4.6 Article

Uncertainty quantification by optimal spline dimensional decomposition

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Engineering, Multidisciplinary

ISOGEOMETRIC METHODS FOR KARHUNEN-LOEVE REPRESENTATION OF RANDOM FIELDS ON ARBITRARY MULTIPATCH DOMAINS

R. Jahanbin et al.

Summary: This paper introduces isogeometric Galerkin and collocation methods for solving the Fredholm integral eigenvalue problem on arbitrary multipatch domains, delivering the Karhunen-Loeve expansion for random field discretization. Numerical analyses show that both methods provide convergent and accurate eigensolutions, with the collocation method being markedly more economical due to eliminating one d-dimensional domain integration in forming the system matrices. These methods can greatly improve computational efficiency for uncertainty quantification analysis of complex engineering structures with multipatch geometry.

INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION (2021)

Article Mathematics, Interdisciplinary Applications

A Spline Chaos Expansion

Sharif Rahman

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION (2020)

Article Engineering, Multidisciplinary

An isogeometric collocation method for efficient random field discretization

Ramin Jahanbin et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2019)

Article Engineering, Multidisciplinary

A Galerkin isogeometric method for Karhunen-Loeve approximation of random fields

Sharif Rahman

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2018)

Article Mathematics, Interdisciplinary Applications

Mathematical Properties of Polynomial Dimensional Decomposition

Sharif Rahman

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION (2018)

Article Computer Science, Interdisciplinary Applications

Data-driven uncertainty quantification of structural systems via B-spline expansion

V. K. Dertimanis et al.

COMPUTERS & STRUCTURES (2018)

Article Engineering, Multidisciplinary

Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing

Vaibhav Yadav et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2014)

Article Mathematics, Applied

APPROXIMATION ERRORS IN TRUNCATED DIMENSIONAL DECOMPOSITIONS

Sharif Rahman

MATHEMATICS OF COMPUTATION (2014)

Article Computer Science, Theory & Methods

Dimension-wise integration of high-dimensional functions with applications to finance

Michael Griebel et al.

JOURNAL OF COMPLEXITY (2010)

Article Engineering, Multidisciplinary

A polynomial dimensional decomposition for stochastic computing

Sharif Rahman

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2008)

Article Mathematics, Applied

A stochastic collocation method for elliptic partial differential equations with random input data

Ivo Babuska et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2007)

Article Mathematics, Applied

High-order collocation methods for differential equations with random inputs

DB Xiu et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2005)

Article Engineering, Multidisciplinary

A generalized dimension-reduction method for multidimensional integration in stochastic mechanics

H Xu et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2004)

Article Mathematics, Applied

The Wiener-Askey polynomial chaos for stochastic differential equations

DB Xiu et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2002)