International Journal for Numerical Methods in Engineering最新文献

{"title":"Fracture Modeling of Nearly Incompressible Hyperelastic Materials: A Phase-Field Approach via Simo–Taylor–Pister Three-Field Variation","authors":"Le Zhang,&nbsp;Bin Li,&nbsp;Dong Zhao,&nbsp;Bo Yin,&nbsp;Michael Kaliske","doi":"10.1002/nme.70436","DOIUrl":"https://doi.org/10.1002/nme.70436","url":null,"abstract":"<p>Incompressibility is commonly observed in the majority of hyperelastic materials, which are fundamental to a wide range of technical applications owing to their distinctive properties, particularly their flexibility, stretchability, and resilience. However, the incompressibility constraint poses a significant challenge in modeling such materials, further complicating efforts to accurately describe or reproduce crack propagation through numerical simulations. Mixed element formulations, for example, the so-called Q1P0 approach, are extensively employed to mitigate locking issues associated with incompressibility at finite deformations. In this study, the Q1P0 approach is formulated via the Simo–Taylor–Pister (STP) three-field formulation, which emanates from the <span>Hu-Washizu</span> variational principle, resulting in an equivalent single-field displacement formulation. This framework is subsequently coupled with the phase-field method to predict finite strain fracture of nearly incompressible hyperelastic materials. To the best of the authors' knowledge, this represents the first successful coupling of the phase-field approach with the STP-based Q1P0 formulation. Through a consistent derivation and condensation of the pressure field, the novel four-field formulation is reduced to a pure displacement-phase-field approach. This reduction constitutes a major advantage of the proposed formulation, as it preserves the size of the global system without introducing additional degrees of freedom. To alleviate the innate conflict between the incompressibility constraint and diffuse crack opening, a tailored phase-field degradation function is integrated into the volumetric contribution, accelerating pressure release and thereby facilitating crack opening. Accordingly, the incompressibility constraint is relaxed in damaged material while remaining strictly enforced in intact material. The proposed formulation offers two more benefits: (i) it provides enhanced generality and applicability with respect to the choice of the volumetric strain-energy function, and (ii) it results in a physically consistent material response in both the nearly incompressible and the compressible regimes. Subsequently, several numerical examples are presented to illustrate the characteristics of the proposed formulation.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 19","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099427","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":"Topology Optimization With a Local-Like Global Stress Constraint Using a Fully Differentiable Aggregation Function","authors":"Tarcísio Ladeia de Oliveira,&nbsp;Jonas de Carvalho,&nbsp;Alessandro Roger Rodrigues","doi":"10.1002/nme.70434","DOIUrl":"https://doi.org/10.1002/nme.70434","url":null,"abstract":"<p>Over the last few decades, topology optimization (TO) has been developed into a valuable optimization method in many engineering fields. In structural optimization, limiting maximum mechanical stress is critical to the design of safe and reliable structures, a constraint that can be handled using TO. However, the non-differentiability of the calculation of maximum stress, as well as the local nature of stress, led to a variety of approaches, such as smooth aggregation functions and Lagrange-based local stress constraints, each with its own advantages and disadvantages. This paper, however, proposes a new aggregation function which is able to combine the strengths of both of those approaches: it consists of a single aggregated constraint which behaves similarly to local stress constraints. Some sample problems are used to illustrate its properties as well as the effects of the parameters it requires, so that the appropriate ones may be chosen for each problem. It is shown that it manages to obtain topologies with highly homogeneous stress distributions, with maximum stress arbitrarily close to the specified limit (but generally less than it), although it depends on the correct choice of parameters in order to avoid undesirable oscillations in the optimization process.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 19","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70434","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099413","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 Second-Order Fully Decoupled Scheme and Its Optimal Finite Element Error Estimate for a Two-Phase Magnetohydrodynamics Model","authors":"Dongmei Duan,&nbsp;Fuzheng Gao,&nbsp;Xiaoming He,&nbsp;Yanping Lin","doi":"10.1002/nme.70433","DOIUrl":"https://doi.org/10.1002/nme.70433","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes a fully decoupled, linear, second-order accurate, fully discrete numerical scheme with unconditional energy stability for the reformulated two-phase magnetohydrodynamics model. The reformulation itself is achieved by unifying the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods via a time-dependent auxiliary variable. The scheme achieves second-order temporal accuracy by second-order backward differential formula (BDF2), realizes decoupling and linearity among the phase, flow, and magnetic fields via the unified SAV–ZEC method and a fully explicit treatment of the nonlinear terms and their coefficients, and attains intra-field decoupling within the flow field by the second-order pressure-correction projection method. The unconditional energy stability and optimal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^2 $$</annotation>\u0000 </semantics></math> error estimate of the scheme are established. One simplification in the phase-field analysis involves embedding the inverse of discrete Laplacian into the test functions. This embedding induces an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^2 $$</annotation>\u0000 </semantics></math>–<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}^{-2} $$</annotation>\u0000 </semantics></math> norm transformation, which allows the associated terms to be estimated directly. One technique to achieve second-order temporal accuracy involves an auxiliary function that incorporates a first-order temporal pressure approximation for canceling the lower-order temporal terms. The introduction of a Stokes quasi-projection operator similarly prevents the loss of the spatial convergence rate. Four numerical examples are presented to verify the efficacy of the proposed scheme.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149047999","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":"Multiphysics Simulation of Positive Streamer Discharge in Air Using Finite Element Method","authors":"Hasupama Jayasinghe,&nbsp;Bilen Emek Abali,&nbsp;Liliana Arevalo,&nbsp;Vernon Cooray","doi":"10.1002/nme.70417","DOIUrl":"https://doi.org/10.1002/nme.70417","url":null,"abstract":"<p>Streamer discharge modeling by means of the Finite Element Method (FEM) presents a formidable challenge in computational physics due to its nonlinear and convection-dominated characteristics that cause numerical instabilities, including negative densities of charged particles. A possible remedy relies on modifying the numerical scheme using flux correction or stabilization techniques, yet their effects on numerical accuracy are unexplored. This study presents a detailed and rigorous implementation of two different FEM approaches: with and without modifications to the numerical scheme. We investigate how different solution strategies, including fully coupled versus staggered schemes and time discretization techniques affect the solution. All FEM approaches are implemented within the open-source Firedrake framework. A comprehensive comparison against benchmark data of 2D streamer discharge is performed to evaluate the accuracy of each approach and to quantify the impact of the chosen coupling strategy and time discretization on key streamer parameters such as maximum electric field, streamer length, and the total charge. The results show that both approaches provide an accurate description of the streamer dynamics and the resulting discharge channel with varying levels of numerical efficiency. The choice of coupling strategy, inclusion of source stabilization and the time discretization method further alter streamer front dynamics, stability, and computational cost, demonstrating that these numerical design choices in FEM have a measurable impact on the streamer dynamics.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70417","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149047998","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":"Regularity and Numerical Analysis of Multi-Term General Fractional Advection-Diffusion Equations With Scale and Weight Dependencies","authors":"Shivani Gupta,&nbsp;Rahul Kumar Maurya,&nbsp;Vineet Kumar Singh","doi":"10.1002/nme.70432","DOIUrl":"https://doi.org/10.1002/nme.70432","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This article investigates a multi-term general fractional advection-diffusion equation, where the time derivative is a general Caputo fractional operator incorporating a weight and a strictly increasing scale function. First, the analytical solution is derived using the weighted Laplace transform and the weighted Fourier sine transform. A thorough regularity analysis of the solution is then conducted, revealing that it exhibits a weak singularity at the initial time &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ t=0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, characterized by a term of the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(1+{left(xi (t)-xi (0)right)}^{alpha_1-l}right),0&lt;{alpha}_1&lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This initial layer necessitates specialized temporal discretizations. To handle this singularity effectively, we develop and analyze a numerical scheme. The temporal discretization is implemented on uniform, graded, and adaptive meshes, while a high-order compact difference scheme is employed for the spatial domain. The adaptive ","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994270","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 Multiobjective Topology Optimization Method Based on Modified Hypervolume Increment","authors":"Zheng Li,&nbsp;Yongcheng Song,&nbsp;Xuyuan Miao,&nbsp;Shilun Ruan,&nbsp;Junfeng Gu,&nbsp;Genzi Li,&nbsp;Changyu Shen","doi":"10.1002/nme.70431","DOIUrl":"https://doi.org/10.1002/nme.70431","url":null,"abstract":"<div>\u0000 \u0000 <p>The topology optimization involves time-consuming numerical simulations; therefore, it is desired to achieve a high quality Pareto set with a limit number of optimizations when there are multiple conflicted objectives. In this paper, a high-performance multiobjective topology optimization method is developed. The basic idea is to maximize the hypervolume, which is the only quality metric with Pareto consistency. The sparse regions of Pareto points are identified by the local potential hypervolume increment, and a modified hypervolume increment function is adopted to search the new Pareto point. The developed method is compared to several existing approaches based on five examples. The results show that the developed method performs the best, and the advantage is more obvious with more objectives.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994551","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":"Numerical Models for the Scattering Properties of Multilayered Structures With Periodic Cells","authors":"Mathilde Maréchal,&nbsp;Olivier Dazel,&nbsp;Vicente Romero-García,&nbsp;Jean-Philippe Groby","doi":"10.1002/nme.70429","DOIUrl":"https://doi.org/10.1002/nme.70429","url":null,"abstract":"<div>\u0000 \u0000 <p>The objective of this work is to model the acoustic response of multilayered structures composed of both homogeneous layers and periodic cells so as to obtain their scattering properties (i.e., reflection and transmission coefficients). The host material of each layer is either elastic, fluid, or poroelastic. The homogeneous layers are modelled with waves, while the periodic layers are modelled with higher-order FEM. Two modelling methods from the literature, the Global Method and the Transfer Matrix Method, initially dedicated to the modelling of stacks of homogeneous layers, are extended. They are then tested on examples from the literature or adaptations thereof, to cover a complete panel of test configurations. Additionally, a comparison of results obtained via a commercial finite element software is proposed. Results confirm that the methods are well suited to higher-order finite elements and also show that, while the method derived from the Transfer Matrix Method suffers from stability issues, those derived from the Global Method remain stable for all studied configurations.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994259","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":"Material Point Method-Based One-Step Inverse Forming Analysis for Non-Matching Interfaces","authors":"Changsheng Wang,&nbsp;Jingyu Mu,&nbsp;Bohan Xing","doi":"10.1002/nme.70430","DOIUrl":"https://doi.org/10.1002/nme.70430","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a unified iCPDI2-based computational framework for one-step inverse forming of complex sheet metal parts with non-matching interfaces. The formulation consists of two main stages: A linear elastic reverse deformation stage for initial solution estimation, and an implicit plastic solution stage that accounts for material nonlinearity and predicts the post-forming distributions of thickness, equivalent strain, and equivalent stress. By introducing an Eulerian background grid as a kinematic mediator, the method decouples the physical domain from the computational domain. The momentum equations defined on the non-matching physical domain are mapped onto a matching background grid for solution, thereby effectively resolving the challenges associated with non-matching interfaces in CAE simulations of complex components. The proposed method is validated through three numerical examples. The results show that it achieves high accuracy relative to standard FEM solutions, effectively handles non-matching interfaces, and accurately predicts the post-forming distributions of thickness, equivalent strain, and equivalent stress. These findings confirm the effectiveness and robustness of the proposed approach for inverse forming analysis of complex sheet metal components with non-matching interfaces.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148950550","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":"Direct Construction of Quantized Tensor Trains With Small Rank for Laplace- or Gaussian-Transformed Analytic Functions","authors":"Katsuhiro Endo,&nbsp;Kazuaki Z. Takahashi","doi":"10.1002/nme.70391","DOIUrl":"https://doi.org/10.1002/nme.70391","url":null,"abstract":"<p>Preparing quantum states with desired amplitude distributions is a key bottleneck in the implementation of quantum linear and nonlinear dynamics solvers, including Linear Combination of Hamiltonian Simulation (LCHS) and Schrödingerization. We present a direct, closed-form construction of Quantized Tensor Train (QTT) representations for two important classes of analytic functions—Laplace-transformed and Gaussian-transformed functions—which include the states required for implementing LCHS and Schrödingerization. Our approach removes the need for data-driven QTT construction procedures, such as TT-SVD or TT-Cross, which often lack analytical rank-accuracy guarantees. Instead, we utilize the analytic structure of these functions through a double-exponential quadrature formula and truncated polynomial approximation. Using these techniques, we establish provable bounds: such Laplace-transformed functions admit QTT representations with TT-rank <span></span><math>\u0000 <mrow>\u0000 <mover>\u0000 <mrow>\u0000 <mi>𝒪</mi>\u0000 </mrow>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>log</mi>\u0000 <mi>ϵ</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>, while Gaussian-transformed functions admit TT-rank <span></span><math>\u0000 <mrow>\u0000 <mover>\u0000 <mrow>\u0000 <mi>𝒪</mi>\u0000 </mrow>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>log</mi>\u0000 <mi>ϵ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>9</mn>\u0000 <mo>/</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow></math> to achieve a target accuracy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ϵ</mi>\u0000 </mrow>\u0000 <annotation>$$ epsilon $$</annotation>\u0000 </semantics></math>. Moreover, applying data-driven rank minimization to our analytically constructed QTTs further reduces maximal TT-ranks without sacrificing accuracy. The resulting pipeline provides analytically controlled, implementation-ready QTTs, which effectively reduce the cost of state preparation in quantum algorithms and suggest a path toward closed-form QTTs for broader classes of functions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 18","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70391","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148950551","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":"Hybrid Coupling With Operator Inference and the Overlapping Schwarz Alternating Method","authors":"Irina Tezaur,&nbsp;Eric Parish,&nbsp;Anthony Gruber,&nbsp;Ian Moore,&nbsp;Christopher Wentland,&nbsp;Alejandro Mota","doi":"10.1002/nme.70408","DOIUrl":"https://doi.org/10.1002/nme.70408","url":null,"abstract":"<p>This paper presents a hybrid approach for coupling subdomain-local, nonintrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local, high-fidelity full order models (FOMs) using the overlapping Schwarz alternating method (O-SAM). The proposed methodology addresses significant challenges in multiscale modeling and simulation, particularly the long runtime and complex mesh generation requirements associated with traditional high-fidelity simulations. By leveraging the flexibility of O-SAM, we enable the seamless integration of disparate models, meshes, and time integration schemes, enhancing computational efficiency while maintaining high accuracy. Our approach is demonstrated through a series of numerical experiments on increasingly complex three-dimensional solid dynamics problems, showcasing speedups of up to 106 times compared to conventional FOM–FOM couplings. This work paves the way for more efficient simulation workflows in engineering applications, with potential extensions to a wide range of partial differential equations.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70408","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942668","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}