Article
Mathematics, Applied
Mario Kapl, Vito Vitrih
Summary: In this study, we investigate the space of C-1 isogeometric spline functions on trilinearly parameterized multi-patch volumes. We present a general framework based on the two-patch construction that allows for the design of the C-1 isogeometric spline space and associated basis functions. We specifically focus on trilinear multi-patch volumes with one inner edge and compute the dimension of the resulting C-1 isogeometric spline space, as well as explore the approximation properties using L-2 approximation.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Margarita Chasapi, Pablo Antolin, Annalisa Buffa
Summary: This work presents a reduced order modeling framework for parameterized second-order linear elliptic partial differential equations on unfitted geometries. Efficient projection-based models utilizing reduced basis method and discrete empirical interpolation are proposed, which can handle geometrical parameters in unfitted domain discretizations. The proposed method is computationally efficient and accurate, agnostic to the underlying discretization choice. Numerical experiments on benchmark problems demonstrate significant reduction of online computational cost compared to standard ROMs with the same level of accuracy. The methodology is also applicable to three-dimensional geometries of linear elastic problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Rainer Schneckenleitner, Stefan Takacs
Summary: We study the Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for non-conforming multi-patch discretizations of a generalized Poisson problem. The coupling between patches is achieved using a symmetric interior penalty discontinuous Galerkin (SIPG) approach. We relax the requirement that the interfaces between patches always consist of whole edges and allow for the presence of T-junctions, which is crucial for considering sliding interfaces. We propose the concept of "fat vertices" for the choice of primal degrees of freedom and show a condition number bound that is consistent with the conforming case.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Di Miao, Zhihui Zou, Michael A. Scott, Michael J. Borden, Derek C. Thomas
Summary: This paper presents a novel isogeometric Bezier dual mortar method for coupling multi-patch Kirchhoff-Love shell structures. The proposed approach weakly enforces the continuity of the solution at patch interfaces and can be applied to both conforming and non-conforming discretizations. The resulting stiffness matrix is sparse and the coupling accuracy is optimal.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vazquez
Summary: Isogeometric analysis is used to solve high order partial differential equations by leveraging the smoothness of splines. This paper focuses on adaptive isogeometric methods with hierarchical splines and extends the construction of C-1 isogeometric spline spaces to multi-patch planar domains. A refinement algorithm is developed to ensure the linear independence of hierarchical splines on suitable hierarchical multi-patch mesh configurations, and it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Carlo Garoni, Carla Manni, Francesca Pelosi, Hendrik Speleers
Summary: This paper introduces a new immersed Galerkin discretization based on tensor-product cardinal B-splines for general variable-coefficient Poisson problems. The method does not require tuning of user-defined parameters and the system matrices are symmetric for symmetric problems. Analysis shows that these matrices have an asymptotic spectral distribution as the matrix size tends to infinity.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Jie Gao, Xiaomeng Wu, Mi Xiao, Vinh Phu Nguyen, Liang Gao, Timon Rabczuk
Summary: This study proposes a Multi-Patch Isogeometric Topology Optimization (MP-ITO) method for the design of periodic or graded cellular structures. The method applies Nitsche's method to couple non-conforming meshes and conducts multi-patch isogeometric analysis. A multi-patch topology description model is developed to improve smoothness and continuity of boundaries at interfaces within adjacent subdomains. The effectiveness and capabilities of the MP-ITO method are demonstrated through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Cesare Bracco, Carlotta Giannelli, Alessandro Reali, Michele Torre, Rafael Vazquez
Summary: We propose an adaptive scheme for isogeometric phase-field modeling that allows suitable hierarchical refinement and coarsening on single- and multi-patch geometries. The scheme considers truncated hierarchical splines to ensure C1 continuity between patches. The accuracy and effectiveness of the proposed grading strategy are verified through numerical examples, demonstrating the performance of the adaptive isogeometric analysis with smooth hierarchical spline constructions in simulating standard modes of phase separation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Andrea Farahat, Bert Juettler, Mario Kapl, Thomas Takacs
Summary: This paper presents a framework for constructing a globally C1-smooth isogeometric spline space over a specific class of G1-smooth multi-patch surfaces called analysis-suitable G1 (AS-G1) multi-patch surfaces. The proposed method extends previous work on planar AS-G1 multi-patch parameterizations to the case of AS-G1 multi-patch surfaces. The C1-smooth isogeometric spline space is generated using locally supported and explicitly given basis functions of three different types corresponding to the patches, interfaces, and vertices of the AS-G1 multi-patch surface.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Ion Gabriel Ion, Dimitrios Loukrezis, Herbert De Gersem
Summary: This work presents a numerical solver combining isogeometric analysis (IGA) and tensor train (TT) decomposition for approximating parameter-dependent PDEs on geometries. The proposed method effectively handles parameter dependencies and demonstrates high computational efficiency and compression ratios.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Stefano Frambati, Helene Barucq, Henri Calandra, Julien Diaz
Summary: This work demonstrates how recent advances in simplex spline spaces can be applied to construct a polynomial-reproducing space for unstructured splines on multi-patch domains with arbitrary shape and topology. By reproducing the traces of these functions on subdomain boundaries, which align with the standard polynomial bases used in discontinuous Galerkin approximations, theoretical and practical tools from these methods can be utilized. Additionally, theoretical results on the construction and evaluation of simplex spline spaces are reinterpreted into an explicit, algorithmic form. Together, these efforts enable the formulation of a practical, efficient, and fully unstructured multi-patch discontinuous Galerkin - isogeometric analysis scheme, bridging the gap between current multi-patch isogeometric analysis approaches and the more traditional mesh-based interior penalty discontinuous Galerkin method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Qingyuan Hu, Yuan Liang, Menghao Liu, Manfeng Hu, Yawen Mao
Summary: This paper conducts research on the structural topology optimization algorithm within the framework of isogeometric analysis and adopts the Nitsche method and integer programming algorithm for multi-component structures. The sensitivity filtering method and a simple averaging method along coupling interfaces are employed to improve the effectiveness of the algorithm.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Engineering, Mechanical
Qingyuan Hu, Davide Baroli, Shuzhen Rao
Summary: This research introduces the nonlinear formulation of solid-shell elements and a basic method for constructing 3D models, proposing a non-symmetric variant of Nitsche's formulation for multi-patch coupling along with an empirical formula for stabilization parameter. Various integration schemes are presented to address locking syndrome, and a quasi-Newton iteration format is derived as solver.
ACTA MECHANICA SINICA
(2021)
Article
Engineering, Multidisciplinary
Andrea Farahat, Hugo M. Verhelst, Josef Kiendl, Mario Kapl
Summary: We propose an isogeometric method for the Kirchhoff-Love shell analysis of shell structures with multiple patches and extraordinary vertices. The method is based on the approximation of the mid-surface using a class of multi-patch surfaces and the use of a globally C1-smooth isogeometric multi-patch spline space. Numerical results demonstrate the potential of the method for efficient shell analysis of geometrically complex multi-patch structures.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Luca Coradello, Gabriele Loli, Annalisa Buffa
Summary: This work focuses on developing a super-penalty strategy and coupling algorithm to achieve C-1 continuity between non-conforming isogeometric Kirchhoff plates, guaranteeing optimal accuracy and avoiding boundary locking issues. By studying benchmark examples, the proposed algorithm demonstrates higher accuracy compared to other choices of penalty parameters, achieving optimal rates of convergence achievable by B-splines.
COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Alexander Seitz, Wolfgang A. Wall, Alexander Popp
COMPUTATIONAL MECHANICS
(2019)
Article
Engineering, Multidisciplinary
Thomas Horger, Alessandro Reali, Barbara Wohlmuth, Linus Wunderlich
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2019)
Article
Mathematics, Interdisciplinary Applications
Jacopo Bonari, Maria R. Marulli, Nora Hagmeyer, Matthias Mayr, Alexander Popp, Marco Paggi
COMPUTATIONAL MECHANICS
(2020)
Article
Computer Science, Software Engineering
Sandra Marschke, Linus Wunderlich, Wolfgang Ring, Klaus Achterhold, Franz Pfeiffer
COMPUTER AIDED GEOMETRIC DESIGN
(2020)
Article
Mathematics, Interdisciplinary Applications
Ivo Steinbrecher, Matthias Mayr, Maximilian J. Grill, Johannes Kremheller, Christoph Meier, Alexander Popp
COMPUTATIONAL MECHANICS
(2020)
Article
Engineering, Multidisciplinary
Tobias A. Wiesner, Matthias Mayr, Alexander Popp, Michael W. Gee, Wolfgang A. Wall
Summary: In this article, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. The main contributions include the development and open-source implementation of an interface aggregation strategy suitable for coupling structural equilibrium equations with contact constraints, as well as a review of saddle point smoothers in the context of constrained interface problems. The new method demonstrates robustness and scalability in complex dynamic contact problems.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Ivo Steinbrecher, Alexander Popp, Christoph Meier
Summary: The article introduces a mortar-type finite element formulation for embedding curved, slender beams into 3D solid volumes, along with a consistent coupling scheme for rotational and translational constraints. It demonstrates spatial convergence behavior and avoidance of potential locking effects through numerical tests when combined with suitable solid triad definitions. The proposed formulation shows potential for investigating complex mechanical systems involving curved, slender fibers with arbitrary orientation in matrix materials.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
M. D. Alaydin, D. J. Benson, Y. Bazilevs
Summary: A comprehensive Isogeometric Kirchhoff-Love shell framework capable of undergoing large elasto-plastic deformations is proposed, with key aspects including the reformulation of thin-shell equations in terms of mid-surface velocity degrees of freedom and the introduction of penalty coupling techniques for complex multipatch geometries. Numerical examples validate the accuracy, efficiency, and robustness of the framework.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Masoud Behzadinasab, Mert Alaydin, Nathaniel Trask, Yuri Bazilevs
Summary: A comprehensive rotation-free KL shell formulation for PD is proposed to model large elasto-plastic deformations and fracture in thin-walled structures. Principal Component Analysis is employed in a meshfree setting to develop a local parameterization, with a bond-stabilization technique used for stability of the discrete solution. The method allows for a wide range of material behavior simulation and enables the discretization of shell theory with higher-order smoothness on an unstructured surface mesh.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Kathrin Glau, Linus Wunderlich
Summary: This paper proposes a deep parametric PDE method for solving high-dimensional parametric partial differential equations in financial applications. The method uses a single neural network to approximate the solution of the entire PDE family, without the need for sample solutions. As a practical application, the method is used to compute option prices and Greeks in the multivariate Black-Scholes model, providing efficient results for different times, states, and model parameters after a single training phase.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Interdisciplinary Applications
R. Pinto Carvalho, A. M. Couto Carneiro, F. M. Andrade Pires, A. Popp
Summary: In this work, the dual mortar method is used to handle the contact between deformable bodies and rigid obstacles. The proposed contributions include modifying the weighted gap function and introducing a new definition for the nodal orthonormal moving frame, which simplify the calculations and reduce the computational complexity.
COMPUTATIONAL MECHANICS
(2023)
Article
Operations Research & Management Science
Kathrin Glau, Linus Wunderlich
Summary: The recently introduced deep parametric PDE method combines the efficiency of deep learning for high-dimensional problems with the reliability of classical PDE models. The accuracy of the deep parametric PDE method is determined by the best-approximation property of neural networks. We provide (to the best of our knowledge) the first approximation results, which feature a dimension-independent rate of convergence for deep neural networks with a hyperbolic tangent as the activation function. Numerical results confirm that the deep parametric PDE method performs well in high-dimensional settings by presenting in a risk management problem of high interest for the financial industry.
ANNALS OF OPERATIONS RESEARCH
(2023)
Article
Engineering, Aerospace
Julian D. Pauw, Lucrezia Veggi, Oskar J. Haidn, Christian Wagner, Thomas Thuemmel, Daniel J. Rixen, Christoph Ager, Andy Wirtz, Alexander Popp, Wolfgang A. Wall, Bernd Wagner
CEAS SPACE JOURNAL
(2019)
Review
Computer Science, Interdisciplinary Applications
Christoph Meier, Alexander Popp, Wolfgang A. Wall
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2019)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
