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.
A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen–Loève expansion
M.L. Mika, R.R. Hiemstra, T.J.R. Hughes and D. Schillinger
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 methods that claim to efficiently solve for the
K–L expansion: (1) the matrix-free isogeometric Galerkin method using interpolation based quadrature proposed
by the authors in  and (2) our new matrix-free implementation of the isogeometric collocation method proposed in .
Two three-dimensional benchmark problems indicate that the Galerkin method performs significantly better for smooth
covariance kernels, while the collocation method performs slightly better for rough covariance kernels.
Electrostatic sensor modeling for torque measurements
M.L. Mika, M. Dannert, F. Mett, H. Weber, W. Mathis and U. Nackenhorst
Based on a simple draft of an exemplary measurement setup,
this paper discusses the general idea behind an electrostatic
capacitive torque sensor. For better understanding of the working
principle of the sensor the electrostatics, the geometry and the mechanics of
the considered measurement setup are modeled.
Visualization of finite element analysis results on 3D printed models
This project explores the
possibilities of visualization of finite element analysis results using
3D printed models. By outer-surface extraction and implementation of a
VRML interface the interpolated datasets are prepared for a 3D print.