相关论文: Unfitted Nitsche's method for computing band struc…

Flat bands - single-particle energy bands - in tight-binding networks have attracted attention due to the presence of macroscopic degeneracies and their extreme sensitivity to perturbations. This makes them natural candidates for emerging…

Backward waves and negative refraction are shown to exist in plasmonic crystals whose lattice cell size is a very small fraction of the vacuum wavelength (less than 1/40th in an illustrative example). Such ``quasi-homogeneity'' is…

The weak imposition of essential boundary conditions is an integral aspect of unfitted finite element methods, where the physical boundary does not in general coincide with the computational domain. In this regard, the symmetric Nitsche's…

Flat band (FB) systems, featuring dispersionless energy bands, have garnered significant interest due to their compact localized states (CLSs). However, a detailed account on how local impurities affect the physical properties of…

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126…

When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of…

The simulation of the elastodynamics equations at high-frequency suffers from the well known pollution effect. We present a Petrov--Galerkin multiscale sub-grid correction method that remains pollution free in natural resolution and…

We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell…

This paper establishes optimal error estimates in the $L^2$ for the non-symmetric Nitsche method in an unfitted interface finite element setting. Extending our earlier work, we give a complete analysis for the Poisson interface model and,…

We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method is…

In this paper we study the topology of the bands of a plasmonic crystal composed of graphene and of a metallic grating. Firstly, we derive a Kronig-Penney type of equation for the plasmonic bands as function of the Bloch wavevector and…

In crystalline solids, disorder breaks translational symmetry and obscures k-resolved Bloch states, limiting an accurate description of wavefunction-based observables. In this work, we present a method that unfolds not only the band…

This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy…

This thesis presents a physics-informed machine learning framework for solving the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry, due to its…

Band crossings in electronic band structures play an important role in determining the electronic, topological, and transport properties in solid-state systems, making them central to both condensed matter physics and materials science. The…

There has been much recent interest and progress on topological structures of the non-Hermitian Bloch bands. Here, we study the topological structures of non-Bloch bands of non-Hermitian multiband quantum systems under open boundary…

We show the stability of a penalty-free asymmetric Nitsche's method using N\'ed\'elec edge elements for solving curl-curl-type problems with tangential Dirichlet boundary conditions imposed weakly. The main result is an inf-sup stability…

Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates which can be seen as artificial defects…

We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…

Boundary perturbations are generally irrelevant for bulk properties in the thermodynamic limit, as they are edge-confined and subextensive. We show that this expectation breaks down in boundary-driven systems exhibiting the non-Hermitian…