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Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam
Thi-Hoa Nguyen, René R. Hiemstra, Dominik Schillinger
In this paper, we take a fresh look at using spectral analysis for assessing locking phenomena in finite element formulations. We propose to "measure" locking by comparing the diff…
A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen--Loève expansion
Michal Lukasz Mika, René Rinke Hiemstra, Thomas Joseph Robert Hughes +1
Numerical computation of the Karhunen--Loève expansion is computationally challenging in terms of both memory requirements and computing time. We compare two state-of-the-art metho…
A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature
Michal Lukasz Mika, Thomas Joseph Robert Hughes, Dominik Schillinger +2
The Karhunen-Loève series expansion (KLE) decomposes a stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise -orthogonal functions.…