samples are regenerated along with the RVM updates. To prevent unnecessary updates of RVM, the proposed method considers the positions of the samples in the current design of experiment. In addition, based on the statistical properties of RVM and iCE, an error-based stopping criterion is proposed. The accuracy and efficiency of the proposed method were validated through four benchmark examples. Finally, the proposed method is applied to engineering problems which are working in extreme environment.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-Set MMV Topology Optimization Approach for Sliding Surface Texture Design","authors":"Weisheng Zhang,&nbsp;Honghao Tian,&nbsp;Bao Zhu,&nbsp;Xu Guo,&nbsp;Sung-Kie Youn","doi":"10.1002/nme.7612","DOIUrl":"https://doi.org/10.1002/nme.7612","url":null,"abstract":"<div>\u0000 \u0000 <p>Surface texture is of great practical importance in applications due to its significant effect on the tribological performance of the sliding surface. In the present work, an explicit topology optimization framework for surface texture design is proposed. For this purpose, the moving morphable void (MMV)-based explicit topology optimization approach is used to maximize the load carrying capacity (LCC) of the bearing by optimizing the distribution of the surface texture. A multi-set of voids is established to describe the multi-film thickness of the texture. By using the explicit geometry information in MMV, the present work can be seamlessly linked to the CAD system, resulting in the accurate processing of complex surface textures. Besides some numerical examples to demonstrate the effectiveness of the proposed approach, experimental tests are also provided to verify the validity of the optimization results.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Discrete Sine-Cosine Transforms Galerkin Method for the Conductivity of Heterogeneous Materials With Mixed Dirichlet/Neumann Boundary Conditions","authors":"Joseph Paux,&nbsp;Léo Morin,&nbsp;Lionel Gélébart","doi":"10.1002/nme.7615","DOIUrl":"https://doi.org/10.1002/nme.7615","url":null,"abstract":"<p>This work aims at developing a numerical method for conductivity problems in heterogeneous media subjected to mixed Dirichlet/Neumann boundary conditions. The method relies on a fixed-point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space spanned by mixed cosine-sine series. The solution field is written as a known term verifying the boundary conditions and an unknown term described by cosine-sine series, having no contribution on the boundary. Discrete sine-cosine transforms, of Type I and III depending on the boundary conditions, are used to approximate the elementary integrals involved in the Galerkin formulation, which makes the method relying on the numerical complexity of fast Fourier transforms. The method is finally assessed in a problem of a composite material.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7615","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A General Bipenalty Formulation for Explicit Contact-Impact Analysis With a Parameter Selection Criterion","authors":"Yun-Jae Kwon,&nbsp;Jin-Gyun Kim,&nbsp;Sang Soon Cho,&nbsp;José A. González","doi":"10.1002/nme.7614","DOIUrl":"https://doi.org/10.1002/nme.7614","url":null,"abstract":"<p>A general bipenalty formulation with a parameter selection criterion is proposed for explicit contact-impact finite element analysis. In order to model the contact phenomenon using penalties, it is necessary to introduce an artificial contact stiffness that can increase the maximum natural frequency of the system. When a large stiffness penalty parameter is used, the stability condition forces to reduce the time step size, increasing at the same time the computational demands. A solution to avoid the small time step size requirement and possible instabilities is to include a mass penalty in addition to the stiffness penalty term, using a technique known as the <i>bipenalty</i> method. However, this method presents some other challenges, mainly related to the parameter selection criterion and its final accuracy. In this work, two important improvements for the bipenalty method are presented. (i) An element-type and dimension-independent criterion for the selection of penalty mass and stiffness parameters. (ii) A modified predictor-corrector scheme, specifically designed for the bipenalty method, that improves the accuracy of contact-impact problems. Different 1D, 2D, and 3D contact-impact examples are used to illustrate the stability, applicability to general contact cases, and reduction of the zigzag effect and spurious oscillations exhibited by the proposed methods.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7614","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive FEM-SPIM Coupling for Phase-Field Modeling of Fracture","authors":"Larissa Novelli,&nbsp;Roque Luiz da Silva Pitangueira,&nbsp;Lapo Gori","doi":"10.1002/nme.7609","DOIUrl":"https://doi.org/10.1002/nme.7609","url":null,"abstract":"<div>\u0000 \u0000 <p>This article proposes an adaptive coupling strategy between the standard FEM and smoothed point interpolation methods (SPIMs) for the solution of phase-field fracture problems, where the SPIM discretization is used to model the fracture propagation regions. Adaptive strategies are an important tool for problems that demand highly refined meshes in localized regions, such as in phase-field problems. In the proposed strategy, the problem is initially discretized with a coarse FEM mesh, that is automatically replaced and refined by an SPIM discretization when and where fracture occurs. Five different benchmark tests are presented to illustrate the robustness of the proposed strategy. Brittle and quasi-brittle problems are simulated and evaluated in terms of phase-field contour plots and load-displacement paths, showing good agreement with literature results and with results obtained with previously refined FEM models. The numerical simulations consider different criteria for the identification of the regions where the discretization replacement and refinement must occur, different sizes of the substitution regions, and different SPIM strategies. The proposed strategy relies on three properties of the meshfree strategy: (i) the reduced connectivity that ease the adaptive refinement, (ii) the presence of the Kronecker-delta property, that makes the coupling with the FEM mesh straightforward, and (iii) the presence of nonpolynomial approximation functions, that provide a better approximation of the phase-field profile. As illustrated by the simulations, this new strategy results in computational times that are comparable with the ones of a previously refined FEM mesh, without requiring an a priori knowledge of the replacement regions.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Dynamic Problems in Fully Saturated Porous Media Using an Embedded Velocity Integration Formulation With an Adaptive Runge–Kutta Method","authors":"J. Sunten,&nbsp;A. Schwarz,&nbsp;J. Bluhm,&nbsp;J. Schröder","doi":"10.1002/nme.7610","DOIUrl":"https://doi.org/10.1002/nme.7610","url":null,"abstract":"<p>This contribution presents a dynamic binary Theory of Porous Media (TPM) model using an embedded velocity integration (EVI) formulation. The inclusion of dynamic effects into a TPM model leads to an increase in the number of unknown quantities and may also limit the choice of fitting time integration methods. By switching to a velocity formulation the amount of unknown quantities is kept to a minimum and the necessity of a time integration scheme being able to produce a second material time derivative is avoided. The used EVI formulation was verified and its advantage concerning computational time was shown by a comparison to a classic approach by Diebels and Ehlers. Both approaches were simulated with an adaptive, embedded, stiffly accurate, explicit, singly, diagonally implicit Runge–Kutta (saESDIRK) time integration method to decrease the computational time even more.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7610","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}