Polytopal templates for the formulation of semi-continuous vectorial finite elements of arbitrary order

The Hilbert spaces $H(\mathrm{curl})$ and $H(\mathrm{div})$ are needed for variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Consequently, the construction of conforming subspaces is a crucial step in the formulation of viable numerical solutions. Alternatively to the standard definition of a finite element as per Ciarlet, given by the triplet of a domain, a polynomial space and degrees of freedom, this work aims to introduce a novel, simple method of directly constructing semi-continuous vectorial base functions on the reference element via polytopal templates and an underlying $H^1$-conforming polynomial subspace. The base functions are then mapped from the reference element to the element in the physical domain via consistent Piola transformations. The method is defined in such a way, that the underlying $H^1$-conforming subspace can be chosen independently, thus allowing for constructions of arbitrary polynomial order. The base functions arise by multiplication of the basis with template vectors defined for each polytope of the reference element. We prove a unisolvent construction of N\'ed\'elec elements of the first and second type, Brezzi-Douglas-Marini elements, and Raviart-Thomas elements. An application for the method is demonstrated with two examples in the relaxed micromorphic mode

A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence $\boldsymbol{M} \in \mathcal{HZ} \subset H^{\mathrm{sym}}(\mathrm{Div})$. The latter results in highly accurate approximations of the bending moments $\boldsymbol{M}$ and in the rotation field being in the discontinuous Lebesgue space $\boldsymbol{\phi} \in [L]^2$, such that the Kirchhoff-Love constraint can be satisfied for $t \to 0$. In order to preserve optimal convergence rates across all variables for the case $t \to 0$, we present an extension of the formulation using Raviart-Thomas elements for the shear stress $\mathbf{q} \in \mathcal{RT} \subset H(\mathrm{div})$. We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments $\boldsymbol{M}$. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods.Comment: Additional implementation material in: https://github.com/Askys/NGSolve_HuZhang_Elemen

Novel H(symCurl)H(\mathrm{sym} \mathrm{Curl})-conforming finite elements for the relaxed micromorphic sequence

In this work we construct novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the $\mathrm{div} \mathrm{Div}$-sequence with respect to the $H(\mathrm{sym} \mathrm{Curl})$-space. The elements respect $H(\mathrm{Curl})$-regularity and their lowest order versions converge optimally for $[H(\mathrm{sym} \mathrm{Curl}) \setminus H(\mathrm{Curl})]$-fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model

A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence. The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the discontinuous Lebesgue space , such that the Kirchhoff-Love constraint can be satisfied for t tending to zero. In order to preserve optimal convergence rates across all variables for the case t tending to zero, we present an extension of the formulation using Raviart-Thomas elements for the shear stress. We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods.Pre-prin

Design of Nanoparticulate Group 2 Influenza Virus Hemagglutinin Stem Antigens That Activate Unmutated Ancestor B Cell Receptors of Broadly Neutralizing Antibody Lineages.

Influenza vaccines targeting the highly conserved stem of the hemagglutinin (HA) surface glycoprotein have the potential to protect against pandemic and drifted seasonal influenza viruses not covered by current vaccines. While HA stem-based immunogens derived from group 1 influenza A viruses have been shown to induce intragroup heterosubtypic protection, HA stem-specific antibody lineages originating from group 2 may be more likely to possess broad cross-group reactivity. We report the structure-guided development of mammalian-cell-expressed candidate vaccine immunogens based on influenza A virus group 2 H3 and H7 HA stem trimers displayed on self-assembling ferritin nanoparticles using an iterative, multipronged approach involving helix stabilization, loop optimization, disulfide bond addition, and side-chain repacking. These immunogens were thermostable, formed uniform and symmetric nanoparticles, were recognized by cross-group-reactive broadly neutralizing antibodies (bNAbs) with nanomolar affinity, and elicited protective, homosubtypic antibodies in mice. Importantly, several immunogens were able to activate B cells expressing inferred unmutated common ancestor (UCA) versions of cross-group-reactive human bNAbs from two multidonor classes, suggesting they could initiate elicitation of these bNAbs in humans. Current influenza vaccines are primarily strain specific, requiring annual updates, and offer minimal protection against drifted seasonal or pandemic strains. The highly conserved stem region of hemagglutinin (HA) of group 2 influenza A virus subtypes is a promising target for vaccine elicitation of broad cross-group protection against divergent strains. We used structure-guided protein engineering employing multiple protein stabilization methods simultaneously to develop group 2 HA stem-based candidate influenza A virus immunogens displayed as trimers on self-assembling nanoparticles. Characterization of antigenicity, thermostability, and particle formation confirmed structural integrity. Group 2 HA stem antigen designs were identified that, when displayed on ferritin nanoparticles, activated B cells expressing inferred unmutated common ancestor (UCA) versions of human antibody lineages associated with cross-group-reactive, broadly neutralizing antibodies (bNAbs). Immunization of mice led to protection against a lethal homosubtypic influenza virus challenge. These candidate vaccines are now being manufactured for clinical evaluation

Fabrication and hydrogen sorption behaviour of nanoparticulate MgH_2 incorporated in a porous carbon host

Nanoparticles of MgH_2 incorporated in a mesoporous carbon aerogel demonstrated accelerated hydrogen exchange kinetics but no thermodynamic change in the equilibrium hydrogen pressure. Aerogels contained pores from <2 to ~30 nm in diameter with a peak at 13 nm in the pore size distribution. Nanoscale MgH_2 was fabricated by depositing wetting layers of nickel or copper on the aerogel surface, melting Mg into the aerogel, and hydrogenating the Mg to MgH_2. Aerogels with metal wetting layers incorporated 9–16 wt% MgH_2, while a metal free aerogel incorporated only 3.6 wt% MgH_2. The improved hydrogen sorption kinetics are due to both the aerogel limiting the maximum MgH_2 particle diameter and a catalytic effect from the Ni and Cu wetting layers. At 250 °C, MgH_2 filled Ni decorated and Cu decorated carbon aerogels released H_2 at 25 wt% h^−1 and 5.5 wt% h^−1, respectively, while a MgH_2 filled aerogel without catalyst desorbed only 2.2 wt% h^−1 (all wt% h^−1 values are with respect to MgH_2 mass). At the same temperature, MgH_2 ball milled with synthetic graphite desorbed only 0.12 wt% h^−1, which demonstrated the advantage of incorporating nanoparticles in a porous host