Article
Mathematics, Applied
D. Cho, L. F. Pavarino, S. Scacchi
Summary: The study focuses on constructing Overlapping Additive Schwarz (OAS) preconditioners for isogeometric collocation discretizations of linear elasticity in both two and three space dimensions. Numerical results show that two-level OAS preconditioners are scalable, quasi-optimal with respect to mesh size, and optimal with respect to spline polynomial degree. Additionally, two-level OAS preconditioners are more robust in certain material and geometry deformation scenarios than one-level OAS and non-preconditioned GMRES solvers.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Christos Gkritzalis, Manolis Papadrakakis
Summary: Isogeometric collocation methods are introduced as an alternative to isogeometric Galerkin formulations to improve computational cost. However, collocation formulations result in non-symmetric matrices of higher dimensions, requiring special attention for large-scale simulations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Pierre Jolivet, Jose E. Roman, Stefano Zampini
Summary: This paper explains the interfacing of PETSc and HPDDM libraries to provide robust preconditioners and advanced Krylov methods for solving linear systems of different structures. The flexibility of the implementation is showcased through minimalist examples covering various application domains.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Nicolas A. Barnafi, Luca F. Pavarino, Simone Scacchi
Summary: In this study, a performance comparison is provided between the Balancing Domain Decomposition by Constraints (BDDC) and the Algebraic Multigrid (AMG) preconditioners for cardiac mechanics. The impact of different parameters of the BDDC preconditioner is explored, and the performance is evaluated through a realistic electromechanical simulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Nicolas Marsic, Christophe Geuzaine, Herbert De Gersem
Summary: In this paper, different transmission operators for the non-overlapping Schwarz method are discussed for solving the time-harmonic Helmholtz equation in cavities. New operators that take into account back-propagating waves are explored and compared with established operators neglecting these contributions. The focus is on rectangular cavities, but deviations from this ideal geometry are also considered. Computation of acoustic noise in a three-dimensional model shows a 46% reduction in iteration count when using an operator optimized for cavities compared to those optimized for unbounded problems.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Marco Discacciati, Ben J. Evans, Matteo Giacomini
Summary: This article proposes a non-intrusive proper generalized decomposition (PGD) strategy coupled with an overlapping domain decomposition (DD) method to construct surrogate models for parametric linear elliptic problems. The approach utilizes the linearity of the operator and an overlapping Schwarz method to efficiently solve and glue together local surrogate models. Numerical results demonstrate the accuracy, robustness, and superior performance of the proposed strategy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Mathematics, Applied
Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, Olof B. Widlund
Summary: A new reduced-dimension adaptive generalized Dryja-Smith-Widlund (GDSW) overlapping Schwarz method is proposed for linear second-order elliptic problems in three dimensions. The method is robust and insensitive to the contrast of coefficients in the partial differential equations. By using a new interface decomposition, the method achieves a smaller coarse space while maintaining efficiency.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics
Dario Martinez, Henar Herrero, Francisco Pla
Summary: In this work, an alternate Schwarz domain decomposition method is proposed to solve a Rayleigh-Benard problem. The method overcomes the ill conditioning of Legendre collocation and achieves efficient solutions close to turbulence or in domains with large aspect ratios. The computational cost is comparable to other methods, and the code is parallelizable.
Article
Engineering, Multidisciplinary
Angelo Iollo, Giulia Sambataro, Tommaso Taddei
Summary: A component-based parametric model order reduction approach for parameterized nonlinear elliptic PDEs based on overlapping subdomains is proposed. It utilizes a constrained optimization statement, penalizes the jump at interfaces, and satisfies the PDE in each local subdomain. The approach decomposes the local states into a port component and a bubble component, enabling it to be reformulated as a nonlinear least-squares problem for solution using the Gauss-Newton method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Ruiyang Dai, Axel Modave, Jean-Francois Remacle, Christophe Geuzaine
Summary: This paper explores a family of generalized sweeping preconditioners for Helmholtz problems with non-overlapping checkerboard partition. By using high-order transmission conditions and cross-point treatments in the domain decomposition procedure, combined with the flexible version of GMRES, the rapid transfer of information between different areas and accelerated convergence can be achieved. Experimental results demonstrate the good performance of the preconditioners in different sweeping directions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Martin J. Gander, Stephan B. Lunowa, Christian Rohde
Summary: In this paper, a non-overlapping domain decomposition algorithm of Schwarz waveform-relaxation (SWR) type is proposed for solving nonlinear advection-diffusion equations. The algorithm relies on nonlinear zeroth-order (or Robin) transmission conditions between sub-domains to ensure the continuity of the converged solution and its normal flux across the interface. Existence of unique iterative solutions and the convergence of the algorithm are proved. Numerical results confirm the theoretical findings, particularly the convergence of the algorithm.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Interdisciplinary Applications
Bjoern Kiefer, Stefan Prueger, Oliver Rheinbach, Friederike Roever
Summary: We use the swelling of hydrogels as an example to demonstrate the strong coupling between mechanical balance relations and mass diffusion in a chemo-mechanical problem. By formulating the problem as a minimization problem and using a time-explicit approach, we obtain symmetric matrices for iterative solvers. Our MPI-parallel implementation utilizes the deal.II, p4est, and FROSch software libraries. FROSch is part of Trilinos library and is used in fully algebraic mode, constructing the preconditioner from the monolithic system matrix.
COMPUTATIONAL MECHANICS
(2023)
Article
Mathematics, Applied
Pei Zhou, Chun -Gang Zhu
Summary: In this paper, we propose a new residual parameterization method for planar physical domains in isogeometric collocation (IGC), aiming to improve the numerical accuracy of solving partial differential equations (PDEs). The method minimizes objective functions consisting of geometry-related functionals and analysis-related residual norms in an unconstrained optimization problem. Reduced quadrature rules are applied to simplify the computation of residual norms. Numerical examples show that the proposed method achieves a significantly higher numerical accuracy compared to the standard IGC method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Alexander Heinlein, Mauro Perego, Sivasankaran Rajamanickam
Summary: This study focuses on the numerical simulations of Greenland and Antarctic ice sheets and proposes a two-level Schwarz preconditioner to improve computational efficiency. The study shows that the proposed preconditioner has good scalability and robustness for single physics problems, and it is the first time it has been applied to ice sheet problems. Additionally, the study explores methods to further improve performance and conducts weak and strong scaling studies.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Alexander Heinlein, Oliver Rheinbach, Friederike Roever
Summary: This paper investigates the parallel performance of three-level fast and robust overlapping Schwarz (FROSch) preconditioners for linear elasticity. The paper describes the additional steps in the implementation of the recursive FROSch preconditioner and shows that explicit geometric information is not needed. Parallel results obtained on different supercomputers are discussed, highlighting the impact of hierarchical communication operations on computing time. Further analysis on large supercomputers with dragonfly interconnects is deemed necessary.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
L. Beirao Da Veiga, D. Mora, G. Rivera
MATHEMATICS OF COMPUTATION
(2019)
Article
Engineering, Multidisciplinary
Heng Chi, Lourenco Beirao da Veiga, Glaucio H. Paulino
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2019)
Article
Mathematics, Applied
L. Beirao da Veiga, A. Russo, G. Vacca
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2019)
Article
Mathematics, Applied
L. Beirao da Veiga, G. Manzini, L. Mascotto
NUMERISCHE MATHEMATIK
(2019)
Article
Mathematics, Applied
L. Beirao da Veiga, D. Mora, G. Vacca
JOURNAL OF SCIENTIFIC COMPUTING
(2019)
Article
Engineering, Multidisciplinary
E. Artioli, L. Beirao da Veiga, F. Dassi
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Dassi, G. Vacca
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2020)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Brezzi, L. D. Marini, A. Russo
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2020)
Review
Mathematics, Applied
E. Artioli, L. Beirao da Veiga, M. Verani
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2020)
Article
Engineering, Multidisciplinary
Fadi Aldakheel, Blaz Hudobivnik, Edoardo Artioli, Lourenco Beirao da Veiga, Peter Wriggers
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
L. Beirao da Veiga, A. Pichler, G. Vacca
Summary: This paper presents a virtual element (VE) discretization for a time-dependent coupled system of nonlinear partial differential equations, aiming to investigate the capabilities of virtual element methods (VEM) for complex fluid flow problems. By combining VEM with a time stepping scheme, a theoretical analysis of the method was developed under the assumption of a regular solution. The scheme was then tested on both regular and realistic test cases to validate its effectiveness.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Dassi, G. Manzini, L. Mascotto
Summary: We introduce a low order virtual element discretization for time dependent Maxwell's equations, which allows for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori estimates and validate them through numerical experiments. As key findings, we discuss novel inequalities associated with de Rahm sequences of nodal, edge, and face virtual element spaces.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
L. Beirao da Veiga, C. Canuto, R. H. Nochetto, G. Vacca
Summary: This study investigates the equilibrium of a hinged rigid leaflet with an attached rotational spring in a stationary incompressible fluid within a rigid channel using theoretical and numerical methods. Sufficient conditions for the existence and uniqueness of equilibrium positions are identified based on properties of the domain functional. The proposed numerical technique utilizes the mesh flexibility of the Virtual Element Method and proves quasi-optimal error estimates through a variety of numerical experiments.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Jian Meng, Lourenco Beirao da Veiga, Lorenzo Mascotto
Summary: In this paper, we establish stability bounds for Stokes-like virtual element spaces in both two and three dimensions. These bounds are crucial for deriving optimal interpolation estimates. In addition, we conduct numerical tests to investigate the behavior of the stability constants from a practical perspective.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
L. Beirao da Veiga, D. Mora, A. Silgado
Summary: In this paper, a fully-coupled virtual element method is proposed for solving the nonstationary Boussinesq system in 2D. The method utilizes the stream-function and temperature fields and employs C1- and C0-conforming virtual element approaches for spatial discretization. The temporal variable is discretized using a backward Euler scheme. The well-posedness and unconditional stability of the fully-discrete problem are proved, and error estimates in H2- and H1-norms are derived for the stream-function and temperature fields. Benchmark tests are conducted to validate the theoretical error bounds and demonstrate the behavior of the fully-discrete scheme.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
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)
