Related papers: Data-driven Stabilization of Nitsche's Method
As X-FEM approximation does not need meshing of the crack, the method has garnered a lot of attention from industrial point of view. This thesis report summarises some of the concepts involved in Nitsche approach for resolving boundary…
Efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff-Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. We solve the model…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
In this article, we develop a fully discrete numerical scheme for the one-dimensional (1D) and two-dimensional (2D) viscous Burgers equations with nonlinear Neumann boundary feedback control. The temporal discretization employs a…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
This thesis addresses challenges related to data and parameter efficiency in neural language models, with a focus on representation analysis and the introduction of new optimization techniques. The first part examines the properties and…
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…
Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
We are interested in the approximation of partial differential equations with a data-driven approach based on the reduced basis method and machine learning. We suppose that the phenomenon of interest can be modeled by a parametrized partial…