Multi-index stochastic collocation for random PDEs
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for
computing statistics of the solution of a PDE with random data. MISC is a combination …
computing statistics of the solution of a PDE with random data. MISC is a combination …
The Sparse Grids Matlab kit--a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
C Piazzola, L Tamellini - arXiv preprint arXiv:2203.09314, 2022 - arxiv.org
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be
used for approximating high-dimensional functions and, in particular, for surrogate-model …
used for approximating high-dimensional functions and, in particular, for surrogate-model …
Investigations on the restrictions of stochastic collocation methods for high dimensional and nonlinear engineering applications
Sophisticated sampling techniques used for solving stochastic partial differential equations
efficiently and robustly are still in a state of development. It is known in the scientific …
efficiently and robustly are still in a state of development. It is known in the scientific …
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-
grids stochastic collocation method we presented in a previous work:“On the optimal …
grids stochastic collocation method we presented in a previous work:“On the optimal …
Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance
This paper presents a comparison of two multi-fidelity methods for the forward uncertainty
quantification of a naval engineering problem. Specifically, we consider the problem of …
quantification of a naval engineering problem. Specifically, we consider the problem of …
Sparse-grids uncertainty quantification of part-scale additive manufacturing processes
M Chiappetta, C Piazzola, M Carraturo… - International Journal of …, 2023 - Elsevier
The present paper aims at applying uncertainty quantification methodologies to process
simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical …
simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical …
An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient
In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M.
Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version …
Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version …
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Convergence of an adaptive collocation method for the parametric stationary diffusion
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
[图书][B] Construction of optimal cubature algorithms with applications to econometrics and uncertainty quantification
J Oettershagen - 2017 - ins.uni-bonn.de
The integration of multivariate functions plays a fundamental role in numerical mathematics
with applications in all scientific fields where expectations and probabilities need to be …
with applications in all scientific fields where expectations and probabilities need to be …
An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use
A Galetzka, D Loukrezis, N Georg… - International Journal …, 2023 - Wiley Online Library
This article introduces an hp hp‐adaptive multi‐element stochastic collocation method,
which additionally allows to re‐use existing model evaluations during either hh‐or pp …
which additionally allows to re‐use existing model evaluations during either hh‐or pp …