Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Simulating the Behavior of MEMS Devices: Computational Methods and Needs
IEEE Computational Science & Engineering
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Journal of Computational Physics
Efficient mixed-domain analysis of electrostatic MEMS
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification
Journal of Computational Physics
Journal of Computational Physics
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
Hi-index | 31.47 |
This work proposes a domain adaptive stochastic collocation approach for uncertainty quantification, suitable for effective handling of discontinuities or sharp variations in the random domain. The basic idea of the proposed methodology is to adaptively decompose the random domain into subdomains. Within each subdomain, a sparse grid interpolant is constructed using the classical Smolyak construction [S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963) 240-243], to approximate the stochastic solution locally. The adaptive strategy is governed by the hierarchical surpluses, which are computed as part of the interpolation procedure. These hierarchical surpluses then serve as an error indicator for each subdomain, and lead to subdivision whenever it becomes greater than a threshold value. The hierarchical surpluses also provide information about the more important dimensions, and accordingly the random elements can be split along those dimensions. The proposed adaptive approach is employed to quantify the effect of uncertainty in input parameters on the performance of micro-electromechanical systems (MEMS). Specifically, we study the effect of uncertain material properties and geometrical parameters on the pull-in behavior and actuation properties of a MEMS switch. Using the adaptive approach, we resolve the pull-in instability in MEMS switches. The results from the proposed approach are verified using Monte Carlo simulations and it is demonstrated that it computes the required statistics effectively.