When two resonant modes in a system with gain or loss coalesce both their resonance position and width, so-called exceptional point occurs, which acts as source of non-trivial physics diverse range systems. Lasers provide natural setting to study such non-Hermitian degeneracies, they feature material basic constituents. Here we show that points can be conveniently induced photonic molecule laser by suitable variation the applied pump. Using pair coupled microdisk quantum cascade lasers,...

Reliable a posteriori error estimates without generic constants can be obtained by comparison of the finite element solution with feasible function for dual problem. A cheap computation such functions via equilibration is well known scalar equations second order. We simplify and modify that it applied to curl-curl equation edge elements. The construction more involved elements since has performed on subsets different dimensions. For this reason, Raviart–Thomas are extended in spirit distributions.

We consider large scale sparse linear systems in saddle point form. A natural property of such indefinite 2-by-2 block is the positivity (1,1) on kernel (2,1) block. Many solution methods, however, require that satisfied everywhere. To enforce everywhere, an augmented Lagrangian approach usually chosen. However, adjustment involved parameters a critical issue. will present different not based explicit augmentation technique. For considered class symmetric and preconditioners, assumptions are...

Maxwell equations are posed as variational boundary value problems in the function space $H(\operatorname {curl})$ and discretized by Nédélec finite elements. In Beck et al., 2000, a residual type posteriori error estimator was proposed analyzed under certain conditions onto domain. present paper, we prove reliability of that on Lipschitz domains. The key is to establish new estimates for commuting quasi-interpolation operators recently introduced J. Schöberl,

Abstract Purpose – The goal of the presented work is efficient computation Maxwell boundary and eigenvalue problems using high order H(curl) finite elements. Design/methodology/approach Discusses a systematic strategy for realization arbitrary hierarchic H(curl)‐conforming elements triangular tetrahedral element geometries. shape functions are classified as lowest Nédélec, higher‐order edge‐based, face‐based (only in 3D) element‐based ones. Findings Our new provide not only global complete...

Abstract This paper presents an algebraic multigrid method for the efficient solution of linear system arising from a finite element discretization variational problems in H 0 (curl,Ω). The spaces are generated by Nédélec's edge elements. A coarsening technique is presented, which allows construction suitable coarse spaces, corresponding transfer operators and appropriate smoothers. prolongation operator designed such that grid kernel functions curl‐operator mapped to fine functions....

We propose and analyse a new finite-element method for convection–diffusion problems based on the combination of mixed elliptic discontinuous Galerkin (DG) hyperbolic part problem. The two methods are made compatible via hybridization both is appropriate solution intermediate problems. By construction, discrete solutions obtained limiting subproblems coincide with ones by DG present type analysis that explicitly takes into account Lagrange multipliers introduced hybridization. use adequate...

In this paper, we introduce new finite elements to approximate the Hellinger Reissner formulation of elasticity. The are vector-valued tangential continuous Nédélec for displacements, and symmetric tensor-valued, normal–normal stresses. These do neither suffer from volume locking as Poisson ratio approaches ½, nor shear when anisotropic used thin structures. We present analysis elements, discuss their implementation, give numerical results.

Classical inf-sup stable mixed finite elements for the incompressible (Navier--)Stokes equations are not pressure-robust, i.e., their velocity errors depend on continuous pressure. However, a modification only in right-hand side of Stokes discretization is able to reestablish pressure-robustness, as shown recently several with discontinuous discrete pressures. In this contribution, idea extended low and high order Taylor--Hood mini elements, which have For reconstruction operator constructed...

Many surface acoustic wave (SAW) devices consist of quasiperiodic structures that are designed by successive repetition a base cell. The precise numerical simulation such devices, including all physical effects, is currently beyond the capacity high-end computation. Therefore, we have to restrict analysis periodic substructure. By using finite-element method (FEM), this can be done introducing boundary conditions (PBCs) at special artificial boundaries. To able describe complete dispersion...

We propose a new discretization method for the Stokes equations. The is an improved version of recently presented in [C. Lehrenfeld and J. Schöberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which based on $H({div})$-conforming finite element space hybrid discontinuous Galerkin (HDG) formulation viscous forces. $H({div})$-conformity results favorable properties such as pointwise divergence-free solutions pressure robustness. However, approximation velocity with polynomial degree $k$, it...

Abstract In this paper, we present a framework for automated shape differentiation in the finite element software . Our approach combines mathematical Lagrangian differentiating PDE-constrained functions with capabilities of The user can decide which degree automatisation is required, thus allowing either more custom-like or black-box–like behaviour software. We discuss automatic generation first- and second-order derivatives unconstrained model problems as well realistic that are...

Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for generic two-dimensional high-lift configuration with leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing approach. To avoid unphysical reflections boundaries of truncated computational domain, perfectly matched layer absorbing boundary conditions implemented in form complex scaling method atomic molecular physics. It shown...