A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature
M.L. Mika, T.J.R. Hughes, D. Schillinger, P. Wriggers and R.R. Hiemstra
February 9th, 2021;
The Karhunen-Loève series expansion decomposes a Gaussian stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise L2 orthogonal functions. The computational complexity of standard Galerkin finite element formation and assembly techniques, as well as memory requirements of direct solution techniques become quickly computationally intractable with increasing polynomial degree and the number of elements. In this work we present a novel matrix-free solution strategy that scales optimally with the problem size, is indepedent of the polynomial degree and is emberassingly parallel. A high-order three-dimensional benchmark illustrates exceptional computational performance combined with high accuracy and robustness.
