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A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the…
Theoretically, the electric field becomes infinite at corners of two and three dimensions and edges of three dimensions. Conventional finite-element and boundary element methods do not yield satisfactory results at close proximity to these…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…
The magnetic fields of spiral galaxies are so strong that they cannot be primordial. Their typical values are over one billion times higher than any value predicted for the early Universe. Explaining this immense growth and incorporating it…
By considering the continuous model for graphene, we analytically study a special gauge field for the edge state. The gauge field explains the properties of the edge state such as the existence only on the zigzag edge, the partial…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…
Magnetic fields pervade astrophysical systems and strongly influence their dynamics. Because magnetic diffusion is usually much faster than system evolution, ancient fields cannot explain the present magnetization of planets, stars, and…
With the development of condensed-matter physics and nanotechnology, attention has turned to the fields near and on surfaces that result from interactions between electric dipole radiation and mesoscale structures. It is hoped that studying…
Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies, and the early Universe are discussed. We focus particularly on aspects of spatio-temporal nonlocality, which is one…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
A method is described to model the magnetic field in the vicinity of constellations of multiple satellites using field and plasma current measurements. This quadratic model has the properties that the divergence is zero everywhere and…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…