Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Back-Projection Diffusion: Solving the wideband inverse scattering problem with diffusion models","authors":"Borong Zhang ,&nbsp;Martin Guerra ,&nbsp;Qin Li ,&nbsp;Leonardo Zepeda-Núñez","doi":"10.1016/j.cma.2025.118036","DOIUrl":"10.1016/j.cma.2025.118036","url":null,"abstract":"<div><div>We present <em>Wideband Back-Projection Diffusion</em>, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure is factored into two steps: the first step, inspired by the filtered back-propagation formula, transforms data into a physics-based latent representation, while the second step learns a conditional score function conditioned on this latent representation. These two steps individually obey their associated symmetries and are amenable to compression by imposing the rank structure found in the filtered back-projection formula. Empirically, our framework has both low sample and computational complexity, with its number of parameters scaling only sub-linearly with the target resolution, and has stable training dynamics. It provides sharp reconstructions effortlessly and is capable of recovering even sub-Nyquist features in the multiple-scattering regime.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118036"},"PeriodicalIF":6.9,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071126","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":"Physics-informed non-intrusive reduced-order modeling of parameterized dynamical systems","authors":"Himanshu Dave ,&nbsp;Léo Cotteleer ,&nbsp;Alessandro Parente","doi":"10.1016/j.cma.2025.118045","DOIUrl":"10.1016/j.cma.2025.118045","url":null,"abstract":"<div><div>In this study, we present a new framework of physics-informed non-intrusive reduced-order modeling (ROM) of dynamical systems modeled by parametric, partial differential equations (PDEs). Given new time and parameter values of a PDE, the framework utilizes trained physics-informed ML models to quickly estimate high-fidelity solutions while simultaneously observing the constraints and dynamics of the system. In the <em>offline training</em> phase, proper orthogonal decomposition (POD) decomposes a training database of high-fidelity solutions into POD modes and POD coefficients. A feed-forward neural network is trained to map time-parameter values to the few dominant POD coefficients. The loss function is composed of two terms: (1) error between original data and reconstructed data and (2) PDE residuals where each term of the PDE is expressed using Galerkin expansion on the reduced basis composed of the most dominant POD modes. The PDE residuals are not evaluated using POD–Galerkin (reduced-order) equations. The novelty of this work lies in the construction of PDE residual term and an <em>a priori</em> analysis that allows one to select weighting factor (or Lagrange multiplier) ahead of it. It has been found that a physics-informed ROM minimizing the two terms generates new solutions orders-of-magnitude accurate than a vanilla ROM that minimizes only the first error term. Besides estimating reconstruction error on a database, the framework also allows estimation of reconstruction quality of different terms such as advection and diffusion in the PDE. This is expected to promote better integration and interpretation of ML in reduced-order modeling of dynamical systems. During the <em>online prediction</em> phase, given new values of time and parameters, the generalized coordinates are quickly estimated and used in reconstruction. High-fidelity solutions are thus obtained orders-of-magnitude faster than a conventional numerical simulation. The framework is demonstrated on 1D and 2D Burgers’ equations and an incompressible flow over a backward facing step.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118045"},"PeriodicalIF":6.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067233","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":"The Fast Forward Quantum Optimization Algorithm: A study of convergence and novel unconstrained optimization","authors":"Pritpal Singh","doi":"10.1016/j.cma.2025.118039","DOIUrl":"10.1016/j.cma.2025.118039","url":null,"abstract":"<div><div>The Fast Forward Quantum Optimization Algorithm (FFQOA) is a novel quantum-inspired heuristic search algorithm, drawing inspiration from the movement and displacement activities of wavefunctions associated with quantum particles. This algorithm has demonstrated remarkable effectiveness in predicting time series, clustering biomedical images, and optimizing the performance of convolutional neural networks. However, there has been no comprehensive study to investigate the convergence behavior and performance of FFQOA on standard optimization test functions. Motivated by this gap, we extend our research in three significant directions. First, we analyze the convergence behavior of FFQOA by studying the local and global displacements of its wavefunctions. To achieve this, martingale theory is employed to analyze the sequence of displacements, and we establish a necessary and sufficient condition for attaining the global convergence state of FFQOA. Second, we introduce 20 novel unconstrained optimization test functions, termed the <em>Singh optimization functions</em>. The mathematical properties of these functions are rigorously derived and comprehensively discussed. Finally, leveraging these optimization functions, the performance of FFQOA is evaluated and compared against well-established metaheuristic algorithms, including the Genetic Algorithm, Simulated Annealing, Cultural Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Firefly Algorithm, and Grey Wolf Optimizer. Our analysis reveals that most existing algorithms struggle to effectively balance exploration and exploitation in the early stages of iterations, often failing to achieve global convergence. In contrast, FFQOA not only satisfies the global convergence criteria but also consistently identifies the global optimal solutions for the proposed Singh optimization functions. [<strong>Source Code:</strong> The source code for this study is available upon request by contacting the author via emails at <span><span><span>[email protected]</span></span><svg><path></path></svg></span>, <span><span><span>[email protected]</span></span><svg><path></path></svg></span>].</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118039"},"PeriodicalIF":6.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143946574","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 stress-intensity-factor-driven phase field modeling of mixed mode fracture","authors":"Xuan Hu,&nbsp;Shaofan Li","doi":"10.1016/j.cma.2025.118058","DOIUrl":"10.1016/j.cma.2025.118058","url":null,"abstract":"<div><div>Conventional phase field modeling of fracture uses the degraded strain energy density (SED) at the crack tip as a material damage index to drive crack growth. To avoid non-physical evolution in crack phase-field, various SED splitting schemes have been adopted, resulting in the development of “anisotropic”-SED-based formulations to better capture the realistic crack nucleation and propagation under mixed-mode loading. In this work, we propose a stress-intensity-factor-driven (SIF-driven) phase field method as an alternative to achieve the same goal. By using the crack phase-field distribution as a marker for the material configurational change and leveraging the phase-field landscape and its gradient, the nonlocal SIF-powered fracture energy release rate near the crack tip is computed based on the principles of linear elastic fracture mechanics (LEFM). This nonlocal energy release rate is then incorporated into a variational phase field modeling framework as the driving force for material configurational changes, i.e. the crack phase-field evolution.</div><div>The proposed formulation is validated through multiple numerical examples, demonstrating its capability to capture mode I, mode II, and mixed-mode fracture behaviors without mesh dependency. The key contributions of this work include: (1) accurate representation of crack-tip stress asymptotic field, (2) precise prediction of crack growth and material failure without the need for additional splitting techniques, (3) introducing a physics-based stress-intensity-factor-governed crack driving force to replace the SED-based approach, thereby effectively bridging the gape between phase-field formulation for fracture and well-established LEFM theories, and (4) providing a numerically efficient and straightforward implementation that closely resembles that of conventional phase field methods. This work establishes a robust connection between the phase field method and the full-fledged fracture mechanics, offering a practical and physics-consistent tool for cleavage fracture analysis in engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118058"},"PeriodicalIF":6.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943622","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":"Strength-based concurrent topology and fiber orientation optimization considering different failure modes","authors":"Yongjia Dong,&nbsp;Hongling Ye,&nbsp;Jicheng Li,&nbsp;Sujun Wang,&nbsp;Weiwei Wang","doi":"10.1016/j.cma.2025.118086","DOIUrl":"10.1016/j.cma.2025.118086","url":null,"abstract":"<div><div>The designability of Continuous fiber-reinforced polymers (CFRPs) and the advance in additive manufacturing create more opportunities for tailorable topology and fiber-paths, thereby enhancing structural performance. However, challenges for structural optimization imposed by the complex failure modes of composite require further resolution. This study develops a novel strength-based optimization method for light-weight design of CFRP components. The global strength constraint considering failure modes is formulated based on the Hashin criterion and <em>p</em>-norm function. Multi-constrained lightweight design framework considering structural compliance and strength is established to optimize the structural topology and fiber orientation simultaneously. A fiber orientation filtering scheme is proposed to reduce the effect of stress concentration caused by discontinuous fiber orientation on optimization. Comprehensive numerical case studies validate the efficacy and stability of the developed methodology. Comparative analysis among the designs with Hashin criterion, Tsai-Wu criterion and stiffness-based is conducted to demonstrate the applicability and superiority of the presented approach. The effect of different aggregation coefficient, stress relaxation coefficient and initial fiber orientations on the optimization results are discussed. The developed methodology provides a theoretical foundation for multi-scale optimization of CFRP structures while mitigating the risk of structural failure.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118086"},"PeriodicalIF":6.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143946851","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 parallel parameterized level set method for large-scale structural topology optimization under design-dependent load","authors":"Peng Wei ,&nbsp;Ben Cheng ,&nbsp;Haoju Lin ,&nbsp;Hui Liu","doi":"10.1016/j.cma.2025.118032","DOIUrl":"10.1016/j.cma.2025.118032","url":null,"abstract":"<div><div>This paper proposes a topology optimization framework for three-dimensional continuum structures subjected to design-dependent loads, including gravity, centrifugal, and hydrostatic pressure loads. First, this study utilizes the parameterized level set method (PLSM) with unstructured meshes to effectively handle complex structural shapes and boundary conditions. Second, this work employs parallel computing techniques and uses the shape function as the basis function in PLSM to significantly enhance computational efficiency. Additionally, this study comprehensively analyzes design-dependent loads and addresses topology optimization of large-scale structures under complex load conditions. This study overcomes the lack of research on complicated 3D design-dependent load problems. It aims to broaden the application of topology optimization techniques, making them more applicable to engineering practices, such as large-scale underwater structures. Finally, several 3D examples demonstrate the proposed framework’s efficiency, stability, and ability to generate innovative structural designs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118032"},"PeriodicalIF":6.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943621","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":"Accelerating crash simulations with Finite Element Method Integrated Networks (FEMIN): Comparing two approaches to replace large portions of a FEM simulation","authors":"Simon Thel ,&nbsp;Lars Greve ,&nbsp;Maximilian Karl ,&nbsp;Patrick van der Smagt","doi":"10.1016/j.cma.2025.118046","DOIUrl":"10.1016/j.cma.2025.118046","url":null,"abstract":"<div><div>The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks (FEMIN) framework integrates neural networks (NNs) with FEM solvers. We discuss two different approaches to integrate the predictions of NNs into explicit FEM simulation: A coupled approach predicting forces (f-FEMIN) and a newly introduced, uncoupled approach predicting kinematics (k-FEMIN). For the f-FEMIN approach, we introduce a novel adaption of the Deep Variational Bayes Filter (DVBF). The adapted DVBF outperforms deterministic NNs from a previous study in terms of accuracy. We investigate the differences of the two FEMIN approaches across two small-scale and one large-scale load case. Although the adaptation of the DVBF and the f-FEMIN approach offers good accuracy for the small-scale load cases, the k-FEMIN approach is superior for scaling to large-scale load cases. k-FEMIN shows its excellent acceleration of the FEM crash simulations without overhead during runtime and keeps compute costs during training low.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118046"},"PeriodicalIF":6.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936700","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":"Goal-oriented dual-weighted residual error estimation for the Virtual Elements Method","authors":"C. Sellmann,&nbsp;P. Junker","doi":"10.1016/j.cma.2025.118034","DOIUrl":"10.1016/j.cma.2025.118034","url":null,"abstract":"<div><div>Goal-oriented a posteriori error estimation is crucial for solving partial differential equations (PDEs) efficiently and reliably. The Virtual Element Method (VEM) shows promise in this context due to its ability to handle general polygonal elements, eliminating the need for special treatment of hanging nodes. However, a suitable framework for goal-oriented error estimation in VEM has not been developed so far. This work addresses this gap by deriving an appropriate estimator formulation for linear PDEs using VEM. We tackle two key challenges for first-order Virtual Elements: approximating virtual basis functions within elements and efficiently approximating the exact adjoint solution, where standard methods used for finite element approximations are not suitable. To overcome these challenges, we introduce new techniques, including the Gauss-Point Reconstruction Method (GPRM). Our theoretical developments are verified through diverse numerical experiments, demonstrating their correctness and effectiveness. We further showcase the practical utility of our framework through its application to adaptive mesh refinement, which enhances solution accuracy while optimizing computational resources. This work lays the foundation for extending goal-oriented error estimation to more complex problems using VEM.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118034"},"PeriodicalIF":6.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943634","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":"Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations","authors":"Jesús Bonilla ,&nbsp;Juan Vicente Gutiérrez-Santacreu","doi":"10.1016/j.cma.2025.118035","DOIUrl":"10.1016/j.cma.2025.118035","url":null,"abstract":"<div><div>We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118035"},"PeriodicalIF":6.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936702","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":"Parametric Gaussian quadratures for discrete unified gas kinetic scheme","authors":"Lu Wang,&nbsp;Hong Liang,&nbsp;Jiangrong Xu","doi":"10.1016/j.cma.2025.118053","DOIUrl":"10.1016/j.cma.2025.118053","url":null,"abstract":"<div><div>The discrete unified gas kinetic scheme (DUGKS) has emerged as a promising Boltzmann solver capable of effectively capturing flow physics across all Knudsen numbers. However, simulating rarefied flows at high Knudsen numbers remains computationally demanding. This paper introduces a parametric Gaussian quadrature (PGQ) rule designed to improve the computational efficiency of DUGKS. The PGQ rule employs Gaussian functions for weighting and introduces several novel forms of higher-dimensional Gauss–Hermite quadrature. Initially, the velocity space is mapped to polar or spherical coordinates using a parameterized integral transformation method, which converts multiple integrals into repeated parametric integrals. Subsequently, Gaussian points and weight coefficients are computed based on the newly defined parametric weight functions. The parameters in PGQ allow the distribution of Gaussian points to be adjusted according to computational requirements, addressing the limitations of traditional Gaussian quadratures where Gaussian points are difficult to match the distribution of real particles in rarefied flows. To validate the proposed approach, numerical examples across various Knudsen numbers are provided. The simulation results demonstrate that PGQ offers superior computational efficiency and flexibility compared to the traditional Newton–Cotes rule and the half-range Gaussian Hermite rule, achieving computational efficiency that is tens of times higher than that of the Newton–Cotes method. This significantly enhances the computational efficiency of DUGKS and augments its ability to accurately simulate rarefied flow dynamics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118053"},"PeriodicalIF":6.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936699","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}