Article
Engineering, Electrical & Electronic
Shi Jie Wang, Jie Liu, Qing Huo Liu
Summary: A mixed Nitsche's method based on a hybrid tetrahedron-hexahedron mesh is proposed for solving Maxwell's eigenvalue problems, which is flexible for different types of meshes. The method features unique rules for selecting high-order hierarchical basis functions and suppressing Ritz vectors in the Arnoldi algorithm, demonstrating higher efficiency in numerical experiments.
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES
(2022)
Article
Mathematics, Applied
Qian Zhang, Zhiyue Zhang
Summary: This paper presents Nitsche's method for solving elliptic Dirichlet boundary control problems on curved domains with control constraints. By using Nitsche's method to handle inhomogeneous Dirichlet boundary conditions, the L-2 boundary control is naturally incorporated into the variational formulation. The method was first used in Chang et al.'s study, where the curved boundary was approximated by a broken line and a locally defined mapping was required to obtain numerical control on the curved boundary.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Timo Betcke, Erik Burman, Matthew W. Scroggs
Summary: This paper considers the use of boundary element methods to solve boundary condition problems, where the Calderón projector is used as the system matrix and boundary conditions are weakly imposed using a variational boundary operator designed with augmented Lagrangian methods. Both the primal trace variable and the flux are approximated regardless of the boundary conditions. The paper specifically focuses on the imposition of Dirichlet conditions on the Helmholtz equation and extends the analysis of the Laplace problem to this case. The theory is demonstrated through numerical examples.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Tiantian Zhang, Wenwen Xu, Xindong Li, Yan Wang
Summary: This paper investigates the application of the semi-discrete multipoint flux mixed finite element method for parabolic optimal control problems, approximating the state and control variables to solve the problem. The advantage lies in decoupling the state and adjoint state variables, obtaining convergence orders and error estimates.
Article
Mathematics, Applied
Fanyi Yang, Xiaoping Xie
Summary: In this study, an unfitted finite element method of arbitrary order is proposed and analyzed for solving elliptic problems on domains with curved boundaries and interfaces. The method extends the finite element space from interior elements to the whole domain, without any degree of freedom on boundary/interface elements. The method is shown to be stable without any mesh adjustment or special stabilization. Numerical results demonstrate the accuracy and robustness of the method in both two and three dimensions.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Huadong Gao, Meng Li
Summary: This paper investigates the splitting mixed finite element method and proves its equivalence to the conventional mixed finite element method when the initial data is carefully chosen. The equivalence also holds for more complex models. Numerical comparisons demonstrate the efficiency of the splitting mixed method.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Yuki Chiba, Norikazu Saito
Summary: In this paper, we analyze the P-1 finite-element method for an inhomogeneous Robin boundary value problem in smooth bounded domains in Double-struck capital R-n, n = 2, 3. We use Nitsche's method to weakly impose the boundary condition and interpret the Robin BVP as the classical penalty method. We provide optimal-order error estimates and investigate the dependence of epsilon on error estimates, without making any unessential regularity assumptions on the solution. Numerical examples are provided to support the results.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Multidisciplinary
Xujing Li, Xiaodi Zhang, Xinxin Zhou
Summary: In this paper, high-order interface penalty finite element methods are proposed for elliptic interface problems with Robin interface jump conditions. The stability and robustness are ensured by employing the delicate weighting trick and the general Nitsche's method, respectively. Optimal error estimates are proven in the energy norm for the schemes, which are independent of both the cut configurations and the asymptotic parameter. A series of three-dimensional numerical results confirm the robustness and efficiency of the proposed methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado
Summary: The Modified Local Green's Function Method (MLGFM) is an integral method that uses Green's function projections, determined by Finite Element Method, as fundamental solution to solve problems. This paper proposes an alternative formulation to the MLGFM that reduces computational effort by avoiding the need for obtaining these projections. The new formulation presents the same accuracy as the previous one and is applied to problems in solid mechanics and compared with the standard Finite Element Method and the Boundary Element Method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
L. F. Contreras, D. Pardo, E. Abreu, J. Munoz-Matute, C. Diaz, J. Galvis
Summary: This paper focuses on linear and semilinear parabolic problems in high-contrast multiscale media in two dimensions. The presence of high-contrast multiscale media has negative effects on the accuracy, stability, and efficiency of numerical approximations. The authors propose an efficient Generalized Multiscale Finite Element Method (GMsFEM) that combines with exponential integration in time to obtain a good approximation. The experiments presented show the advantages of combining exponential integration and GMsFEM approximations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Hercules de Melo Barcelos, Carlos Friedrich Loeffler, Luciano de Oliveira Castro Lara, Webe Joao Mansur
Summary: Using the Finite Element Method to calculate spatial derivatives of the primal variable results in low accuracy due to order reduction in interpolation functions. To address this issue, this study employs the Boundary Element Method's integral equation to recalculate new values of internal variables based on the Finite Element solution. Computational tests comparing the proposed procedure with standard FEM results confirm the consistency of the model.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Xiaoxiao He, Weibing Deng
Summary: This paper presents a nonconforming cut finite element method based on the nonsymmetric Nitsche method for elliptic interface problems without using interface penalty parameters. The stability of the bilinear form is proved by constructing a special function and using an inf-sup argument, and optimal convergence in the energy norm along with suboptimal convergence in the L-2-norm are derived.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Haifeng Ji
Summary: This paper presents a lowest-order immersed Raviart-Thomas mixed triangular finite element method for solving elliptic interface problems. The method constructs an immersed finite element by modifying the traditional element and derives important properties and error estimates. Numerical examples are provided to validate the theoretical analysis.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Yongfeng Cheng, Zhibao Nie, Shijun Ding, Kaiyuan Liu, Mintao Ding, Zibo Fan
Summary: This paper presents a new iterative method for solving Signorini problems. The method involves establishing boundary integral equations and deriving system equations related to unknown variables on the problem boundary. The Signorini boundary conditions are expressed as equivalent variational inequalities, and the problem is then reduced to a mixed variational inequality problem. The proposed algorithm, based on the projection-contraction algorithm, is demonstrated to be accurate and effective through multiple test cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Ram Manohar, Rajen Kumar Sinha
Summary: This paper presents a method for deriving space-time local a posteriori error estimates for Neumann boundary control problems using finite element approximations. The method is applicable for a convex bounded domain and utilizes piecewise linear and continuous finite elements as well as piecewise constant functions for approximation. The backward Euler method is used for time discretization. Three reliable local a posteriori error estimates are derived for boundary control problems with different types of observations. These estimators have local characteristics and depend on the small neighborhood of the boundary. They can be used to study the behavior of the state and co-state variables around the boundary and provide necessary feedback in terms of error indicators for adaptive mesh refinements in the finite element method. Numerical results validate the effectiveness of the derived estimators.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics
Alfio Quarteroni, Luca Dede, Francesco Regazzoni
Summary: In this paper, we present the electromechanical mathematical model of the human heart and discuss the establishment of numerical methods and challenges. Numerical tests demonstrate the expected theoretical convergence rate of the numerical solutions and prove the preliminary valuable application of our model in tackling clinical problems.
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Computer Science, Interdisciplinary Applications
F. Regazzoni, M. Salvador, P. C. Africa, M. Fedele, L. Dede, A. Quarteroni
Summary: This article proposes a novel mathematical and numerical model for cardiac electromechanics, which combines biophysically detailed core models, an Artificial Neural Network model, and appropriate coupling schemes. The model accurately simulates cardiac function and quantifies the utilization, dissipation, and transfer of energy in the cardiovascular network. Additionally, a robust algorithm is proposed for reconstructing the stress-free reference configuration and validating energy indicators used in clinical practice.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Matteo Salvador, Francesco Regazzoni, Luca Dede, Alfio Quarteroni
Summary: In this study, a Bayesian statistical approach combining Maximum a Posteriori estimation and Hamiltonian Monte Carlo is used to quickly and accurately estimate model parameters of the cardiac function. The use of an Artificial Neural Network surrogate model allows for fast simulations and minimal hardware requirements. The approach is suitable for clinical applications and is compliant with Green Computing practices.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2023)
Article
Engineering, Biomedical
Michele Bucelli, Alberto Zingaro, Pasquale Claudio Africa, Ivan Fumagalli, Luca Dede', Alfio Quarteroni
Summary: We have developed a mathematical and numerical model that simulates the various processes involved in heart function, including electrophysiology, mechanics, and hemodynamics. The model also considers the interactions between the different processes, such as electro-mechanical and mechano-electrical feedback. By using a coupled fluid-structure interaction approach, we are able to represent the three-dimensional nature of the heart muscle and hemodynamics. The model has been validated using a realistic human left heart model and shows qualitative and quantitative agreement with physiological ranges and medical images.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2023)
Article
Mathematics
Paola F. Antonietti, Matteo Caldana, Luca Dede'
Summary: We propose a novel deep learning-based algorithm, using Artificial Neural Networks (ANNs), to accelerate the convergence of Algebraic Multigrid (AMG) methods for solving linear systems of equations from finite element discretizations of Partial Differential Equations (PDEs). By predicting the strong connection parameter with ANNs, we maximize the convergence factor of the AMG scheme. We demonstrate the effectiveness of our algorithm, called AMG-ANN, through solving two-dimensional model problems with highly heterogeneous diffusion coefficients and stationary Stokes equations.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Fabio Marcinno', Alberto Zingaro, Ivan Fumagalli, Luca Dede', Christian Vergara
Summary: In this work, the blood dynamics in the pulmonary arteries is studied using a 3D-0D geometric multiscale approach, and three strategies for the numerical solution of the 3D-0D coupled problem are proposed. Numerical experiments are performed using a patient-specific 3D domain and a physiologically calibrated 0D model, and the effects of connection methods and numerical strategies are discussed. The results demonstrate the potential of this method in clinical applications.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Marco Fedele, Roberto Piersanti, Francesco Regazzoni, Matteo Salvador, Pasquale Claudio Africa, Michele Bucelli, Alberto Zingaro, Luca Dede, Alfio Quarteroni
Summary: This paper presents a biophysically detailed electromechanical model of the whole human heart, considering both atrial and ventricular contraction, as well as the bioelectromechanical interaction within the heart. The model is able to reproduce the healthy cardiac function for all chambers and demonstrates the importance of atrial contraction, fibers-stretch-rate feedback, and stabilization techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Michele Bucelli, Francesco Regazzoni, Luca Dede, Alfio Quarteroni
Summary: This paper proposes a novel method that combines rescaled localized RBF interpolation with SVD to accurately, robustly and efficiently transfer the deformation gradient tensor between meshes of different resolution in cardiac electromechanics simulations. The method overcomes limitations of existing interpolation methods and enhances the flexibility and accuracy of electromechanical simulations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Mattia Corti, Francesca Bonizzoni, Luca Dede, Alfio M. Quarteroni, Paola F. Antonietti
Summary: This paper presents a numerical modelling of the misfolding process of a-synuclein in Parkinson's disease, using a discontinuous Galerkin method. The results demonstrate the stability and accuracy of the proposed method in simulating the spreading of prion proteins, providing valuable insights for understanding the neurodegeneration process.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Tommaso Tassi, Alberto Zingaro, Luca Dede
Summary: This paper proposes using machine learning and artificial neural networks to enhance stabilization methods for advection-dominated differential problems. By generating a dataset and using the neural network to choose the optimal stabilization parameter, our approach yields more accurate solutions than conventional methods.
MATHEMATICS IN ENGINEERING
(2023)
Article
Physics, Mathematical
Michele Bucelli, Luca Dede, Alfio Quarteroni, Christian Vergara
Summary: This paper evaluates and compares different numerical methods for fluid-structure interaction (FSI) in heart modeling, aiming to select the most computationally efficient method for heart FSI simulations. Numerical tests are conducted to mimic the flow regime during systole and diastole in a human ventricle, and the monolithic method is found to be more cost-effective.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Cardiac & Cardiovascular Systems
Antonio Frontera, Stefano Pagani, Luca Rosario Limite, Andrea Peirone, Francesco Fioravanti, Bogdan Enache, Jose Cuellar Silva, Konstantinos Vlachos, Christian Meyer, Giovanni Montesano, Andrea Manzoni, Luca Dede, Alfio Quarteroni, Decebal Gabriel Latcu, Pietro Rossi, Paolo Della Bella
Summary: This study evaluated the progression of electrophysiological phenomena in patients with paroxysmal atrial fibrillation (PAF) and persistent atrial fibrillation (PsAF). The findings suggest that the electrical remodeling is mainly determined by corridors of slow conduction and a higher curvature of wave-front propagation in PsAF patients, which may contribute to the maintenance of atrial fibrillation.
JACC-CLINICAL ELECTROPHYSIOLOGY
(2022)
Article
Mathematical & Computational Biology
Nicola Parolini, Luca Dede', Giovanni Ardenghi, Alfio Quarteroni
Summary: In this paper, an extended SUIHTER model is proposed to analyze the COVID-19 spreading in Italy, taking into account the vaccination campaign and the presence of new variants. The specific features of the variants and vaccines are modeled based on clinical evidence, and the new model is validated by comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses.
INFECTIOUS DISEASE MODELLING
(2022)
Article
Mathematics, Applied
Alberto Zingaro, Ivan Fumagalli, Luca Dede, Marco Fedele, Pasquale C. Africa, Antonio F. Corno, Alfio Quarteroni
Summary: We propose a new computational model for simulating blood flow in the human left heart. This model uses the Navier-Stokes equations and the Resistive Immersed Implicit Surface method to account for endocardium motion and model cardiac valves. It couples a 3D cardiac electromechanical model with a 0D circulation model to impose a physiological displacement of the domain boundary. Additionally, a preprocessing procedure and coupling with a 0D circulation model are used to extend the left ventricle motion to the endocardium of the left atrium and ascending aorta. The model is validated by reproducing correct hemodynamic indicators.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2022)
