Article
Engineering, Multidisciplinary
Tale Bakken Ulfsby, Andre Massing, Simon Sticko
Summary: We propose a novel cut discontinuous Galerkin (CutDG) method for solving stationary advection-reaction problems on surfaces embedded in Rd. The approach involves embedding the surface into a full-dimensional background mesh and using discontinuous piecewise polynomials as test and trial functions. By introducing a suitable stabilization technique, we are able to establish inf-sup stability, a priori error estimates, and condition number estimates using an augmented streamline-diffusion norm. Numerical examples validate our theoretical findings.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Changyin Guo, Xufeng Xiao, Xinlong Feng, Zhijun Tan
Summary: In this article, an immersed finite element approach is introduced for solving interface problems of elliptic PDEs on curved surfaces. The approach avoids the need for complicated body-fitting surface grids and can efficiently capture sharp solutions across the interface. The proposed method performs substantially superior to the conventional surface finite element method, as verified by numerical examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Hauke Sass, Arnold Reusken
Summary: In this paper, a new Eulerian finite element method is proposed for discretization of scalar partial differential equations on evolving surfaces. The method utilizes the restriction of standard space-time finite element spaces on a fixed bulk mesh to the space-time surface and is suitable for a level set representation of the evolving surface. The higher order version of the method is based on a space-time variant of a mesh deformation that is developed for stationary surfaces in the literature. The presented discretization method achieves (optimal) higher order accuracy for smoothly varying surfaces with sufficiently smooth solutions. It can also be used for problems with topological singularities without any modifications, as demonstrated in a numerical study.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Guang-Jun Gao, Qian-Ru Chen, Chen Jiang, Tian-Tian Wang, Ming-Yang Liu, Gui-Rong Liu
Summary: In this paper, a novel characteristic-based polynomial pressure projection (CBP3) scheme is proposed to stabilize finite element method in solving incompressible laminar flow. The effectiveness of the proposed scheme is verified using linear triangular and bilinear quadrilateral elements. The results demonstrate that constant pressure projection is more suitable than linear pressure projection for stabilizing pressure oscillation in the CBP3 scheme.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Mathematics, Applied
Zhuochao Tang, Zhuojia Fu, Meng Chen, Leevan Ling
Summary: This paper presents our first attempt to implement a localized collocation method, GFDM, for the Turing patterns formation problems on smooth, closed, connected surfaces of codimension one in R-3. By projecting surface differential operators to Euclidean differential operators, explicit surface PDEs are given and solved using a set of collocation points distributed on surfaces. The sparse system formed from the localization scheme efficiently solves long time evolution Turing patterns formation problems, as demonstrated through numerical tests on convergence, Turing spot and stripe problems.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Multidisciplinary
Sushrut Pande, Panayiotis Papadopoulos, Ivo Babuska
Summary: This article introduces a cut-cell finite element method for solving Poisson's equation on two-dimensional domains of arbitrary shapes. Numerical experiments demonstrate that the method is stable and achieves the asymptotic convergence rates expected of unstructured body-fitted finite element methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Scott Congreve, Paul Houston
Summary: This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated polygonal/polyhedral meshes are employed for the coarse mesh approximation. By extending the existing error analysis and developing an hp-adaptive two-grid algorithm, the fine and coarse finite element spaces can be adaptively designed in an automatic manner. Numerical experiments demonstrate the computational performance of the proposed method.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Elena Bachini, Gianmarco Manzini, Mario Putti
Summary: A geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells is developed for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The theoretical properties of the classical VEM are extended to the framework by considering the highly anisotropic character of the final discretization, tested extensively on triangular and polygonal meshes with a manufactured solution to verify scheme limitations.
Article
Mathematics, Applied
Shuhao Cao, Chunmei Wang, Junping Wang
Summary: This paper presents a new numerical method for div-curl systems with the normal boundary condition. The method provides accurate and reliable numerical solutions under the assumption of low H-alpha-regularity for the true solution, and effectively approximates normal harmonic vector fields on domains with complex topology.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mofdi El-Amrani, Loubna Salhi, Mohammed Seaid
Summary: We propose a new approach that combines the modified method of characteristics with a unified finite element discretization to solve a class of coupled Darcy-advection-dispersion problems in anisotropic porous media. The proposed method takes advantage of the method of characteristics' ability to handle nonlinear convective terms, while using a unified formulation to apply equal-order finite element approximations and the L2-projection method for all solutions in the problem. Numerical experiments were performed to assess the quality of the proposed approach, showing high performance and the ability to capture dispersion effects in porous media problems.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Elena Bachini, Matthew W. Farthing, Mario Putti
Summary: In this study, a finite element method for PDEs on surfaces was developed based on a geometrically intrinsic formulation. The method was evaluated for steady and transient problems involving diffusion and advection-dominated regimes, showing expected convergence rates and good performance compared to established finite element methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Xiu Ye, Shangyou Zhang
Summary: This paper introduces a stabilizer free weak Galerkin finite element method on polytopal mesh with convergence rates one order higher than optimal convergence rates, achieving superconvergence on polytopal mesh. Numerical examples in 2D and 3D are presented to verify the theorem.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Yue Wang, Fuzheng Gao, Jintao Cui
Summary: A new conforming discontinuous Galerkin method is proposed for solving second order elliptic interface problems with discontinuous coefficient. Compared with known weak Galerkin algorithms, the method studied in this paper has no stabilizer and fewer unknowns. Error estimates in H-1 and L-2 norms are established, showing optimal order convergence.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Maitraya K. Bhattacharyya, David Radice
Summary: A new method that combines the strengths of SN and FPN schemes and mitigates their disadvantages is proposed based on a finite element approach in angle. The method specifies angular variables on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. The resulting method is found to perform well when one of the other methods fails.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Waixiang Cao, Chunmei Wang, Junping Wang
Summary: This paper presents a new Lp-primal-dual weak Galerkin finite element method for solving the div-curl system with the normal boundary condition. The proposed method provides accurate and reliable numerical solutions under low Wα,p-regularity and offers effective approximations of normal harmonic vector fields on domains with complex topology.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Esubalewe Lakie Yedeg, Eddie Wadbro, Peter Hansbo, Mats G. Larson, Martin Berggren
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2016)
Article
Engineering, Multidisciplinary
Erik Burman, Peter Hansbo, Mats G. Larson
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2018)
Article
Mathematics, Applied
Erik Burman, Peter Hansbo, Mats G. Larson
Article
Computer Science, Interdisciplinary Applications
Erik Burman, Peter Hansbo, Mats G. Larson, Karl Larsson
COMPUTERS & FLUIDS
(2019)
Article
Computer Science, Interdisciplinary Applications
Erik Burman, Peter Hansbo, Mats G. Larson
COMPUTATIONAL GEOSCIENCES
(2019)
Article
Engineering, Multidisciplinary
Erik Burman, Daniel Elfverson, Peter Hansbo, Mats G. Larson, Karl Larsson
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2019)
Article
Computer Science, Software Engineering
Erik Burman, Peter Hansbo, Mats G. Larson
BIT NUMERICAL MATHEMATICS
(2020)
Article
Engineering, Multidisciplinary
Erik Burman, Peter Hansbo, Mats G. Larson, Andre Massing, Sara Zahedi
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Erik Burman, Snorre H. Christiansen, Peter Hansbo
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Mirza Cenanovic, Peter Hansbo, Mats G. Larson
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Peter Hansbo, Mats G. Larson
Summary: A hybridized Nitsche finite element method was developed for two dimensional elastic interface problems, allowing for modeling of Euler-Bernoulli beams with axial stiffness and weak coupling with elastic subdomains.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Peter Hansbo, Mats G. Larson
Summary: This article introduces the use of augmented Lagrangian formalism to derive discontinuous Galerkin methods for problems in nonlinear elasticity, and provides examples from plasticity and large deformation hyperelasticity.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Peter Hansbo, Mats G. Larson
Summary: In this paper, a nonconforming rotated bilinear tetrahedral element is applied to the Stokes problem in R-3, demonstrating stability in combination with a piecewise linear, continuous approximation of the pressure. This element provides an approximation similar to the well-known Taylor-Hood element but with fewer degrees of freedom, and fulfills Korn's inequality, ensuring stability even when the Stokes equations are written on stress form for use in free surface flow.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Review
Computer Science, Interdisciplinary Applications
Erik Burman, Peter Hansbo, Mats G. Larson
Summary: In this paper, recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier-free stabilised methods are reviewed. The method combines a standard Lagrange multiplier method with a penalty term to penalise the constraint equations, and is commonly used in iterative algorithms for constrained optimisation problems. The paper first explains how the method can generate Galerkin/Least Squares type schemes for equality constraints, and then extends it to develop new stabilised methods for inequality constraints. Several examples of its application to different problems in computational mechanics are presented.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Erik Burman, Peter Hansbo, Mats G. Larson, Karl Larsson
Summary: In this article, we develop a discrete extension operator for trimmed spline spaces, which consist of piecewise polynomial functions with k continuous derivatives. The construction of the operator relies on polynomial extension from neighboring elements and projection back into the spline space. We prove stability and approximation results for the extension operator, and demonstrate how it can be used to construct a stable cut isogeometric method for solving an elliptic model problem.
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)