International Journal for Numerical Methods in Engineering最新文献

{"title":"Featured Cover","authors":"Yang-Yang Zhang,&nbsp;Wen-Jie Xu","doi":"10.1002/nme.70322","DOIUrl":"https://doi.org/10.1002/nme.70322","url":null,"abstract":"<p>The cover image is based on the article <i>High-Performance Hybrid FVM-DEM Framework for Thermodynamic Analysis of Three-Phase Flow With Broadly Graded Particles</i> by Wen-Jie Xu et al., https://doi.org/10.1002/nme.70298.\u0000\u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70322","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147615114","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":"Designing 3D Thermal Metamaterials at Gigavoxel Resolution on a Single Computer via Hybrid CPU-GPU Architectures","authors":"Tianjie Chen,&nbsp;Yuchen Quan,&nbsp;Xiao-Ming Fu,&nbsp;Ligang Liu,&nbsp;Xiaoya Zhai","doi":"10.1002/nme.70306","DOIUrl":"https://doi.org/10.1002/nme.70306","url":null,"abstract":"<div>\u0000 \u0000 <p>Thermal metamaterials enable engineered control of heat transport in advanced systems by tailoring effective thermal conductivity. However, inverse design at truly 3D gigavoxel-scale resolution remains largely unexplored, even though thermal functionalities often depend on fine-scale features, sharp spatial variations, and complex anisotropies that are poorly captured on coarse grids. Pushing inverse optimization to gigavoxel resolution on a single computer is particularly challenging. In this paper, we develop a novel high-performance computational framework for gigavoxel-resolution inverse optimization of 3D thermal metamaterials on a single computer. The framework rests on two key components: (i) a novel out-of-core data structure that jointly exploits host (CPU) and device (GPU) memory to accommodate extreme-resolution fields, and (ii) an efficient data-transport scheme that overlaps communication with computation to sustain high throughput during PDE solves and sensitivity evaluations. By enabling high-resolution optimization, our method improves the fidelity of the designed conductivity distributions, better resolves fine structural details that govern heat-flow pathways, and reduces discretization-induced performance loss. Numerical studies demonstrate that the proposed approach substantially enhances scalability and practical accessibility while maintaining high design accuracy. This advancement bridges a critical gap in the field and opens new possibilities for the practical engineering of next-generation thermal metamaterials.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566582","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":"Inverse Finite Elastostatics for Isotropic Models Formulated in Principal Stretches","authors":"Zeinab Awada,&nbsp;Abdelghani May,&nbsp;Diego A. Garzón-Alvarado,&nbsp;Salah Ramtani,&nbsp;Boumediene Nedjar","doi":"10.1002/nme.70311","DOIUrl":"https://doi.org/10.1002/nme.70311","url":null,"abstract":"<div>\u0000 \u0000 <p>Inverse finite strain elastostatics has been mainly used for hyperelastic materials based on invariants such as, for instance, neo-Hookean and Mooney–Rivlin models. However, isotropic hyperelasticity can also be formulated with models based on principal stretches. The main objective of this paper is to show how these latter can be used in inverse elastostatics as well. This task is simply accomplished by rewriting the inverse constitutive relation in the form of a classical state law. Then, with the use of spectral decompositions, we provide explicit stress functions and tangent moduli that can be used within a finite element implementation for commonly used models, including Ogden-type models and the classical Hencky model, the latter based on logarithmic stretches. Furthermore, and independently of the specific hyperelastic law, we detail in this paper the consideration of self-weight in the case of compressible materials, since it contributes to the tangent matrix during the iterative solution procedure. The effectiveness of the present framework is then demonstrated through a set of numerical simulations.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566583","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":"Mesh and Model Adaptivity for Multiscale Elastoplastic Models With Prandtl-Reuss Type Material Laws","authors":"Arnold Tchomgue Simeu,&nbsp;Ismail Caylak,&nbsp;Richard Ostwald","doi":"10.1002/nme.70294","DOIUrl":"https://doi.org/10.1002/nme.70294","url":null,"abstract":"<p>Homogenization methods simulate heterogeneous materials like composites effectively, but high computational demands can offset their benefits. This work balances accuracy and efficiency by assessing model and discretization errors of the finite element method (FEM) through an adaptive numerical scheme. Two model hierarchies are introduced, combining mean-field and full-field methods, and nonuniform transformation field analysis (NTFA) with full-field methods. Both hierarchies use a full-field FEM solution of the representative volume element (RVE) as reference. The study highlights the benefits of using effective constitutive equations from mean-field and full-field methods as well as NTFA methods, with a goal-oriented a posteriori error estimator based on duality techniques controlling mesh and model errors in a forwards-in-time manner.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70294","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566502","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 Computationally Efficient Analytical Formulation on the Sound Radiation of a Circular Plate With a Finite Baffle","authors":"Krzysztof Szemela,&nbsp;Wojciech P. Rdzanek,&nbsp;Li Cheng,&nbsp;Jerzy Wiciak","doi":"10.1002/nme.70297","DOIUrl":"https://doi.org/10.1002/nme.70297","url":null,"abstract":"<div>\u0000 \u0000 <p>The computationally efficient formulas to calculate the sound pressure and the sound power radiated by a circular source embedded in an annular planar rigid baffle were obtained by dividing a half-space into three spherical subregions and proposing appropriate solutions for each of them. The proposed solutions were connected through the continuity conditions. The results given by the obtained formulation were compared with the finite element method (FEM) results and with the results given by the solution called here the Dini series and the spherical harmonics solution (DSHS). In most cases, a good agreement between results was achieved. The use of the obtained formulas is less troublesome than using the FEM; therefore, they can be used to calculate the sound pressure at a large distance from a sound source and to analyze the sound radiation for large baffle sizes. The performed numerical simulations proved that the use of the obtained formulation is much more computationally efficient than the use of the DSHS and the FEM. Based on the obtained formulas, the influence of the baffle's size on the sound radiation can be extensively investigated.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566604","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":"Boundary-Information-Enhanced Physics-Informed Neural Network for Solving Partial Differential Equations","authors":"Junliang Li,&nbsp;Eric Li,&nbsp;Xu Xu","doi":"10.1002/nme.70300","DOIUrl":"https://doi.org/10.1002/nme.70300","url":null,"abstract":"<div>\u0000 \u0000 <p>In the rapidly evolving field of scientific machine learning, physics-informed neural networks (PINNs) have emerged as a powerful paradigm for numerically solving partial differential equations (PDEs). Within this framework, boundary conditions serve as pivotal physical prior knowledge; the approximate enforcement of these physical constraints in regions adjacent to the domain boundaries frequently constitutes a critical bottleneck that limits solution accuracy. To address this challenge, we propose a boundary-information-enhanced physics-informed neural network (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 <annotation>$$ bi $$</annotation>\u0000 </semantics></math>-PINN) by embedding boundary-derivative restraints (bd-restraints) into the loss function to systematically strengthen the impact of boundary physics. These derivative relationships typically lack explicit representation in raw boundary data, thus the bd-restraints are derived from governing physical laws or differential-geometric properties. We present a detailed analysis on how to derive bd-restraints for real-world problems. We validate the effectiveness of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 <annotation>$$ bi $$</annotation>\u0000 </semantics></math>-PINN through various benchmark problems that span diverse physical regimes including Poisson equation, elasticity, heat conduction problem, and the KdV equation. Extensive numerical comparisons demonstrate that the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 <annotation>$$ bi $$</annotation>\u0000 </semantics></math>-PINN achieves a one to two-order of magnitude reduction in boundary error and consistently improves accuracy across the entire computational domain compared to conventional PINNs. Our findings highlight the strengths of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 <annotation>$$ bi $$</annotation>\u0000 </semantics></math>-PINN: exceptional computational efficiency and superior performance in high-fidelity simulations of complex problems under conditions of limited physical knowledge, thereby providing a reliable and efficient solution strategy for real-world engineering challenges.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566503","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":"Surrogate Model Based on Proper Generalized Decomposition Method With Applications to Multiscale Topology Optimization","authors":"Jiayi Hu,&nbsp;Weisheng Zhang,&nbsp;Shaoqiang Tang","doi":"10.1002/nme.70301","DOIUrl":"https://doi.org/10.1002/nme.70301","url":null,"abstract":"<div>\u0000 \u0000 <p>Based on the proper generalized decomposition (PGD) method, a surrogate model is proposed for parametrized numerical homogenization, and applied in multiscale topology optimization (TO). The proposed model accurately constructs a mapping from the geometric parameters of microstructures to their effective elasticity tensor. The major features include reduced storage requirements, higher computational efficiency, and no need for independent pointwise sampling over the parameter domain. Using such a surrogate model, a multiscale TO framework is presented under a volume fraction constraint of the matrix material. Three numerical examples illustrate the accuracy and efficiency of the proposed method in numerical homogenization. The corresponding multiscale TO results demonstrate its effectiveness.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566504","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":"Homogenization With Guaranteed Bounds via Primal-Dual Physically Informed Neural Networks","authors":"Liya Gaynutdinova,&nbsp;Ondřej Rokoš,&nbsp;Martin Doškář,&nbsp;Ivana Pultarová","doi":"10.1002/nme.70302","DOIUrl":"https://doi.org/10.1002/nme.70302","url":null,"abstract":"<p>Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with piecewise constant properties. This paper introduces a dual formulation for the PINN framework to improve the reliability of the homogenization of periodic thermo-conductive composites, for both strong and variational (weak) formulations. The dual approach facilitates the derivation of guaranteed upper and lower error bounds, enabling more robust detection of PINN failure. We compare standard PINNs applied to smoothed material approximations with variational PINNs (VPINNs) using both spectral and neural network-based test functions. Our results indicate that while strong-form PINNs may outperform VPINNs in controlled settings, they are sensitive to material discontinuities and may fail without clear diagnostics. In contrast, VPINNs accommodate piecewise constant material parameters directly but require careful selection of test functions to avoid instability. Dual formulation serves as a reliable indicator of convergence quality, and its integration into PINN frameworks enhances their applicability to homogenization problems in micromechanics.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566505","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 Novel Approach for Quad-Dominant Mesh Generation Using Conformal Mapping Compressed Gradient Field","authors":"Rushuang Mu,&nbsp;Long Qi,&nbsp;Jingying Qiu,&nbsp;Fang Han,&nbsp;Yongping Xiong,&nbsp;Yufei Pang,&nbsp;Yang Liu","doi":"10.1002/nme.70303","DOIUrl":"https://doi.org/10.1002/nme.70303","url":null,"abstract":"<div>\u0000 \u0000 <p>The regular topological structure endows quadrilateral meshes with advantages such as high computational accuracy, reduced element requirements, and enhanced computational efficiency, granting them irreplaceable application value in high-end engineering simulation domains. However, significant bottlenecks persist in the fully automatic generation technology of quadrilateral meshes for complex geometric models. Existing methods often encounter key issues such as high mesh distortion rates and insufficient algorithm stability when handling high-curvature boundaries and multiscale feature regions, limiting their widespread application in engineering simulations. This article proposes a quad-dominant mesh generation method based on gradient fields. Firstly, the three-dimensional triangular mesh is transformed into a two-dimensional parametric domain through conformal mapping. Subsequently, based on the compression ratio measured from three-dimensional to two-dimensional, the direction and size of the advancing front are calculated to draw contour lines in the parametric domain. A threshold is set to automatically generate high-quality grids. Based on the extracted contour lines, high-quality quadrilateral grids are generated pairwise along the gradient field directions. For regions that do not meet the threshold requirements, triangular mesh filling is employed to generate a two-dimensional quad-dominant grid. Due to the bijective nature of the mapping, the quad-dominant surface mesh is obtained through the inverse transformation from the 2D parametric domain back to the 3D space.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566501","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":"Algebraic Multigrid Based Preconditioning Approaches for Generalized Continuum Models and Indirect Displacement Control Techniques","authors":"Nasser Alkmim,&nbsp;Peter Gamnitzer,&nbsp;Alexander Dummer,&nbsp;Matthias Neuner,&nbsp;Günter Hofstetter","doi":"10.1002/nme.70309","DOIUrl":"https://doi.org/10.1002/nme.70309","url":null,"abstract":"<p>The contribution deals with algebraic multigrid (AMG) based preconditioning methods for the iterative solution of a coupled linear system of equations arising in numerical simulations of failure of quasi-brittle materials using generalized continuum approaches. In particular, the focus is on the solution of large and sparse linear systems originating from a gradient-enhanced micropolar formulation with coupled fields of displacements, microrotations, and non-local damage. Moreover, due to the possible presence of snap-back behavior in quasi-brittle materials, indirect displacement control techniques are discussed in the context of iterative linear solvers. The respective linear systems exhibit a distinct block structure representing the coupled fields of unknowns, which requires specialized preconditioners to iteratively solve the fully coupled linear system. Firstly, the present paper describes and investigates monolithic multigrid strategies for such problems which treat the block structure within the AMG hierarchy. An evaluation of the performance of the monolithic multigrid strategy for displacement controlled problems is carried out. This is done by a comparison to the performance of a previously published AMG based preconditioning strategy that applies the AMG to each field separately in a block preconditioning fashion. The results obtained for 2D plane strain and 3D triaxial compression indicate that this monolithic multigrid strategy performs similarly to the reference approach in terms of iteration counts in the majority of the investigated test cases. However, for distinct choices of material parameters, the respective strategy is shown to outperform the reference approach prior to localization and damage initiation. Secondly, for problems relying on indirect displacement control, a novel monolithic solution scheme is proposed that extends the existing block preconditioner to accommodate the additional constraint equation. We present a block preconditioner for the augmented system, for which we show in a 2D simulation of borehole failure that it significantly enhances computational efficiency by combining indirect displacement control and iterative linear solution techniques.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70309","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566506","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}