32 citations · 76 across the 7 of their papers we have counts for
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Partial-differential-algebraic equations of nonlinear dynamics by Physics-Informed Neural-Network: (I) Operator splitting and framework assessment
Loc Vu-Quoc, Alexander Humer
Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are…
New mixed finite elements for the discretization of piezoelectric structures or macro-fibre composites
Astrid Pechstein, Martin Meindlhumer, Alexander Humer
We propose a new three-dimensional formulation based on the mixed Tangential-Displacement Normal-Normal-Stress (TDNNS) method for elasticity. In elastic TDNNS elements, the tangent…
High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials
Astrid S. Pechstein, Martin Meindlhumer, Alexander Humer
An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displac…
Variational inequalities for ferroelectric constitutive modeling
Martin Meindlhumer, Astrid Pechstein, Alexander Humer
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of fr…
The polarization process of ferroelectric materials analyzed in the framework of variational inequalities
Astrid S. Pechstein, Martin Meindlhumer, Alexander Humer
We are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive function…