International Journal for Numerical Methods in Engineering最新文献

{"title":"Matched Asymptotic Expansions-Based Transferable Neural Networks for Singular Perturbation Problems","authors":"Zhequan Shen,&nbsp;Lili Ju,&nbsp;Liyong Zhu","doi":"10.1002/nme.70307","DOIUrl":"https://doi.org/10.1002/nme.70307","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, by utilizing the theory of matched asymptotic expansions, an efficient and accurate neural network method, named as “MAE-TransNet,” is developed for solving singular perturbation problems in general dimensions, whose solutions usually change drastically in some narrow boundary layers. The TransNet is a two-layer neural network with specially pretrained hidden-layer neurons. In the proposed MAE-TransNet, the inner and outer solutions produced from the matched asymptotic expansions are first approximated by a TransNet with nonuniform hidden-layer neurons and a TransNet with uniform hidden-layer neurons, respectively. Then, these two solutions are combined with a matching term to obtain the composite solution, which approximates the asymptotic expansion solution of the singular perturbation problem. This process enables the MAE-TransNet method to retain the precision of the matched asymptotic expansions while maintaining the efficiency and accuracy of TransNet. Meanwhile, the rescaling of the sharp region allows the same pretrained network parameters to be applied to boundary layers with various thicknesses, thereby improving the transferability of the method. Notably, for coupled boundary layer problems, a computational framework based on MAE-TransNet is also constructed to effectively address issues resulting from the lack of relevant matched asymptotic expansion theory in such problems. Our MAE-TransNet is thoroughly compared with TransNet, PINN, and Boundary-Layer PINN (BL-PINN) on various benchmark problems, including 1D linear and nonlinear problems with boundary layers, the 2D Couette flow problem, a 2D coupled boundary layer problem, and the 3D Burgers vortex problem. Numerical results demonstrate that MAE-TransNet significantly outperforms other neural network methods in capturing the characteristics of boundary layers, improving the accuracy, and reducing the computational cost.</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":"147566581","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":"Featured Cover","authors":"Shuran Hu,&nbsp;Kaixin Yu,&nbsp;Zhoufang Xiao,&nbsp;Xunyang Zhu,&nbsp;Hongfei Ye,&nbsp;Jianjun Chen","doi":"10.1002/nme.70315","DOIUrl":"https://doi.org/10.1002/nme.70315","url":null,"abstract":"<p>The cover image is based on the article <i>Fast gradient-limited sizing function for high-quality surface mesh generation</i> by Jianjun Chen et al., https://doi.org/10.1002/nme.70262.\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 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70315","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566250","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":"Stable Model Reduction for Time-Domain Room Acoustics: A Structure-Preserving Formulation for Complex Boundaries","authors":"Satish Bonthu,&nbsp;Hermes Sampedro Llopis,&nbsp;Solvi Thrastarson,&nbsp;Finnur Pind,&nbsp;Runar Unnthorsson","doi":"10.1002/nme.70295","DOIUrl":"https://doi.org/10.1002/nme.70295","url":null,"abstract":"<p>This work presents novel structure-preserving formulations for stable model order reduction in the context of time-domain room acoustics simulations. A solution to address the instability in conventional model order reduction formulations based on the Linearized Euler Equations is derived and validated through numerical experiments. For the scenarios presented, the proposed formulation demonstrates 3.5 times speedup in calculating the full-order model compared to the unstable formulation. A critical stability analysis is performed to identify the eigenvalues of the reduced operator matrices falling on the right half of complex plane along with their out of phase eigen angles as the source of instabilities in the reduced system. The performance of the proposed MOR formulation is tested for perfectly rigid, frequency-independent, and locally reacting frequency-dependent boundary conditions in two-dimensional cases. The study shows that MOR using the stable formulation results in a 100-fold speedup. The proposed formulation is further evaluated to assess its impact on accuracy, computational speedup, and overall reduction potential of the system.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563920","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":"Automated Generation of Hybrid Semi-Structured Meshes via Boundary-Informed Neural Networks","authors":"Hongfei Ye,&nbsp;Taoran Liu,&nbsp;Qiwei Zhan,&nbsp;Ruipeng Zhang,&nbsp;Jianjun Chen","doi":"10.1002/nme.70289","DOIUrl":"https://doi.org/10.1002/nme.70289","url":null,"abstract":"<div>\u0000 \u0000 <p>High-quality anisotropic boundary-layer meshes are crucial for numerical simulations, yet their automated generation for complex geometries remains a significant challenge. This paper presents AnisoMeshNet, a novel deep learning framework that automates the generation of hybrid semi-structured meshes. At its core, AnisoMeshNet learns a smooth guiding vector field for anisotropic meshing by adopting a boundary-informed neural network (BINN) philosophy. Instead of learning the field from scratch, our method first constructs a robust geometric prior—a boundary condition extension (BCE) field—using a K-nearest neighbors (KNN) algorithm. The neural network is then trained to learn a smooth correction field that refines this prior, ensuring strict adherence to BCs through a weighted cosine similarity loss. The resulting composite vector field smoothly guides an advancing layer method (ALM) to generate orthogonality-favored, quad-dominant boundary-layer meshes for complex 2D geometries, demonstrating a robust and automated alternative to traditional methods.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563921","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":"High-Performance Hybrid FVM-DEM Framework for Thermodynamic Analysis of Three-Phase Flow With Broadly Graded Particles","authors":"Yang-Yang Zhang,&nbsp;Wen-Jie Xu","doi":"10.1002/nme.70298","DOIUrl":"https://doi.org/10.1002/nme.70298","url":null,"abstract":"<div>\u0000 \u0000 <p>The thermodynamics of multiphase particle flow systems hold significant theoretical value for engineering applications in fields such as energy and chemical engineering. To address this, a high-performance hybrid FVM-DEM framework, named as CoSim-FVDEM, utilizing GPU acceleration, is proposed. The framework supports unresolved, resolved, and resolved–unresolved coupling methods, making it suitable for multiphase thermodynamic studies involving solid particles of various sizes. The accuracy of the developed algorithms is validated through a series of test cases, including single phase heat transfer, single-particle convective heat transfer, and fluidized bed cases. Numerical experiments are conducted to investigate the thermodynamic behavior of gas–liquid–solid three-phase systems in a fluidized bed comprising broadly graded particles. Based on the numerical results, the thermodynamic behavior of the three-phase particle flow is analyzed and the computational efficiency of the algorithms is evaluated. The results demonstrate that the CoSim-FVDEM developed in this study can be effectively applied to the thermodynamic analysis of large-scale multiphase particle flow.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563588","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":"Application of Discontinuity Layout Optimization to Metal Shells and Assemblies","authors":"John Valentino,&nbsp;Linwei He,&nbsp;Matthew Gilbert","doi":"10.1002/nme.70287","DOIUrl":"https://doi.org/10.1002/nme.70287","url":null,"abstract":"<p>Discontinuity Layout Optimization (DLO) provides a computationally efficient means of determining collapse loads and associated failure mechanisms across a wide spectrum of plasticity problems. The classical DLO method has focused separately on in-plane and out-of-plane plasticity. In the present work, the method is extended to thin-walled shell structures, where the interactions between in-plane and out-of-plane forces and moments are captured through both surface and point contact formulations. To assess the efficacy and generality of the approach, a series of benchmark problems are investigated, including metal sections, cylindrical and spherical shells, T-stub, end-plate connections and assemblies. The results are evaluated against theoretical equations, established numerical benchmarks from the literature and Eurocode standards, thereby demonstrating both the accuracy and practical relevance of the proposed formulations.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70287","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563591","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":"Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators","authors":"Julius Herb,&nbsp;Felix Fritzen","doi":"10.1002/nme.70277","DOIUrl":"https://doi.org/10.1002/nme.70277","url":null,"abstract":"<p>Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures. Designing such materials and predicting their behavior in practical applications requires solving homogenization problems typically governed by PDEs for a wide range of material parameters and microstructures. While classical numerical solvers offer reliable and accurate solutions supported by a solid theoretical foundation, their high computational costs and slow convergence remain limiting factors. As a result, scientific machine learning (ML) is emerging as a promising alternative, aiming to rapidly approximate solutions using surrogate models. However, such approaches often lack guaranteed accuracy and physical consistency. This raises the question of whether it is possible to develop hybrid approaches that combine the advantages of both data-driven methods and classical solvers. To address this, we introduce UNO-CG, a hybrid solver that accelerates conjugate gradient (CG) solvers using specially designed machine-learned preconditioners, while ensuring convergence by construction. As a preconditioner, we propose Unitary Neural Operators (UNOs) as a modification of the established Fourier neural operators (FNOs). Our method can be interpreted as a data-driven discovery of Green's functions, which are then used much like expert knowledge to accelerate iterative solvers. We evaluate UNO-CG on various homogenization problems involving materials with heterogeneous microstructures and millions of degrees of freedom (DOF). Our results demonstrate that UNO-CG enables a substantial reduction in the number of CG iterations and is competitive with handcrafted preconditioners for homogenization problems that involve expert knowledge. Moreover, UNO-CG maintains strong performance across a variety of boundary conditions, where many specialized solvers are not applicable, highlighting its versatility and robustness, which is supported by our extensive numerical study.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563590","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 Two-Stage Adaptive Kriging-Monte Carlo Method for Reliability-Based Design Optimization in Machining Accuracy Reliability Analysis of Five-Axis Computer Numerically Controlled Machine Tools","authors":"Zhiming Wang,&nbsp;Zhiqi Zhang,&nbsp;Gan Wu","doi":"10.1002/nme.70299","DOIUrl":"https://doi.org/10.1002/nme.70299","url":null,"abstract":"<div>\u0000 \u0000 <p>Efficient reliability analysis of high-dimensional and implicit limit-state functions remains a major challenge in reliability-based engineering design. Traditional Kriging-based reliability methods often suffer from high computational cost and reduced efficiency when dealing with such problems. To address these challenges, a general two-stage adaptive Kriging-Monte Carlo simulation (AK-MCS) method with a dynamic <i>HU</i> learning function is proposed in this study. In the proposed method, an accuracy index is introduced to divide the learning process into a global exploration stage and a local refinement stage, while a hybrid <i>HU</i> learning function dynamically integrates the <i>H</i> and <i>U</i> learning functions through an adaptive weighting coefficient to balance convergence efficiency and prediction accuracy. The effectiveness and accuracy of the proposed reliability analysis method are demonstrated through a machining accuracy reliability optimization problem of a five-axis computer numerically controlled (CNC) machine tool, which serves as a representative engineering application. The results show that the proposed method significantly reduces the number of required sample points while maintaining high computational efficiency and low relative error in reliability estimation. Furthermore, the application results indicate that the method can effectively support reliability-based design optimization by accurately evaluating both the mean and minimum reliability indices.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563399","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":"Massively Parallel Simulation of Enhanced Oil Recovery With Polymer Flooding via the Augmented Lagrangian Active Set Algorithm","authors":"Lei Jiang,&nbsp;Haijian Yang,&nbsp;Lijuan Shi","doi":"10.1002/nme.70292","DOIUrl":"https://doi.org/10.1002/nme.70292","url":null,"abstract":"<div>\u0000 \u0000 <p>Polymer injection, as a prevalent enhanced oil recovery technique in the oil and gas industry, involves injecting water mixed with high molecular weight polymers into the reservoir to enhance oil production. In this paper, we propose the black oil model with polymer injection, which aims to provide a more realistic simulation of multiphase flow in reservoirs by accounting for the complexities introduced by polymer injection. This multi-physics coupled reservoir model is an extension of the traditional black oil model, which is commonly used in reservoir engineering to simulate the multiphase flow of oil, gas, and water in porous media. The addition of polymer injection introduces complexities related to adsorption onto reservoir rock, changes in permeability and porosity, and non-Newtonian fluid behavior. To facilitate large-scale simulation, we present the augmented Lagrangian active set algorithm implemented on a parallel computing framework to solve the resultant nonlinear system of equations, which arises from the finite volume discretization of the governing equations on unstructured grids. Nonlinear strategies, including the variational inequality formulation, the Newton–Krylov subspace solver, and the backtracking globalization technique, are introduced to handle the high nonlinearity of the flow problem. Furthermore, a domain decomposition-based linear preconditioner is developed to enhance the efficiency and scalability of the proposed Newton-type active set algorithm. High-resolution reservoir simulation results are obtained and analyzed for benchmark projects as well as realistic reservoir problems on unstructured grids. The parallel performance of the algorithm is studied on a supercomputer, demonstrating scalability to tens of thousands of processor cores.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563398","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":"Breaking Barriers in High-Order Spectral Methods: The Intrinsic Matrix Approach","authors":"Osvaldo Guimarães,&nbsp;José R. C. Piqueira","doi":"10.1002/nme.70281","DOIUrl":"https://doi.org/10.1002/nme.70281","url":null,"abstract":"<p>This paper introduces a unified framework in Hilbert spaces for applying high-order differential operators in bounded domains using Chebyshev, Legendre, and Fourier spectral methods. By exploiting the banded structure of differentiation matrices and embedding boundary conditions directly into the operator through a scaling law relating functions to their derivatives, the proposed approach achieves optimal matrix conditioning, thereby enhancing numerical stability for high-order operators. Furthermore, it ensures consistent nodal and modal representations across Chebyshev, Legendre, and Fourier bases, consolidating similarity transformations. The method provides high accuracy for problems with inhomogeneous boundary conditions, eliminating the need for a priori polynomial factorization, and offers a generalized approach applicable to multi-point boundary value problems. Finally, an error bound estimation is presented using backward consistency analysis. The methodology is validated through theoretical analysis and numerical experiments, demonstrating its robustness and accuracy for high-order boundary value problems.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70281","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563400","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}