4.7 Article

Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression

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

A reduced order model for the finite element approximation of eigenvalue problems

Fleurianne Bertrand et al.

Summary: In this paper, a reduced order method is proposed to approximate the eigensolutions of the Laplace problem with Dirichlet boundary condition. A time continuation technique with a fictitious time parameter is utilized. The POD approach is employed and theoretical results for choosing the optimal dimension of the POD basis are presented. The computational results confirm the optimal behavior of the approximate solution. The computation of the first eigenvalue and the approximation of the next eigenmodes are discussed.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

Article Mathematics, Applied

A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction

Fleurianne Bertrand et al.

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS (2019)

Article Engineering, Multidisciplinary

Data-driven reduced order modeling for time-dependent problems

Mengwu Guo et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2019)

Article Mathematics, Applied

ADAPTIVE FINITE ELEMENT METHOD FOR THE MAXWELL EIGENVALUE PROBLEM

Daniele Boffi et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2019)

Article Mathematics, Applied

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

A. D. Gilbert et al.

NUMERISCHE MATHEMATIK (2019)

Article Nuclear Science & Technology

Reduced-order modeling of parameterized multi-group diffusion κ-eigenvalue problems

Peter German et al.

ANNALS OF NUCLEAR ENERGY (2019)

Article Engineering, Multidisciplinary

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Mengwu Guo et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2018)

Article Mathematics, Applied

ARNOLD-WINTHER MIXED FINITE ELEMENTS FOR STOKES EIGENVALUE PROBLEMS

Joscha Gedicke et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Engineering, Multidisciplinary

Coupled FE-BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

C. J. Zheng et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2017)

Article Mathematics, Applied

SIMULTANEOUS REDUCED BASIS APPROXIMATION OF PARAMETERIZED ELLIPTIC EIGENVALUE PROBLEMS

Thomas Horger et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE (2017)

Article Engineering, Multidisciplinary

A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems

Onder Turk et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2016)

Article Mathematics, Applied

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATES FOR PARAMETRIZED ELLIPTIC EIGENVALUE PROBLEMS

Ivan Fumagalli et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE (2016)

Article Engineering, Multidisciplinary

Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method

Haifeng Gao et al.

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS (2013)

Article Engineering, Multidisciplinary

A POD reduced-order model for eigenvalue problems with application to reactor physics

A. G. Buchan et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2013)

Article Computer Science, Interdisciplinary Applications

Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation

Erell Jamelot et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

Article Mathematics, Applied

Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

M. Hintermueller et al.

APPLIED MATHEMATICS AND OPTIMIZATION (2012)

Article Mathematics, Applied

Adaptive finite element methods for computing band gaps in photonic crystals

S. Giani et al.

NUMERISCHE MATHEMATIK (2012)

Article Mathematics

Finite element approximation of eigenvalue problems

Daniele Boffi

ACTA NUMERICA (2010)

Article Physics, Fluids & Plasmas

Reduced-basis method for band structure calculations

George S. H. Pau

PHYSICAL REVIEW E (2007)

Article Mathematics, Applied

Numerical solution of parametrized Navier-Stokes equations by reduced basis methods

Alfio Quarteroni et al.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2007)

Article Mathematics, Applied

Optimal localization of eigenfunctions in an inhomogeneous medium

DC Dobson et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2004)

Article Engineering, Aerospace

Balanced model reduction via the proper orthogonal decomposition

K Willcox et al.

AIAA JOURNAL (2002)

Article Mathematics, Applied

A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations

C Prud'homme et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE (2002)

Article Mathematics, Applied

Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics

K Kunisch et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2002)

Article Engineering, Mechanical

Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods

C Prud'homme et al.

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME (2002)

Article Mathematics, Applied

Galerkin proper orthogonal decomposition methods for parabolic problems

K Kunisch et al.

NUMERISCHE MATHEMATIK (2001)

Article Computer Science, Interdisciplinary Applications

Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum

SJ Osher et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2001)