5 papers · 1 filter
Bayesian inference calibration of the modulus of elasticity
J. Dick, Q. T. Le Gia, K. Mustapha
This work uses the Bayesian inference technique to infer the Young modulus from the stochastic linear elasticity equation. The Young modulus is modeled by a finite Karhunen Loéve…
A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity
Josef Dick, Seungchan Ko, Quoc Thong Le Gia +2
Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lamé coefficient $λ\…
Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation
Xin An, Josef Dick, Michael Feischl +2
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equ…
A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity
K. Mustapha, W. McLean, J. Dick +1
Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lamé param…
Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties
M. Clarke, J. Dick, Q. T. Le Gia +2
We explore a linear inhomogeneous elasticity equation with random Lamé parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. Th…