Article
Mathematics, Applied
Arielle Carr, Eric de Sturler, Serkan Gugercin
Summary: Preconditioners are crucial for fast convergence in solving linear systems, and recycling them can be advantageous. A new method for updating and reusing preconditioners is introduced, with flexibility in balancing map quality and computational cost, leading to good results across various applications.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Automation & Control Systems
Soheila Ghoroghi Shafiei, Masoud Hajarian
Summary: This paper introduces the application of the Kaczmarz method in solving large-scale linear algebraic systems and Sylvester matrix equations. By deriving the matrix form and extending the algorithm, a new iterative algorithm is proposed and validated through numerical examples.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Software Engineering
Hussam Al Daas, Laura Grigori, Pascal Henon, Philippe Ricoux
Summary: This article discusses deflation strategies for recycling Krylov subspace methods in solving linear systems, introducing various techniques such as Ritz- and harmonic Ritz-based deflation. Through numerical experiments in reservoir simulation, the impact of these strategies is demonstrated.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2021)
Article
Mathematics, Applied
Yuka Hashimoto, Takashi Nodera
Summary: This paper proposes a novel technique for accelerating the Krylov subspace methods for transfer operators by replacing positive definite kernels in RKHS, which is equivalent to preconditioning the transfer operator with a specific linear operator.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Fatemeh P. A. Beik, Mehdi Najafi-Kalyani
Summary: A framework for left/right preconditioning of multi-linear systems with Einstein product was proposed in this paper, and the inverse of preconditioned tensor was analytically derived. The feasibility of preconditioned Krylov subspace methods based on Hessenberg process was experimentally illustrated, and their performances were compared with those based on the Arnoldi process.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Zhao-Zheng Liang, Yan Dou
Summary: This paper focuses on robust iterative solution methods for solving Stokes optimal control problems, proposing two efficient preconditioners which can be implemented in a Krylov acceleration framework. These preconditioners yield similar tight eigenvalue distribution results for the preconditioned matrices, leading to convergence rates independent of the regularization parameter and refinement level. In addition, inexact variants of the preconditioners are suggested to avoid inner-outer implementations, utilizing preconditioned GMRES methods as inner loops, demonstrating robust performance and comparability to existing preconditioners when accelerating Krylov subspace methods.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Fang Chen, Bi-Cong Ren
Summary: This paper presents an effective iteration method for solving the double saddle point problems in liquid crystal director modeling. The convergence property of the method is studied in detail, and a preconditioner is introduced to accelerate the Krylov subspace iteration methods. Moreover, the spectral property of the preconditioned matrix is investigated.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Multidisciplinary
M. Bolten, E. de Sturler, C. Hahn, M. L. Parks
Summary: Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly over time. However, applying this technique in PDE constrained shape optimization can be challenging due to the evolution of geometry and finite element mesh, which leads to changes in linear system matrices and their subspaces.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Paul Escapil-Inchauspe, Carlos Jerez-Hanckes
Summary: This study extends the operator preconditioning framework to Petrov-Galerkin methods, considering parameter-dependent perturbations for both variational forms and their preconditioners. The bi-parametric abstract setting leads to robust and controlled schemes, with exhaustive convergence estimates for iterative solvers in Hilbert spaces.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
David Kay, Vanessa Styles
Summary: This study introduces an efficient solver for saddle point problems in the finite element approximation of nonlocal multi-phase Allen-Cahn variational inequalities. The solver exhibits mesh independence and mild dependence on phase field variables, and converges to the two-phase problem solution within three GMRES iterations regardless of mesh size or interfacial width. Numerical results demonstrate the competitiveness of this approach.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Operations Research & Management Science
Jacek Gondzio, Spyridon Pougkakiotis, John W. Pearson
Summary: This paper presents general-purpose preconditioners for optimization problems and explores positive definite preconditioners suitable for CG and MINRES. It discusses sparsifications that prevent the eigenvalues of the preconditioned matrix from becoming complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Shi-Ping Tang, Yu-Mei Huang
Summary: In this paper, fast second-order numerical methods are proposed for solving one- and two-dimensional space-fractional advection-diffusion equations defined on a finite domain. We analyze the stability and convergence of the proposed methods, and propose new approximate preconditioners for solving the discretized linear systems. The numerical results demonstrate the effectiveness of the proposed methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Joris Tavernier, Jaak Simm, Karl Meerbergen, Yves Moreau
Summary: The paper introduces a two-level preconditioner for regularized least squares linear systems involving feature or data matrices, which can be applied in various machine learning applications and has demonstrated acceleration effects on artificial and real-life data.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
T. Abe, A. T. Chronopoulos
Summary: Iterative methods, especially Krylov subspace methods (KSM), are useful for solving large and sparse linear systems problems in science and engineering modeling. Recently, nested loop KSM, such as residual cutting (RC) and generalized residual cutting (GRC), have been proposed to improve the convergence of traditional KSM. In this article, we review RC and GRC as nested loop methods for solving large and sparse linear systems problems, and demonstrate that GRC is an equivalent KSM to Orthomin with variable preconditioning. We also present a stable GRC algorithm derived using the modified Gram-Schmidt method, and show that GRC provides a general framework for constructing a class of hybrid (nested) KSM based on inner loop method selection. Numerical experiments using nonsymmetric indefinite matrices from a widely used library of sparse matrices validate the efficiency and robustness of the proposed methods.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Min-Li Zeng, Jun-Feng Yang, Guo-Feng Zhang
Summary: In this paper, we investigate the structure of discretized linear systems derived from spatial fractional diffusion equations. We propose a new approximate inverse preconditioner based on the diagonal-plus-Toeplitz structure of the coefficient matrices. The tau matrix-based approximate inverse (TAI) preconditioning technique, implemented using discrete sine transforms (DST), is shown to achieve fast convergence in Krylov subspace methods. Numerical experiments demonstrate that the performance of the tau-matrix based preconditioning technique is superior to other tested preconditioners.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Mechanical
Phanisri P. Pratapa, Ke Liu, Siva P. Vasudevan, Glaucio H. Paulino
Summary: This research investigates the folding kinematics of a Morph pattern structure through rigid panel assumptions, exploring the different modes and hybrid states that can be achieved. It discusses the interplay between local and global kinematics, studying how folding deformations can result in reprogrammable morphing behavior. Through numerical simulations, the study verifies the deformation characteristics predicted analytically.
JOURNAL OF MECHANISMS AND ROBOTICS-TRANSACTIONS OF THE ASME
(2021)
Article
Mechanics
Ke Liu, Tomohiro Tachi, Glaucio H. Paulino
Summary: This paper introduces a novel origami pattern called the Shrimp pattern, which is applied to multi-phase architected metamaterials that achieve phase transition mechanically through snap-through. By tessellating unit cells with different geometries, a complex yet navigable energy landscape is created, leading to multiple metastable phases of the material.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2021)
Article
Mathematics, Applied
Jiahua Jiang, Julianne Chung, Eric De Sturler
Summary: The proposed hybrid projection method with recycling techniques can effectively solve large linear inverse problems by reducing memory requirements and computational cost, integrating previously computed information, and improving reconstruction speed and accuracy. Numerical examples in image processing demonstrate the potential benefits of combining recycling with hybrid projection methods.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Chemistry, Multidisciplinary
Fernando Senhora, Emily D. Sanders, Glaucio H. Paulino
Summary: Spinodal architected materials optimize design of multiscale structures by varying spinodal class, orientation, and porosity, leading to efficient material placement along stress trajectories with enhanced mechanical and biological functions.
ADVANCED MATERIALS
(2022)
Article
Engineering, Multidisciplinary
M. Bolten, E. de Sturler, C. Hahn, M. L. Parks
Summary: Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly over time. However, applying this technique in PDE constrained shape optimization can be challenging due to the evolution of geometry and finite element mesh, which leads to changes in linear system matrices and their subspaces.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Fufu Yang, Miao Zhang, Jiayao Ma, Zhong You, Ying Yu, Yan Chen, Glaucio H. Paulino
Summary: Resch patterns are tessellation origami patterns consisting of more than one type of polygons. They are generally rigid foldable but have a large number of degrees of freedom. In order to achieve one-DOF forms of triangular Resch pattern units, the thick-panel technique is employed to replace spherical linkages with spatial linkages. The compatibility among all the vertices is studied by kinematic analysis, and two design schemes are obtained to form a one-DOF origami structure.
MECHANISM AND MACHINE THEORY
(2022)
Article
Multidisciplinary Sciences
Qiji Ze, Shuai Wu, Jun Nishikawa, Jize Dai, Yue Sun, Sophie Leanza, Cole Zemelka, Larissa S. Novelino, Glaucio H. Paulino, Ruike Renee Zhao
Summary: Researchers have developed a magnetically actuated small-scale origami crawler with inplane contraction, which can crawl and steer in confined spaces. This crawler has magnetically tunable structural stiffness, allowing it to overcome large resistances, and it has the ability to store and release drugs internally, demonstrating its multifunctionality.
Article
Engineering, Mechanical
Diego Misseroni, Phanisri P. Pratapa, Ke Liu, Glaucio H. Paulino
Summary: This study presents a novel experimental setup for studying the Poisson effects in 2D origami tessellations. The setup was used to measure the Poisson's ratio of the Morph, Miura-ori, and Eggbox patterns, and the results were consistent with theory and simulations. This experimental technique can be applied to investigate other tunable properties of origami metamaterials.
EXTREME MECHANICS LETTERS
(2022)
Article
Chemistry, Multidisciplinary
Ke Liu, Phanisri P. Pratapa, Diego Misseroni, Tomohiro Tachi, Glaucio H. Paulino
Summary: This research explores the geometrical-frustration-induced anisotropy and inhomogeneity to achieve unique properties of metamaterials. Using a triclinic metamaterial system based on a Trimorph origami pattern, a folding motion is created that results in an unusual Poisson effect and reversible auxeticity. Tessellating tristable unit cells produces phenomena resembling linear and point defects due to geometric frustration. This frustration can be reprogrammed into distinct stable and inhomogeneous states by selecting the location of point defects. These findings have potential applications in wave propagation control and compliant microrobots.
ADVANCED MATERIALS
(2022)
Article
Engineering, Multidisciplinary
Fernando V. Senhora, Heng Chi, Yuyu Zhang, Lucia Mirabella, Tsz Ling Elaine Tang, Glaucio H. Paulino
Summary: This article proposes an artificial intelligence approach to accelerate topology optimization, capturing the underlying physics of the problem. The framework demonstrates effectiveness and scalability through various design examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Multidisciplinary Sciences
James McInerney, Glaucio H. Paulino, D. Zeb Rocklin
Summary: This study develops a formalism to investigate the interplay between geometric symmetries and functionality in origami crease patterns. It reveals that the anticommuting symmetry defines a class of crease pattern geometries with equal and opposite Poisson's ratios.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Jonathan B. Russ, Miguel A. Aguilo, Glaucio H. Paulino
Summary: This study presents a formulation for topology optimization of structures with constraints on the first principal stress, solved using the augmented Lagrangian method to consider local stress constraints. Numerical examples demonstrate the effectiveness of the framework for practical problems with numerous local constraints, such as the three-dimensional antenna support bracket with over one million constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Materials Science, Multidisciplinary
Jonathan B. Russ, Glaucio H. Paulino
Summary: In order to enhance structural resistance to material failure, numerous topology optimization formulations have been proposed. This research extends the former method by constraining local failure criteria in a manner inspired by typical gradient-enhanced damage models. The proposed formulation relies on linear physics during the optimization procedure, greatly increasing its speed and robustness. Additionally, the study investigates the size effect introduced by using a numerical model and provides select observations, such as spurious fin-like patterns that can emerge depending on the structure and loading conditions. Finally, the load capacity of each optimized design is verified through a post-optimization verification procedure unaffected by the design parameterization and material interpolation schemes.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Multidisciplinary Sciences
Fernando V. Senhora, Ivan F. M. Menezes, Glaucio H. Paulino
Summary: Topology optimization problems often focus on a single or a few discrete load cases, while practical structures are subjected to infinitely many load cases that vary in intensity, location, and direction. This study proposes a locally stress-constrained topology optimization method that considers continuously varying load directions to ensure structural integrity under more realistic loading conditions.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mathematics, Applied
Arielle Carr, Eric de Sturler, Serkan Gugercin
Summary: Preconditioners are crucial for fast convergence in solving linear systems, and recycling them can be advantageous. A new method for updating and reusing preconditioners is introduced, with flexibility in balancing map quality and computational cost, leading to good results across various applications.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
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)