Algorithmic realization of the solution to the sign conflict problem for hanging nodes on hp-hexahedral N\'ed\'elec elements

While working with N\'ed\'elec elements on adaptively refined meshes with hanging nodes, the orientation of the hanging edges and faces must be taken into account. Indeed, for non-orientable meshes, there was no solution and implementation available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell's equations are adopted because N\'ed\'elec elements constitute their natural discretization. The implementation is performed within the finite element library deal.II. The algorithms and implementation are demonstrated through four numerical examples on different uniformly and adaptively refined meshes

A residual‐based error estimator and mesh adaptivity for the time harmonic Maxwell equations applied to a Y‐beam splitter

In this work, local mesh adaptivity for the time harmonic Maxwell equations is studied. The main purpose is to apply a known a posteriori residual-based error estimator from the literature and to investigate its performance for a Y-beam splitter setting. This configuration is an important prototype for the design of optical systems within the excellence cluster PhoenixD. Specifically, the branching region is of interest and requires a high accuracy of the numerical simulation. One numerical example shows the performance of our approach

Numerical Methods for Algorithmic Systems and Neural Networks

These lecture notes are devoted to numerical concepts and solution of algorithmic systems and neural networks. The course is divided into four parts: traditional AI (artificial intelligence), deep learning in neural networks, applications to (and with) differential equations, and project work. Throughout this course an emphasis is on mathematical ingredients from which several are rigorously proven. In the project work, the participants usually form groups and work together on a given problem to train themselves on mathematical modeling, design of algorithms, implementation, and analysis and intepretation of the simulation results

dealii/candi: v9.4.2-r2

candi - (Compile & Install) - Downloads, configures, builds and installs deal.I