A5078280058- Electromagnetic Simulation and Numerical Methods
- Advanced Numerical Methods in Computational Mathematics
- Advanced Fiber Laser Technologies
- Model Reduction and Neural Networks
- Electromagnetic Scattering and Analysis
- Photonic Crystal and Fiber Optics
- Numerical methods in engineering
- Computational Geometry and Mesh Generation
- Magnetic Properties and Applications
- Radiation Detection and Scintillator Technologies
- Radiation Effects in Electronics
- Contact Mechanics and Variational Inequalities
- Diamond and Carbon-based Materials Research
- Neural Networks and Applications
- Numerical methods for differential equations
- Laser-Matter Interactions and Applications
- Structural Analysis and Optimization
Leibniz University Hannover
2021-2024
Abstract This paper provides an overview of the new features finite element library deal.II, version 9.6.
We numerically explore synthetic crystal diamond for realizing novel light sources in ranges which are up to now difficult achieve with other materials, such as sub-10-fs pulse durations and challenging spectral ranges. assess the performance of on-chip waveguides controlling generation by means nonlinear soliton dynamics. The considered silica-embedded waveguide model exhibits two zero-dispersion points, delimiting an anomalous dispersion range that exceeds octave. Various propagation...
In this work, we consider the design of a geometric multigrid method with multiplicative Schwarz smoothers for eddy-current problem and time-harmonic Maxwell equations. The main purpose is to show numerically that straightforward application works former problem, but not latter. well-known key special decomposition function spaces within algorithm. failures performance are shown help numerical test, implemented in modern finite element library deal.II, including github link implementation.
In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, propose feedforward neural network-enhanced approximation of interface conditions between subdomains. The advantage is that condition can be updated without recomputing Maxwell system at each step. main part consists detailed description construction network for training process. To substantiate proof concept, investigate few subdomains in...
In this work, restricted additive Schwarz (RAS) and optimized (ORAS) preconditioners from the Trilinos package FROSch (Fast Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling is implemented. While RAS have been available before, ORAS newly added FROSch. The FROSch-deal.II works both Lagrange-based N\'ed\'elec finite elements. Here, as problems, nonstationary,...
Abstract In this work, local mesh adaptivity for the time harmonic Maxwell equations is studied. The main purpose to apply a known posteriori residual‐based error estimator from literature and investigate its performance Y‐beam splitter setting. This configuration an important prototype design of optical systems within excellence cluster PhoenixD. Specifically, branching region interest requires high accuracy numerical simulation. One example shows our approach.
While working with N\'ed\'elec elements on adaptively refined meshes hanging nodes, the orientation of edges and faces must be taken into account. Indeed, for non-orientable meshes, there was no solution implementation available to date. The problem statement corresponding algorithms are described in great detail. As a model problem, time-harmonic Maxwell's equations adopted because constitute their natural discretization. is performed within finite element library deal.II. demonstrated...
We numerically explore synthetic crystal diamond for realizing novel light sources in ranges which are up to now difficult achieve with other materials, such as sub-10-fs pulse durations and challenging spectral ranges. assess the performance of on-chip waveguides controlling generation by means nonlinear soliton dynamics. Tailoring cross-section allows design dispersion profiles custom zero-dispersion points anomalous exceeding an octave. Various propagation dynamics, including...
The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications modern physics. In this work, we present parallel finite element solver for the compare different preconditioners. We show numerically that standard preconditioners like incomplete LU additive Schwarz method lead to slow convergence iterative solvers generalized minimal residuals, especially high wave numbers. Even more also specialized methods Schur complement...