Computer Methods in Applied Mechanics and Engineering最新文献

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A theoretically-consistent parallel enrichment strategy for Bayesian active learning reliability analysis
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117752
Tong Zhou , Tong Guo , Xujia Zhu , Masaru Kitahara , Jize Zhang
{"title":"A theoretically-consistent parallel enrichment strategy for Bayesian active learning reliability analysis","authors":"Tong Zhou ,&nbsp;Tong Guo ,&nbsp;Xujia Zhu ,&nbsp;Masaru Kitahara ,&nbsp;Jize Zhang","doi":"10.1016/j.cma.2025.117752","DOIUrl":"10.1016/j.cma.2025.117752","url":null,"abstract":"<div><div>Although parallel active learning reliability analysis is promising and has been widely studied, there remains an open question regarding how to achieve better theoretical consistency and avoid reliance on empirical practices heavily. A new parallel Bayesian active learning reliability method is developed in this study. First, in Bayesian failure probability estimation, a metric called integrated probability of misclassification (IPM) is defined from the upper bound of mean absolute deviation of failure probability. Then, a multi-point learning function called <span><math><mi>k</mi></math></span>-point integrated probability of misclassification reduction (<span><math><mi>k</mi></math></span>-IPMR) is proposed to guide the selection of a batch of <span><math><mrow><mi>k</mi><mrow><mo>(</mo><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> new samples that maximize the expected reduction of IPM. To further reduce the computational overhead, the fast <span><math><mi>k</mi></math></span>-IPMR-guided parallel Bayesian active learning reliability analysis is conducted through four key workarounds. (i) The <span><math><mi>k</mi></math></span>-IPMR is substituted by its theoretically analogous but computationally cheaper variant. (ii) A stepwise maximization of <span><math><mi>k</mi></math></span>-IPMR is deployed to replace the cumbersome direct maximization approach. (iii) The number of new samples added per iteration is identified in an adaptive manner. (iv) A hybrid convergence criterion is specified according to the actual reduction of IPM at each iteration. Owing to the core role of IPM, we fuse the three major ingredients, i.e., Bayesian inference of failure probability, multi-point enrichment process, and convergence criterion, in a theoretically consistent way. The performance of the proposed method is testified on four examples of varying complexity. The results indicate that the proposed approach needs a fewer number of iterations than those existing ones and thus is more computationally efficient, particularly when dealing with time-intensive complex reliability problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117752"},"PeriodicalIF":6.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027317","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}
引用次数: 0
Causality enforcing parametric heat transfer solvers for evolving geometries in advanced manufacturing
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117764
Akshay J. Thomas , Ilias Bilionis , Eduardo Barocio , R. Byron Pipes
{"title":"Causality enforcing parametric heat transfer solvers for evolving geometries in advanced manufacturing","authors":"Akshay J. Thomas ,&nbsp;Ilias Bilionis ,&nbsp;Eduardo Barocio ,&nbsp;R. Byron Pipes","doi":"10.1016/j.cma.2025.117764","DOIUrl":"10.1016/j.cma.2025.117764","url":null,"abstract":"<div><div>We introduce a new method for solving parametric heat transfer partial differential equations on evolving geometries in advanced manufacturing applications. Physics-informed neural networks (PINNs) are a popular framework for integrating experimental data with known physical laws specified via partial differential equations (PDEs). Despite their increasing popularity, applying PINNs to manufacturing problems is limited compared to fluid and solid mechanics problems. The applications of PINNs acting as PDE solvers are absent where material is being added or removed. The objective of our work is to address this gap. By proposing a new loss function, we aim to expand the applications of PINNs for heat transfer to manufacturing problems with evolving geometries. Our method obviates the need for mesh-based discretization and time-marching schemes for evolving geometries. We consider predicting the transient temperature history in additive manufacturing as a single bead of material is deposited. We consider various evolving mixed Dirichlet and Neumann boundary condition cases to test our methodology. We verify our methodology by comparing our results with a validated finite element (FE) solver and observe that the results are in excellent agreement. Our method is naturally biased to respect causality, achieved by an automatic decrease in collocation point density as the geometry evolves. We extend our method to solve a parametric heat transfer equation for the single bead addition problem and outline the advantages in computational cost provided by our parametric solver compared to running multiple instances of an FE solver.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117764"},"PeriodicalIF":6.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027318","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}
引用次数: 0
A deep generative multiscale topology optimization framework considering manufacturing defects and parametrical uncertainties
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117778
Yichen Wu , Lei Wang , Zeshang Li , Lianmei Wu , Yaru Liu
{"title":"A deep generative multiscale topology optimization framework considering manufacturing defects and parametrical uncertainties","authors":"Yichen Wu ,&nbsp;Lei Wang ,&nbsp;Zeshang Li ,&nbsp;Lianmei Wu ,&nbsp;Yaru Liu","doi":"10.1016/j.cma.2025.117778","DOIUrl":"10.1016/j.cma.2025.117778","url":null,"abstract":"<div><div>The increasing demand for load-carrying multiscale structures with ultimate lightness requires corresponding development in topology optimization methods. However, current multiscale topology optimization methods are hindered by the contradiction between the freedom of design space and the dimensionality of the design variables. Moreover, the unstable additive manufacturing process and working conditions would result in possible structural failure of the multiscale structure optimized under deterministic conditions. To address these problems, we propose a deep generative multiscale topology optimization framework considering both manufacturing defects and parametrical uncertainties. A database consisting of minimum volume unit cell topologies is obtained via the inverse homogenization method. Then the variational autoencoder network is introduced to capture the patterns in the database and to reconstruct unit cells with a low-dimensional latent vector, which effectively compresses the number of design variables for a microstructure. Then, a self-adaptive clustering strategy is proposed to efficiently quantify the influence of random manufacturing defects in microstructures. A reliability-based optimization framework is constructed with a reliability index to evaluate the complex effect of multisource uncertainties. The effectiveness of the proposed framework is validated through a series of numerical examples, and conclusions are presented at the end of the article.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117778"},"PeriodicalIF":6.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027315","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}
引用次数: 0
Differentiable finite element method with Galerkin discretization for fast and accurate inverse analysis of multidimensional heterogeneous engineering structures
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117755
Xi Wang , Zhen-Yu Yin , Wei Wu , He-Hua Zhu
{"title":"Differentiable finite element method with Galerkin discretization for fast and accurate inverse analysis of multidimensional heterogeneous engineering structures","authors":"Xi Wang ,&nbsp;Zhen-Yu Yin ,&nbsp;Wei Wu ,&nbsp;He-Hua Zhu","doi":"10.1016/j.cma.2025.117755","DOIUrl":"10.1016/j.cma.2025.117755","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) are well-regarded for their capabilities in inverse analysis. However, efficient convergence is hard to achieve due to the necessity of simultaneously handling physics constraints, data constraints, blackbox weights, and blackbox biases. Consequently, PINNs are highly challenged in the inverse analysis of unknown boundary loadings and heterogeneous material parameters, particularly for three-dimensional engineering structures. To address these limitations, this study develops a novel differentiable finite element method (DFEM) based on Galerkin discretization for diverse inverse analysis. The proposed DFEM directly embeds the weak form of the partial differential equation into a discretized and differentiable computational graph, yielding a loss function from fully interpretable trainable parameters. Moreover, the labeled data, including boundary conditions, are strictly encoded into the computational graph without additional training. Finally, two benchmarks validate the DFEM's superior efficiency and accuracy: (1) With only 0.3 % training iterations, the DFEM can achieve an accuracy three orders of magnitude higher for the inverse analysis of unknown loadings. (2) With a training time five orders of magnitude faster, the DFEM is validated to be five orders of magnitude more accurate in determining unknown material parameters. Furthermore, two cases validate DFEM as effective for three-dimensional engineering structures: (1) A damaged cantilever beam characterized by twenty heterogeneous materials with forty unknown parameters is efficiently solved. (2) A tunnel lining ring with sparse noisy data under unknown heterogeneous boundary loadings is successfully analyzed. These problems are solved in seconds, corroborating DFEM's potential for engineering applications. Additionally, the DFEM framework can be generalized to a Physics-Encoded Numerical Network (PENN) for further development and exploration.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117755"},"PeriodicalIF":6.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An univariate method for multi-material topology optimization and its application to engineering structures with unstructured meshes
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117749
Haitao Liao, Wenhao Yuan, Shigang Ai, Xujin Yuan
{"title":"An univariate method for multi-material topology optimization and its application to engineering structures with unstructured meshes","authors":"Haitao Liao,&nbsp;Wenhao Yuan,&nbsp;Shigang Ai,&nbsp;Xujin Yuan","doi":"10.1016/j.cma.2025.117749","DOIUrl":"10.1016/j.cma.2025.117749","url":null,"abstract":"<div><div>Multi-material topology optimization as a research hotspot has been widely investigated and all the reported multi-material interpolation models add m or m-1 design variables/level set equations to handle m levels or phases and the number of design variables is proportional to the number of material type. The current single variable interpolation model as an attractive alternative selection often leads to the emergence of interphase enclosed within the adjacent materials which excessively restricts the design space, resulting in a suboptimal solution and consequently placing limitations on the potential realistic application. To tackle the aforementioned challenges, a pioneering framework by incorporating the univariate characteristic function into the Discrete Material Optimization (DMO) scheme for the first time is proposed for both structured grids and unstructured meshes. Firstly, the univariate characteristic function is devised to transform the original single design variable field into a set of topology density functions, each independently controlling single material topology. The smoothing mechanism using the Helmholtz Partial Differential Equation (PDE) filter is applied for each topology density function field to ensure spatial correlation and continuity of single material distribution. Each filtered topology density field is in turn passed to a regularized Heaviside projection function that generates physical density field for a continuous representation of non-existence or existence for each material. All the resulting physical topology density fields ranging from 0 to 1 are then subsequently integrated to construct a composite interpolation model by virtue of the DMO scheme, preventing material overlaps due to the Helmholtz PDE filtering. The design variables allotted to nodes are updated using the method of moving asymptotes. An adaptive continuation strategy is introduced to adjust the projection slope and penalization parameters, enhancing optimization efficiency and accelerating optimization simulation. Finally, extensive numerical experiments including two practical real-world engineering examples are conducted to validate the performance of the proposed scheme. Numerical results show that the proposed method works well for both structured and unstructured meshes, while inheriting the benefits and favourable properties of both the univariate characteristic function and the DMO scheme, effectively addressing material envelope bottlenecks and reducing excessive design variables. The proposed approach offers a well-founded and flexible platform for solving multi-material topology optimization problems, making the approach practical for real-world engineering scenarios.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117749"},"PeriodicalIF":6.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027366","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}
引用次数: 0
Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2024.117725
Karl A. Kalina , Jörg Brummund , WaiChing Sun , Markus Kästner
{"title":"Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions","authors":"Karl A. Kalina ,&nbsp;Jörg Brummund ,&nbsp;WaiChing Sun ,&nbsp;Markus Kästner","doi":"10.1016/j.cma.2024.117725","DOIUrl":"10.1016/j.cma.2024.117725","url":null,"abstract":"<div><div>We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. By using a set of invariants as input, an energy-type output and by adding several correction terms to the overall energy density functional, the model fulfills multiple physical principles by construction. The invariants are formed from the right Cauchy–Green deformation tensor and fully symmetric 2nd, 4th or 6th order structure tensors which enables to describe a wide range of symmetry groups. Besides the network parameters, the structure tensors are simultaneously calibrated during training so that the underlying anisotropy of the material is reproduced most accurately. In addition, sparsity of the model with respect to the number of invariants is enforced by adding a trainable gate layer and using <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> regularization. Our approach works for data containing tuples of deformation, stress and material tangent, but also for data consisting only of tuples of deformation and stress, as is the case in real experiments. The developed approach is exemplarily applied to several representative examples, where necessary data for the training of the PANN surrogate model are collected via computational homogenization. We show that the proposed model achieves excellent interpolation and extrapolation behaviors. In addition, the approach is benchmarked against an NN model based on the components of the right Cauchy–Green deformation tensor.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117725"},"PeriodicalIF":6.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Data-driven multifidelity topology design with multi-channel variational auto-encoder for concurrent optimization of multiple design variable fields
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117772
Hiroki Kawabe , Kentaro Yaji , Yuichiro Aoki
{"title":"Data-driven multifidelity topology design with multi-channel variational auto-encoder for concurrent optimization of multiple design variable fields","authors":"Hiroki Kawabe ,&nbsp;Kentaro Yaji ,&nbsp;Yuichiro Aoki","doi":"10.1016/j.cma.2025.117772","DOIUrl":"10.1016/j.cma.2025.117772","url":null,"abstract":"<div><div>Topology optimization can generate high-performance structures with a high degree of freedom. Regardless, it generally confronts entrapment in undesirable local optima especially in problems characterized by strong non-linearity. This study aims to establish a gradient-free topology optimization framework that facilitates more global solution searches to avoid the entrapment. The framework utilizes a data-driven multifidelity topology design (MFTD), where solution candidates initially generated by solving low-fidelity (LF) optimization problems are iteratively updated by a variational auto-encoder (VAE) and high-fidelity (HF) evaluation. A key procedure of the solution update is to construct HF models by extruding material distributions obtained by the VAE to thickness distribution, which is spcatially constant across all solution candidates in the conventional data-driven MFTD. This constant assignment leads to no exploration of the thickness space, which necessitates extensive parametric studies outside the optimization loop. To enable a more comprehensive optimization in a single run, we propose a multi-channel image data architecture that stores material distributions in the first channel and other design variable fields like thickness distribution in the second or subsequent channels. This significant shift enables a thorough exploration of the additional design variable fields space with no necessity of parametric studies afterwards, by simultaneously optimizing both material distributions and those variable fields. We apply the framework to a maximum stress minimization problem, where the LF optimization problem is formulated with approximation techniques, whereas the HF evaluation is conducted by accurately analyzing the stress field, bypassing any approximation techniques. We first validate that the framework can successfully identify high-performance solutions superior to the reference solutions by effectively exploring both material and thickness distributions in a fundamental stiffness maximization. Then we demonstrate the framework can identify promising solutions for the original maximum stress minimization problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117772"},"PeriodicalIF":6.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the use of physics-based constraints and validation KPI for data-driven elastoplastic constitutive modelling
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117743
Rúben Lourenço , Aiman Tariq , Petia Georgieva , A. Andrade-Campos , Babür Deliktaş
{"title":"On the use of physics-based constraints and validation KPI for data-driven elastoplastic constitutive modelling","authors":"Rúben Lourenço ,&nbsp;Aiman Tariq ,&nbsp;Petia Georgieva ,&nbsp;A. Andrade-Campos ,&nbsp;Babür Deliktaş","doi":"10.1016/j.cma.2025.117743","DOIUrl":"10.1016/j.cma.2025.117743","url":null,"abstract":"<div><div>Constitutive modelling based on machine learning (ML) approaches has surged in the last couple of decades due to novel and more robust model architectures and computational power. The dependency of these models on large amounts of training data can be mitigated by imposing some phenomenological knowledge as constraints, which also helps maintain the quality of learning. This paper highlights the importance of physics-based constraints in elastoplastic data-driven constitutive modelling and focuses on model validation methods. Specifically, seven constraints applied to elastoplastic behaviour are identified that can be used during the model training process. To study the effects of these constraints, a set of recurrent neural network (RNN) models is trained using data from virtual mechanical experiments, based on a biaxial cruciform specimen. The models’ ability to accurately learn and predict the fundamental constitutive behaviour is then assessed using the different validation checkpoints, which include (i) statistical metrics, (ii) tests on previously unseen data, from virtual experiments based on different heterogeneous mechanical specimens, (iii) external key performance indicators (KPI) and (iv) single-element finite element analysis (FEA) tests. It was observed that the benefits of adding constraints to the training process were three-fold, resulting in (i) improved model predictive capacity, as well as (ii) enhanced extrapolation capabilities when tested on different mechanical specimens and (iii) overall improved training speed and stability. The use of independent validation KPI for data-driven constitutive modelling is highlighted and suggested as standard practice in future researches in the field.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117743"},"PeriodicalIF":6.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tree–cotree-based tearing and interconnecting for 3D magnetostatics: A dual–primal approach
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117737
Mario Mally , Bernard Kapidani , Melina Merkel , Sebastian Schöps , Rafael Vázquez
{"title":"Tree–cotree-based tearing and interconnecting for 3D magnetostatics: A dual–primal approach","authors":"Mario Mally ,&nbsp;Bernard Kapidani ,&nbsp;Melina Merkel ,&nbsp;Sebastian Schöps ,&nbsp;Rafael Vázquez","doi":"10.1016/j.cma.2025.117737","DOIUrl":"10.1016/j.cma.2025.117737","url":null,"abstract":"<div><div>The simulation of electromagnetic devices with complex geometries and large-scale discrete systems benefits from advanced computational methods like IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both concepts in an Isogeometric Tearing and Interconnecting method to enable the use of parallel computations for magnetostatic problems. We address the underlying non-uniqueness by using a graph-theoretic approach, the tree–cotree decomposition. The classical tree–cotree gauging is adapted to be feasible for parallelization, which requires that all local subsystems are uniquely solvable. Our contribution consists of an explicit algorithm for constructing compatible trees and combining it with a dual–primal approach to enable parallelization. The correctness of the proposed approach is proved and verified by numerical experiments, showing its accuracy, scalability and optimal convergence.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117737"},"PeriodicalIF":6.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase-field hydraulic fracturing operator network based on En-DeepONet with integrated physics-informed mechanisms
IF 6.9 1区 工程技术
Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117750
Xiaoqiang Wang , Peichao Li , Detang Lu
{"title":"Phase-field hydraulic fracturing operator network based on En-DeepONet with integrated physics-informed mechanisms","authors":"Xiaoqiang Wang ,&nbsp;Peichao Li ,&nbsp;Detang Lu","doi":"10.1016/j.cma.2025.117750","DOIUrl":"10.1016/j.cma.2025.117750","url":null,"abstract":"<div><div>Hydraulic fracturing in porous media, driven by fluid injection, presents a formidable computational challenge due to the intricate interplay of fluid flow and fracture mechanics. The phase-field method offers a powerful approach for modeling such complex phenomena, but its high computational demands limit its practical application in large-scale scenarios. This work introduces a phase-field hydraulic fracturing operator network aimed at efficiently predicting fracture propagation and facilitating in the design of fracturing strategies. We develop a multi-input, multi-physics operator network based on the Enriched-DeepONet framework, incorporating multiple root networks to simultaneously handle diverse physics fields while integrating physical laws into the training process. The governing physical equations are formulated using the widely recognized phase-field hydraulic fracturing model, with Darcy’s law describing fluid flow in both fractures and the surrounding porous media. The hydraulic response across different computational domains is captured through interpolation of Darcy’s parameters using an indicator function derived from the phase-field variable. This methodology allows for the comprehensive representation of hydraulic fracturing processes through coupled partial differential equations, enabling the solution within the operator network framework. By embedding physical constraints into the loss function, the proposed model achieves enhanced convergence and accuracy during training. The effectiveness of the proposed approach is demonstrated through three numerical experiments varying in permeability, in-situ stress, critical energy release rate, and Young’s modulus. The results underscore the critical importance of integrating physical constraints to improve the accuracy of the training process. Our findings indicate that the developed phase-field hydraulic fracturing operator network is a promising advancement for enhancing the simulation capabilities of hydraulic fracturing processes.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117750"},"PeriodicalIF":6.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027320","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}
引用次数: 0
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