Stochastic Computational Fluid Mechanics
Computing in Science and Engineering
Stochastic formulation of SPICE-type electronic circuit simulation with polynomial chaos
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Binning optimization based on SSTA for transparently-latched circuits
Proceedings of the 2009 International Conference on Computer-Aided Design
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Hybrid energy storage system integration for vehicles
Proceedings of the 16th ACM/IEEE international symposium on Low power electronics and design
Roe solver with entropy corrector for uncertain hyperbolic systems
Journal of Computational and Applied Mathematics
Sparse Tensor Discretization of Elliptic sPDEs
SIAM Journal on Scientific Computing
Structural and Multidisciplinary Optimization
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System
SIAM Journal on Scientific Computing
Data-free inference of the joint distribution of uncertain model parameters
Journal of Computational Physics
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
Journal of Computational Physics
Multi-output local Gaussian process regression: Applications to uncertainty quantification
Journal of Computational Physics
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
Journal of Computational Physics
High-order methods as an alternative to using sparse tensor products for stochastic Galerkin FEM
Computers & Mathematics with Applications
Hi-index | 0.09 |
We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs. Given a stochastic input with an arbitrary probability measure, its random space is decomposed into smaller elements. Subsequently, in each element a new random variable with respect to a conditional probability density function (PDF) is defined, and a set of orthogonal polynomials in terms of this random variable is constructed numerically. Then, the generalized polynomial chaos (gPC) method is implemented element-by-element. Numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost. Efficiency and convergence of ME-gPC are studied numerically by considering some commonly used random variables. ME-gPC provides an efficient and flexible approach to solving differential equations with random inputs, especially for problems related to long-term integration, large perturbation, and stochastic discontinuities.