Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction

Hoang, Chi; Choi, Youngsoo; Carlberg, Kevin

doi:10.1016/j.cma.2021.113997

Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction

Journal Article · Fri Oct 01 00:00:00 EDT 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.113997· OSTI ID:1894413

; ; Carlberg, Kevin

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Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1894413

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 384; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (52)

Multi-time-step explicit-implicit method for non-linear structural dynamics Gravouil, Anthony; Combescure, Alain International Journal for Numerical Methods in Engineering, Vol. 50, Issue 1 https://doi.org/10.1002/1097-0207(20010110)50:1<199::AID-NME132>3.0.CO;2-A	journal	January 2000
Explicit reduced-order models for the stabilized finite element approximation of the incompressible Navier-Stokes equations: EXPLICIT ROMS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS Baiges, Joan; Codina, Ramon; Idelsohn, Sergio International Journal for Numerical Methods in Fluids, Vol. 72, Issue 12 https://doi.org/10.1002/fld.3777	journal	February 2013
A comparative study of null-space factorizations for sparse symmetric saddle point systems: A comparative study of null-space factorizations Rees, Tyrone; Scott, Jennifer Numerical Linear Algebra with Applications, Vol. 25, Issue 1 https://doi.org/10.1002/nla.2103	journal	June 2017
Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 86, Issue 2 https://doi.org/10.1002/nme.3050	journal	October 2010
Port reduction in parametrized component static condensation: approximation and a posteriori error estimation: PORT REDUCTION IN PARAMETRIZED COMPONENT STATIC CONDENSATION Eftang, Jens L.; Patera, Anthony T. International Journal for Numerical Methods in Engineering, Vol. 96, Issue 5 https://doi.org/10.1002/nme.4543	journal	July 2013
An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems: GOAL-ORIENTED SAMPLING STRATEGY USING RB METHOD Hoang, K. C.; Kerfriden, P.; Khoo, B. C. Numerical Methods for Partial Differential Equations, Vol. 31, Issue 2 https://doi.org/10.1002/num.21932	journal	October 2014
Design optimization using hyper-reduced-order models Amsallem, David; Zahr, Matthew; Choi, Youngsoo Structural and Multidisciplinary Optimization, Vol. 51, Issue 4 https://doi.org/10.1007/s00158-014-1183-y	journal	November 2014
A dual mesh method with adaptivity for stress-constrained topology optimization White, Daniel A.; Choi, Youngsoo; Kudo, Jun Structural and Multidisciplinary Optimization, Vol. 61, Issue 2 https://doi.org/10.1007/s00158-019-02393-6	journal	November 2019
The divergence of the BFGS and Gauss Newton methods Mascarenhas, Walter F. Mathematical Programming, Vol. 147, Issue 1-2 https://doi.org/10.1007/s10107-013-0720-6	journal	November 2013
Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system Martini, Immanuel; Rozza, Gianluigi; Haasdonk, Bernard Advances in Computational Mathematics, Vol. 41, Issue 5 https://doi.org/10.1007/s10444-014-9396-6	journal	November 2014
Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi Computers & Mathematics with Applications, Vol. 71, Issue 1 https://doi.org/10.1016/j.camwa.2015.12.001	journal	January 2016
A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi Computer Methods in Applied Mechanics and Engineering, Vol. 221-222 https://doi.org/10.1016/j.cma.2012.02.005	journal	May 2012
A static condensation reduced basis element method: Complex problems Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. Computer Methods in Applied Mechanics and Engineering, Vol. 259 https://doi.org/10.1016/j.cma.2013.02.013	journal	June 2013
A domain decomposition strategy for reduced order models. Application to the incompressible Navier–Stokes equations Baiges, Joan; Codina, Ramon; Idelsohn, Sergio Computer Methods in Applied Mechanics and Engineering, Vol. 267 https://doi.org/10.1016/j.cma.2013.08.001	journal	December 2013
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem Corigliano, A.; Dossi, M.; Mariani, S. Computer Methods in Applied Mechanics and Engineering, Vol. 290 https://doi.org/10.1016/j.cma.2015.02.021	journal	June 2015
An hp-proper orthogonal decomposition–moving least squares approach for molecular dynamics simulation Hoang, K. C.; Fu, Y.; Song, J. H. Computer Methods in Applied Mechanics and Engineering, Vol. 298 https://doi.org/10.1016/j.cma.2015.10.003	journal	January 2016
A component-based hybrid reduced basis/finite element method for solid mechanics with local nonlinearities Ballani, J.; Huynh, D. B. P.; Knezevic, D. J. Computer Methods in Applied Mechanics and Engineering, Vol. 329 https://doi.org/10.1016/j.cma.2017.09.014	journal	February 2018
Component-wise reduced order model lattice-type structure design McBane, Sean; Choi, Youngsoo Computer Methods in Applied Mechanics and Engineering, Vol. 381 https://doi.org/10.1016/j.cma.2021.113813	journal	August 2021
Iterative methods for model reduction by domain decomposition Buffoni, M.; Telib, H.; Iollo, A. Computers & Fluids, Vol. 38, Issue 6 https://doi.org/10.1016/j.compfluid.2008.11.008	journal	June 2009
A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems Kaulmann, Sven; Ohlberger, Mario; Haasdonk, Bernard Comptes Rendus Mathematique, Vol. 349, Issue 23-24 https://doi.org/10.1016/j.crma.2011.10.024	journal	December 2011
Fast and accurate two-field reduced basis approximation for parametrized thermoelasticity problems Hoang, Khac Chi; Kim, Tae-Yeon; Song, Jeong-Hoon Finite Elements in Analysis and Design, Vol. 141 https://doi.org/10.1016/j.finel.2017.12.004	journal	March 2018
A priori hyperreduction method: an adaptive approach Ryckelynck, D. Journal of Computational Physics, Vol. 202, Issue 1 https://doi.org/10.1016/j.jcp.2004.07.015	journal	January 2005
A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales Nguyen, N. C. Journal of Computational Physics, Vol. 227, Issue 23 https://doi.org/10.1016/j.jcp.2008.07.025	journal	December 2008
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows Carlberg, Kevin; Farhat, Charbel; Cortial, Julien Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.028	journal	June 2013
A reduced basis localized orthogonal decomposition Abdulle, Assyr; Henning, Patrick Journal of Computational Physics, Vol. 295 https://doi.org/10.1016/j.jcp.2015.04.016	journal	August 2015
Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction Carlberg, Kevin; Barone, Matthew; Antil, Harbir Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.10.033	journal	February 2017
Conservative model reduction for finite-volume models Carlberg, Kevin; Choi, Youngsoo; Sargsyan, Syuzanna Journal of Computational Physics, Vol. 371 https://doi.org/10.1016/j.jcp.2018.05.019	journal	October 2018
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders Lee, Kookjin; Carlberg, Kevin T. Journal of Computational Physics https://doi.org/10.1016/j.jcp.2019.108973	journal	November 2019
Gradient-based constrained optimization using a database of linear reduced-order models Choi, Youngsoo; Boncoraglio, Gabriele; Anderson, Spenser Journal of Computational Physics, Vol. 423 https://doi.org/10.1016/j.jcp.2020.109787	journal	December 2020
Numerical solution of saddle point problems Benzi, Michele; Golub, Gene H.; Liesen, Jörg Acta Numerica, Vol. 14 https://doi.org/10.1017/S0962492904000212	journal	April 2005
A Reduced-Basis Element Method Maday, Yvon; Rønquist, Einar M. Journal of Scientific Computing, Vol. 17, Issue 1/4, p. 447-459 https://doi.org/10.1023/A:1015197908587	journal	January 2002
A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation Phuong Huynh, Dinh Bao; Knezevic, David J.; Patera, Anthony T. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 47, Issue 1 https://doi.org/10.1051/m2an/2012022	journal	November 2012
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations Grepl, Martin A.; Maday, Yvon; Nguyen, Ngoc C. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 41, Issue 3 https://doi.org/10.1051/m2an:2007031	journal	May 2007
The parallel solution of dense saddle-point linear systems arising in stochastic programming Lubin, Miles; Petra, Cosmin G.; Anitescu, Mihai Optimization Methods and Software, Vol. 27, Issue 4-5 https://doi.org/10.1080/10556788.2011.602976	journal	October 2012
Turbulence and the dynamics of coherent structures. I. Coherent structures Sirovich, Lawrence Quarterly of Applied Mathematics, Vol. 45, Issue 3 https://doi.org/10.1090/qam/910462	journal	January 1987
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition Astrid, Patricia; Weiland, Siep; Willcox, Karen IEEE Transactions on Automatic Control, Vol. 53, Issue 10 https://doi.org/10.1109/TAC.2008.2006102	journal	November 2008
Physics-Based Character Skinning Using Multidomain Subspace Deformations Kim, T.; James, D. L. IEEE Transactions on Visualization and Computer Graphics, Vol. 18, Issue 8 https://doi.org/10.1109/TVCG.2012.78	journal	August 2012
Boundary-Aware Multidomain Subspace Deformation Yang, Yin; Xu, Weiwei; Guo, Xiaohu IEEE Transactions on Visualization and Computer Graphics, Vol. 19, Issue 10 https://doi.org/10.1109/TVCG.2013.12	journal	October 2013
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space Bui-Thanh, T.; Willcox, K.; Ghattas, O. SIAM Journal on Scientific Computing, Vol. 30, Issue 6 https://doi.org/10.1137/070694855	journal	January 2008
Nonlinear Model Reduction via Discrete Empirical Interpolation Chaturantabut, Saifon; Sorensen, Danny C. SIAM Journal on Scientific Computing, Vol. 32, Issue 5 https://doi.org/10.1137/090766498	journal	January 2010
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions Halko, N.; Martinsson, P. G.; Tropp, J. A. SIAM Review, Vol. 53, Issue 2 https://doi.org/10.1137/090771806	journal	January 2011
The Antitriangular Factorization of Saddle Point Matrices Pestana, J.; Wathen, A. J. SIAM Journal on Matrix Analysis and Applications, Vol. 35, Issue 2 https://doi.org/10.1137/130934933	journal	January 2014
Error Control for the Localized Reduced Basis Multiscale Method with Adaptive On-Line Enrichment Ohlberger, M.; Schindler, F. SIAM Journal on Scientific Computing, Vol. 37, Issue 6 https://doi.org/10.1137/151003660	journal	January 2015
ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications Buhr, Andreas; Engwer, Christian; Ohlberger, Mario SIAM Journal on Scientific Computing, Vol. 39, Issue 4 https://doi.org/10.1137/15M1054213	journal	January 2017
Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction Choi, Youngsoo; Carlberg, Kevin SIAM Journal on Scientific Computing, Vol. 41, Issue 1 https://doi.org/10.1137/17M1120531	journal	January 2019
SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction Choi, Youngsoo; Coombs, Deshawn; Anderson, Robert SIAM Journal on Scientific Computing, Vol. 42, Issue 2 https://doi.org/10.1137/19M1242963	journal	January 2020
The Reduced Basis Element Method: Application to a Thermal Fin Problem Maday, Yvon; Ronquist, Einar M. SIAM Journal on Scientific Computing, Vol. 26, Issue 1 https://doi.org/10.1137/S1064827502419932	journal	January 2004
Real-time large-deformation substructuring Barbič, Jernej; Zhao, Yili ACM Transactions on Graphics, Vol. 30, Issue 4 https://doi.org/10.1145/2010324.1964986	journal	July 2011
Subspace condensation: full space adaptivity for subspace deformations Teng, Yun; Meyer, Mark; DeRose, Tony ACM Transactions on Graphics, Vol. 34, Issue 4 https://doi.org/10.1145/2766904	journal	July 2015
Schur Complement-based Substructuring of Stiff Multibody Systems with Contact Peiret, Albert; Andrews, Sheldon; Kövecses, József ACM Transactions on Graphics, Vol. 38, Issue 5 https://doi.org/10.1145/3355621	journal	November 2019
Karhunen–Loève procedure for gappy data Everson, R.; Sirovich, L. Journal of the Optical Society of America A, Vol. 12, Issue 8 https://doi.org/10.1364/JOSAA.12.001657	journal	January 1995
Adaptive Port Reduction in Static Condensation Eftang, Jl; Huynh, Dbp; Knezevic, Dj IFAC Proceedings Volumes, Vol. 45, Issue 2 https://doi.org/10.3182/20120215-3-AT-3016.00123	journal	January 2012

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