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High-Q optical resonances in photonic microcavities are investigated numerically using a time-harmonic finite-element method.

Optics · Physics 2011-02-23 S. Burger , J. Pomplun , F. Schmidt , L. Zschiedrich

In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…

Optics · Physics 2024-12-03 Fan Xiao , Jingwei Wang , Zhongfei Xiong , Yuntian Chen

We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility…

Optics · Physics 2025-12-22 Jérémy Itier , Gilles Renversez , Frédéric Zolla

Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…

Numerical Analysis · Mathematics 2025-06-09 Harald Garcke , Robert Nürnberg

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…

Numerical Analysis · Computer Science 2022-02-04 Teseo Schneider , Jeremie Dumas , Xifeng Gao , Mario Botsch , Daniele Panozzo , Denis Zorin

Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…

Numerical Analysis · Mathematics 2023-04-05 Shuhao Cao , Long Chen , Ruchi Guo

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…

Light scattering in disordered media plays an important role in various areas of applied science from biophysics to astronomy. In this paper we study two approaches to calculate scattering properties of semi-infinite densely packed media…

Computational Physics · Physics 2023-04-12 Sofia Ponomareva , Alexey A. Shcherbakov

In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…

Numerical Analysis · Mathematics 2019-08-07 Aihua Lin , Per Kristen Jakobsen

Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a…

Optics · Physics 2009-05-28 L. Zschiedrich , S. Burger , J. Pomplun , F. Schmidt

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…

Numerical Analysis · Mathematics 2023-10-03 Alan F. Hegarty , Eugene O'Riordan

In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…

Classical Physics · Physics 2026-03-27 Per Kristen Jakobsen

We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…

Numerical Analysis · Mathematics 2024-10-25 Zhiming Chen , Ke Li , Maohui Lyu , Xueshuang Xiang

This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…

Numerical Analysis · Mathematics 2015-07-07 Paul Houston , Thomas P. Wihler

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…

Optics · Physics 2009-05-28 L. Zschiedrich , S. Burger , A. Schädle , F. Schmidt

This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…

The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive…

Computational Engineering, Finance, and Science · Computer Science 2021-10-13 Jonas Bundschuh , Laura A. M. D'Angelo , Herbert De Gersem

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…

Numerical Analysis · Mathematics 2018-09-26 Ali Özcan , Stefan Kollmannsberger , John N. Jomo , Ernst Rank

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…

Numerical Analysis · Mathematics 2014-03-21 Klaus Deckelnick , Charles M. Elliott , Thomas Ranner