- Algorithmic realization of the answer to the signal battle downside for hanging nodes on hp-hexahedral Nédélec components
Authors: Sebastian Kinnewig, Thomas Wick, Sven Beuchler
Summary: Whereas working with Nédélec components on adaptively refined meshes with hanging nodes, the orientation of the hanging edges and faces should be taken into consideration. Certainly, for non-orientable meshes, there was no resolution and implementation obtainable to this point. The issue assertion and corresponding algorithms are described in nice element. As a mannequin downside, the time-harmonic Maxwell’s equations are adopted as a result of Nédélec components represent their pure discretization. The implementation is carried out inside the finite ingredient library deal.II. The algorithms and implementation are demonstrated by 4 numerical examples on completely different uniformly and adaptively refined meshes.
2. Increased order Bernstein-Bézier and Nédélec finite components for the relaxed micromorphic mannequin
Authors: Adam Sky, Ingo Muench, Gianluca Rizzi, Patrizio Neff
Summary: The relaxed micromorphic mannequin is a generalized continuum mannequin that’s well-posed within the house X=[H1]3×[H(curl)]3. Consequently, finite ingredient formulations of the mannequin depend on H1-conforming subspaces and Nédélec components for discrete options of the corresponding variational downside. This work applies the not too long ago launched polytopal template methodology for the development of Nédélec components. That is accomplished along with Bernstein-Bézier polynomials and twin numbers with a view to compute hp-FEM options of the mannequin. Bernstein-Bézier polynomials permit for optimum complexity within the meeting process as a consequence of their pure factorization into univariate Bernstein base capabilities. On this work, this attribute is additional augmented by means of twin numbers with a view to compute their values and their derivatives concurrently. The applying of the polytopal template methodology for the development of the Nédélec base capabilities permits them to instantly inherit the optimum complexity of the underlying Bernstein-Bézier foundation. We introduce the Bernstein-Bézier foundation together with its factorization to univariate Bernstein base capabilities, the precept of computerized differentiation through twin numbers and an in depth development of Nédélec components based mostly on Bernstein-Bézier polynomials with the polytopal template methodology. That is complemented with a corresponding approach to embed Dirichlet boundary circumstances, with emphasis on the constant coupling situation. The efficiency of the weather is proven in examples of the relaxed micromorphic mannequin.
