Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Decomposition-free variational quantum linear solver: Application in computational mechanics","authors":"Yongchun Xu ,&nbsp;Heng Hu","doi":"10.1016/j.cma.2025.118396","DOIUrl":"10.1016/j.cma.2025.118396","url":null,"abstract":"<div><div>Solving a linear system of equations is a fundamental task in computational mechanics. The recently proposed variational quantum linear solver (VQLS) offers potential acceleration for this task by using quantum computing. However, its application faces a critical bottleneck: the costly requirement to decompose the coefficient matrix into a linear combination of unitary matrices. In this work, we propose a decomposition-free variational quantum linear solver (DF-VQLS) that eliminates this requirement, enabling direct application without matrix decomposition. The key innovation lies in proposing two vectorization techniques, which map the cost functions of VQLS to the inner product of vectors. Specifically, the vectorization techniques reshape the matrix into a vector, and only manipulations on the vector are needed to compute the cost functions, thereby eliminating matrix decomposition entirely. The convergence and accuracy of the proposed method are validated through numerical examples on a quantum simulator. Three application examples in computational mechanics, including bar, truss, and two-dimensional continuum problems, are also presented to show the potential feasibility.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118396"},"PeriodicalIF":7.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Virtual element methods for HJB equations with Cordes coefficients","authors":"Ying Cai ,&nbsp;Hailong Guo ,&nbsp;Zhimin Zhang","doi":"10.1016/j.cma.2025.118362","DOIUrl":"10.1016/j.cma.2025.118362","url":null,"abstract":"<div><div>In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients. By incorporating stabilization terms, we establish the well-posedness of the proposed methods, thus avoiding the need to construct a discrete Miranda-Talenti estimate. We derive the optimal error estimate in the discrete <span><math><msup><mi>H</mi><mn>2</mn></msup></math></span> norm for both numerical formulations. Furthermore, a semismooth Newton’s method is employed to linearize the discrete problems. Several numerical experiments using the lowest-order VEMs are provided to demonstrate the efficacy of the proposed methods and to validate our theoretical results.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118362"},"PeriodicalIF":7.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantized local reduced-order modeling in time (ql-ROM)","authors":"Antonio Colanera ,&nbsp;Luca Magri","doi":"10.1016/j.cma.2025.118393","DOIUrl":"10.1016/j.cma.2025.118393","url":null,"abstract":"<div><div>Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous density, which makes the design of a single (global) nonlinear reduced-order model (ROM) challenging. In this paper, we turn this around. Instead of modeling the manifold with one single model, we partition the manifold into clusters within which the dynamics are locally modeled. This results in a quantized local reduced-order model (ql-ROM), which consists of (i) quantizing the manifold via unsupervised clustering; (ii) constructing intrusive ROMs for each cluster; and (iii) connecting the switching of local models with a change of basis and assignment functions. We test the method on two nonlinear partial differential equations, i.e., the Kuramoto-Sivashinsky and 2D Navier-Stokes equations (Kolmogorov flow), across bursting, chaotic, quasiperiodic, and turbulent regimes. The local models are built via Galerkin projection onto the local principal directions, which are centered on the cluster centroids. The dynamics are modeled by switching the local ROMs based on the cluster proximity. The proposed ql-ROM framework has three advantages over global ROMs (g-ROMs): (i) numerical stability, (ii) improved short-term prediction accuracy in time, and (iii) accurate prediction of long-term statistics, such as energy spectra and probability distributions. The computational overhead is minimal with respect to g-ROMs. The proposed framework retains the interpretability and simplicity of intrusive projection-based ROMs, whilst overcoming their limitations in modeling complex, high-dimensional, nonlinear dynamics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118393"},"PeriodicalIF":7.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Midplane based 3D single pass unbiased segment-to-segment contact interaction using penalty method","authors":"Indrajeet Sahu,&nbsp;Nik Petrinic","doi":"10.1016/j.cma.2025.118335","DOIUrl":"10.1016/j.cma.2025.118335","url":null,"abstract":"<div><div>This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. Contact tractions between interacting discrete segments are evaluated with respect to a midplane in a single pass, inherently maintaining traction equilibrium. These tractions are based on the penalisation of true interpenetration between opposite surfaces, and the procedure of their integral for discrete contacting segments is described. A detailed examination of the possible geometric configurations of interacting 3D segments is provided to support visual understanding and better traction evaluation accuracy. The accuracy and robustness of the proposed method are validated against the analytical solutions of the contact patch test and Hertzian contact, demonstrating the capability to reproduce contact between flat and curved surfaces. The method passes the contact patch test with the uniform transmission of contact pressure matching the accuracy levels of finite elements. It converges towards the analytical solution with appropriate mesh refinement and a suitably high penalty factor in Hertzian contact. Dynamic problems involving elastic and inelastic collisions between two bars, as well as oblique collisions of cylinders, are also presented. The ability of the algorithm to resolve contacts between flat and curved surfaces in nonconformal meshes for both static and dynamic cases with high accuracy demonstrates its versatility for general contact problems, including self-contact.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118335"},"PeriodicalIF":7.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear model reduction using spectral proper orthogonal decomposition","authors":"Peter Frame ,&nbsp;Cong Lin ,&nbsp;Oliver T. Schmidt ,&nbsp;Aaron Towne","doi":"10.1016/j.cma.2025.118382","DOIUrl":"10.1016/j.cma.2025.118382","url":null,"abstract":"<div><div>Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire trajectory of the state over some time interval of interest and then solve for the static coefficients that encode the trajectory on the interval. We use spectral proper orthogonal decomposition (SPOD) modes, which are provably optimal for representing long trajectories and substantially outperform any representation of the trajectory in a purely spatial basis (e.g., POD). We develop a method to solve for the SPOD coefficients that encode the trajectories for forced linear dynamical systems given the forcing and initial condition, thereby obtaining the accurate prediction of the dynamics afforded by the SPOD representation of the trajectory. The method, which we refer to as spectral solution operator projection (SSOP), is derived by projecting the general time-domain solution for a linear time-invariant system onto the SPOD modes. We demonstrate the new method using two examples: a linearized Ginzburg-Landau equation and an advection-diffusion problem. In both cases, the error of the proposed method is orders of magnitude lower than that of POD-Galerkin projection and balanced truncation. The method is also fast, with CPU time comparable to or lower than both benchmarks in our examples. Finally, we describe a data-free space-time method that is a derivative of the proposed method and show that it is also more accurate than balanced truncation in most cases.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118382"},"PeriodicalIF":7.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 meshfree superconvergent Gradient Smoothing Stabilized Collocation Method (GSSCM) for large deformation problems: A concise discretized form","authors":"Zhiyuan Xue ,&nbsp;Lihua Wang ,&nbsp;Yan Li ,&nbsp;Magd Abdel Wahab","doi":"10.1016/j.cma.2025.118364","DOIUrl":"10.1016/j.cma.2025.118364","url":null,"abstract":"<div><div>The strong form Direct Collocation Method (DCM) with Reproducing Kernel (RK) shape function is hindered in its development due to its computational complexity and low efficiency in derivative calculations. Furthermore, the nonlinear large deformation governing equations in strong form, which involve intricate derivative terms, introduce additional challenges for discretization and iterative solutions. This paper proposes a novel efficient and superconvergent Gradient Smoothing Stabilized Collocation Method (GSSCM) using RK shape function. Based upon the divergence theorem, the proposed method converts traditional subdomain integration in the Stabilized Collocation Method (SCM) into subdomain boundary integration by gradient smoothing, which reduces the order of derivatives and simplifies the discretized terms of governing equations. This allows RK shape function with low-order basis functions like the linear basis functions, and enhances computational efficiency. GSSCM ensures exact integration using low-order Gaussian quadrature and improves solution stability. Both conforming and non-conforming smoothing domain are constructed for the gradient smooth. The incremental Newton-Raphson iteration approach is employed to solve the nonlinear discrete equations. Numerical results demonstrate that the proposed approach achieves superconvergent rates when odd RK basis functions are used. The GSSCM can also outperform traditional DCM, SCM and Superconvergent Gradient Smoothing Meshfree Collocation (SGSMC) method with gradient smoothing of shape function in terms of computational efficiency under the same accuracy. Moreover, GSSCM-II with conforming integration subdomains generally outmatches GSSCM-I and SCM with non-conforming subdomains in accuracy, efficiency and stability. The advantages of GSSCMs hold significant promise for nonlinear solid mechanics and engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118364"},"PeriodicalIF":7.3,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fully GPU-accelerated, matrix-free immersed boundary method for complex fiber-reinforced hyperelastic cardiac models","authors":"Pengfei Ma ,&nbsp;Li Cai ,&nbsp;Xuan Wang ,&nbsp;Hao Gao","doi":"10.1016/j.cma.2025.118353","DOIUrl":"10.1016/j.cma.2025.118353","url":null,"abstract":"<div><div>The immersed boundary (IB) method has become a leading approach in cardiac fluid-structure interaction (FSI) modeling due to its ability to handle large deformations and complex geometries without requiring mesh regeneration. However, the use of nonlinear, fiber-reinforced hyperelastic materials for modeling soft cardiac tissues introduces challenges in computational efficiency, particularly due to the additional projection steps required for stability in the IB framework. These steps often involve sparse matrix storage and computation, which can degrade GPU performance. In this work, we present a fully GPU-accelerated, matrix-free IB method for FSI in anatomically realistic cardiac models, which novelly integrates established components into a unified, GPU-optimized system. By employing nodal coupling, our method eliminates the need for projection operations in the finite element space. Additionally, we solve the Navier-Stokes equations using Chorin’s projection method combined with a matrix-free geometric multigrid solver, ensuring the entire FSI algorithm remains matrix-free and highly compatible with GPU acceleration. Our implementation features several GPU-specific optimizations, including the use of constant memory to store values of nodal basis functions and their derivatives at quadrature points, and texture memory to efficiently implement the semi-Lagrangian discretization of convection terms. These innovations maximize GPU utilization while preserving the complex mechanical behavior of soft cardiac tissue. Benchmark tests demonstrate that our GPU-accelerated solver achieves a <span><math><mrow><mn>50</mn><mo>×</mo><mspace></mspace><mo>−</mo><mspace></mspace><mn>100</mn><mo>×</mo></mrow></math></span> speedup compared to a 20-core CPU implementation, with comparable accuracy. Critically, this performance enables clinically viable cardiac valve FSI simulations to be completed within a few hours on a single consumer-grade GPU-an achievement that was previously infeasible using traditional CPU-based frameworks.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118353"},"PeriodicalIF":7.3,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 phase-field cohesive fracture model free from the length scale constraints","authors":"Lu Hai ,&nbsp;Ye Feng","doi":"10.1016/j.cma.2025.118374","DOIUrl":"10.1016/j.cma.2025.118374","url":null,"abstract":"<div><div>In conventional phase-field cohesive fracture methods, an upper bound on the phase-field length scale parameter is typically imposed to ensure the convexity of the energy degradation function. However, this constraint can result in substantial computational costs when analyzing large-scale structures, geological fractures, or fractures in high-strength materials. To overcome this limitation, this work introduces a novel field variable that guarantees the convexity of the energy degradation function is always satisfied, thereby eliminating the physical constraint on the phase-field length scale parameter. Based on this innovation, a new class of phase-field cohesive fracture models is formulated using a variational approach, and the intrinsic relationship between the characteristic function and the cohesive law is established through the one-dimensional analytical solution. Both implicit and explicit dynamic algorithms are developed for the numerical implementation of the model. The effectiveness and robustness of the proposed approach are demonstrated through simulations of several typical fracture problems. The results indicate that the model can efficiently and accurately address large-scale fracture and high-strength material failure analyses, while maintaining insensitivity to the phase-field length scale parameter in both static and dynamic cases. These findings highlight the model’s potential for broad application in the computational analysis of complex fracture phenomena.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118374"},"PeriodicalIF":7.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"History-aware neural operator: Robust data-driven constitutive modeling of path-dependent materials","authors":"Binyao Guo,&nbsp;Zihan Lin,&nbsp;QiZhi He","doi":"10.1016/j.cma.2025.118358","DOIUrl":"10.1016/j.cma.2025.118358","url":null,"abstract":"<div><div>This study presents an end-to-end learning framework for data-driven modeling of path-dependent inelastic materials using neural operators. The novel framework is built on the premise that the irreversible evolution of material responses, governed by hidden dynamics, can be inferred from observable data. We develop the History-Aware Neural Operator (HANO), an autoregressive model that predicts path-dependent material responses from short segments of recent strain-stress history without relying on hidden state variables, thereby overcoming the self-consistency issues commonly encountered in recurrent neural network (RNN)-based models. Built on a Fourier-based neural operator backbone, HANO enables discretization-invariant learning. To further enhance its ability to capture both global loading patterns and critical local path dependencies, we embed a hierarchical self-attention mechanism that facilitates multiscale feature extraction. Beyond ensuring self-consistency, HANO mitigates sensitivity to initial hidden states, a commonly overlooked issue that can lead to instability in recurrent models when applied to generalized loading paths. By modeling stress-strain evolution as a continuous operator rather than relying on fixed input-output mappings, HANO naturally accommodates varying path discretizations and exhibits robust performance under complex conditions, including irregular sampling, multi-cycle loading, noisy data, and pre-stressed states. We evaluate HANO on two benchmark problems: elastoplasticity with hardening and progressive anisotropic damage in brittle solids. Results show that HANO consistently outperforms baseline models in predictive accuracy, generalization, and robustness. With its demonstrated capabilities and discretization-invariant design, HANO provides an effective and flexible data-driven surrogate for simulating a broad class of inelastic materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118358"},"PeriodicalIF":7.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixed-depth physics-informed neural network with nested activation mechanism in solving partial differential equations","authors":"Tianhao Wang ,&nbsp;Guirong Liu ,&nbsp;Eric Li ,&nbsp;Xu Xu","doi":"10.1016/j.cma.2025.118356","DOIUrl":"10.1016/j.cma.2025.118356","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) have become promising tools for solving complex partial differential equations (PDEs), but traditional PINNs suffered from slow convergence, vanishing gradients, and poor handling of local physical features. This paper proposes a mixed-depth physics-informed neural network (<em><span>md</span></em>-PINN) for solving the complex PDEs, aiming to improve the efficiency of network structure and activation function. The contributions are two aspects: (1) the <em><span>md</span></em>-PINN includes the various mixed-depth blocks, each of which contains parallel connected deep sub-network and shallow sub-network. The deep sub-network captures complex physical features, ensuring a comprehensive understanding of the system; while the shallow sub-network focuses on the basic physical features, facilitating the stable training; (2) the <em><span>md</span></em>-PINN introduces a new <em><span>nest-tanh</span></em>(.) activation functions with nested mechanism in shallow sub-networks to enable efficient extraction of complex features using fewer hidden layers, reducing reliance on deep networks. By incorporating mixed-depth structures, <em><span>md</span></em>-PINN enables more efficient information sharing across different layer, leading to faster convergence and improved training efficiency. Theoretical analysis demonstrates that <em><span>md</span></em>-PINN avoids suboptimal convergence with appropriate initialization. The proposed approach is validated across multiple PDEs, including heat transfer scenarios with complex boundaries, bi-material solid mechanical problems, Allen-Cahn equation, fluid dynamics, and the higher order Kuramoto-Sivashinsky equation. Results show that <em><span>md</span></em>-PINN exhibits the superior capabilities in approximating and capturing intricate system features. These findings underscore the computational efficiency and potential of <em><span>md</span></em>-PINN in tackling real-world and complex problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118356"},"PeriodicalIF":7.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}