29 citations · 87 across the 16 of their papers we have counts for
11 papers · 1 filter
Running error bounds in finite element kernels
Michal Habera, Paul T. Kühner, Matteo Croci +1
Rounding errors in finite element computations can lead to a complete loss of accuracy, stalled convergence, and incorrect results. Moreover, the effects of rounding errors accumul…
A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
Lucca Schek, Peter Lewintan, Wolfgang Müller +5
We introduce a new method, dubbed Geometric Structure-Preserving Interpolation (-SPIN) to preserve physics-constraints inherent in the material parameter limits of the finite-st…
Numerically stable evaluation of closed-form expressions for eigenvalues of matrices
Michal Habera, Andreas Zilian
Trigonometric formulas for eigenvalues of matrices that build on Cardano's and Viète's work on algebraic solutions of the cubic are numerically unstable for matrices w…
Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus
Adam Sky, Jack S. Hale, Andreas Zilian +2
We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the mod…
Novel -conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model
Adam Sky, Michael Neunteufel, Peter Lewintan +3
In this work we present a consistent reduction of the relaxed micromorphic model to its corresponding two-dimensional planar model, such that its capacity to capture discontinuous…
Formulae and transformations for simplicial tensorial finite elements via polytopal templates
Adam Sky, Michael Neunteufel, Jack S. Hale +1
We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. T…
Symmetric unisolvent equations for linear elasticity purely in stresses
Adam Sky, Andreas Zilian
In this work we introduce novel stress-only formulations of linear elasticity with special attention to their approximate solution using weighted residual methods. We present four…
Novel -conforming finite elements for the relaxed micromorphic sequence
Adam Sky, Michael Neunteufel, Peter Lewintan +2
In this work we construct novel -conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the…
A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations
Adam Sky, Michael Neunteufel, Jack S. Hale +1
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.…
Symbolic spectral decomposition of 3x3 matrices
Michal Habera, Andreas Zilian
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrice…
A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs
Hamidreza Dehghani, Andreas Zilian
We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solvin…