Search Results - Smolyak approximation. Point Collocation

Data assimilation for real-time dynamic prediction of wind-induced forces in vehicle platooning

Authors: Perelló i Ribas, Rafel

Thesis Advisors: Huerta, Antonio, Zlotnik, Sergio, Escola Tècnica Superior d'Enginyeria de Camins, Canals i Ports de Barcelona

Source: TDX (Tesis Doctorals en Xarxa)

Subject Terms: Computational Fluid Dynamics, surrogate modelling, platoon, overtake, cross-wind, Reynolds-Averaged Navier-Stokes, OpenFOAM, sparse grids, multifidelity, multi-index stochastic collocation, Àrees temàtiques de la UPC::Enginyeria civil, Àrees temàtiques de la UPC::Aeronàutica i espai, Àrees temàtiques de la UPC::Enginyeria mecànica, 629 - Enginyeria dels vehicles de transport, 531/534 - Mecànica. Vibracions. Acústica

File Description: application/pdf

Access URL: http://hdl.handle.net/10803/696187
https://dx.doi.org/10.5821/dissertation-2117-449390

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Authors: Fabio Nobile Raul Tempone Applied Mathematics and Computational Science Program et al.

Contributors: Fabio Nobile Raul Tempone Applied Mathematics and Computational Science Program et al.

Source: International Journal for Numerical Methods in Engineering. 80:979-1006

Subject Terms: Multivariate polynomial approximation, Stochastic Collocation methods, Parabolic equations, PDEs with random data • parabolic equations • multivariate polynomial approximation • Stochastic Galerkin methods • Stochastic Collocation methods • sparse grids • Smolyak approximation • Point Collocation • Monte Carlo sampling, PDEs with random data, Point Collocation, Sparse grids, 0101 mathematics, Stochastic galerkin methods, 01 natural sciences, Smolyak approximation, Monte carlo sampling

Access URL: https://infoscience.epfl.ch/record/180349
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.2656
http://onlinelibrary.wiley.com/doi/10.1002/nme.2656/abstract
http://www.diva-portal.org/smash/record.jsf?pid=diva2:411086
https://re.public.polimi.it/handle/11311/533391
http://ui.adsabs.harvard.edu/abs/2009IJNME..80..979N/abstract

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

Authors: Nobile, F. Tempone, Raul Webster, C. G.

Source: SIAM Journal on Numerical Analysis. 46(5):2309-2345

Subject Terms: collocation techniques, stochastic PDEs, finite elements, uncertainty, quantification, sparse grids, Smolyak approximation, multivariate, polynomial approximation, polynomial chaos, quadrature, interpolation, coefficients

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-17702

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Authors: Ivo Babus caron Raul Tempone Fabio Nobile et al.

Contributors: Ivo Babus caron Raul Tempone Fabio Nobile et al.

Source: SIAM Journal on Numerical Analysis. 45:1005-1034

Subject Terms: uncertainty quantification, convergence rates, partial differential equations with random inputs, finite elements, stochastic collocation method, multivariate polynomial approximation, Smolyak approximation, anisotropic sparse approximation, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: https://repository.kaust.edu.sa/bitstream/10754/555664/1/100786356.pdf
https://dblp.uni-trier.de/db/journals/siamnum/siamnum45.html#BabuskaNT07
http://kth.diva-portal.org/smash/record.jsf?pid=diva2:334790
https://research.kaust.edu.sa/en/publications/a-stochastic-collocation-method-for-elliptic-partial-differential-2
http://www.diva-portal.org/smash/record.jsf?pid=diva2:334790
https://dl.acm.org/doi/10.1137/050645142
https://epubs.siam.org/doi/10.1137/050645142
https://hdl.handle.net/11311/551573
https://doi.org/10.1137/050645142
https://hdl.handle.net/11311/573742
http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SIREAD000052000002000317000001&idtype=cvips&gifs=Yes
https://doi.org/10.1137/100786356

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

Authors: Nobile, F. Tempone, Raul Webster, C. G.

Source: SIAM Journal on Numerical Analysis. 46(5):2411-2442

Subject Terms: collocation techniques, PDEs with random data, differential equations, finite elements, uncertainty quantification, anisotropic sparse grids, Smolyak sparse approximation, multivariate polynomial approximation, elliptic problems, finite-elements, uncertainty, coefficients, approximations, propagation, expansions, quadrature, chaos

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-17703

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Authors: Fabio Nobile Raul Tempone The Pennsylvania State University CiteSeerX Archives

Contributors: Fabio Nobile Raul Tempone The Pennsylvania State University CiteSeerX Archives

Source: http://mox.polimi.it/it/progetti/pubblicazioni/quaderni/22-2008.pdf.

Subject Terms: PDEs with random data, parabolic equations, multivariate polynomial approximation, Stochastic Galerkin methods, Stochastic Collo- cation methods, sparse grids, Smolyak approximation, Point Collocation, Monte Carlo Sampling

File Description: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.242

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.242
http://mox.polimi.it/it/progetti/pubblicazioni/quaderni/22-2008.pdf

MATHICSE Technical Report : Convergence of quasi-optimal sparse grid approximation of Hilbert-valued functions: application to random elliptic PDEs

Authors: Nobile, Fabio Tamellini, Lorenzo Tempone, Raúl et al.

Contributors: Nobile, Fabio Tamellini, Lorenzo Tempone, Raúl et al.

Subject Terms: Uncertainty Quantification, random PDEs, linear elliptic equations, multivariate polynomial approximation, best M-terms polynomial, approximation, Smolyak approximation, Sparse grids, Stochastic Collocation method

Relation: https://infoscience.epfl.ch/record/263221/files/12-2014NEW_FN-LT-RT.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153701

Availability: https://doi.org/10.5075/epfl-MATHICSE-263221
https://infoscience.epfl.ch/handle/20.500.14299/153701
https://hdl.handle.net/20.500.14299/153701

A SPARSE COMPOSITE COLLOCATION FINITE ELEMENT METHOD FOR ELLIPTIC SPDEs

Authors: BIERI, MARCEL

Source: SIAM Journal on Numerical Analysis, 2011 Jan 01. 49(5/6), 2277-2301.

Access URL: http://dx.doi.org/10.1137/090750743

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Authors: Nobile, Fabio Tamellini, Lorenzo Tempone, Raul

Subject Terms: Uncertainty Quantification, random PDEs, linear elliptic equations, multivariate polynomial approximation, best M-terms polynomial approximation, Smolyak approximation, Sparse grids, Stochastic Collocation method

Relation: https://infoscience.epfl.ch/record/196966/files/2016_Nobile_Tamellini_Tempone_NM_Convergence.pdf; Numerische Mathematik; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/100963; WOS:000382146600005

Availability: https://doi.org/10.1007/s00211-015-0773-y
https://infoscience.epfl.ch/handle/20.500.14299/100963
https://hdl.handle.net/20.500.14299/100963

The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.

Contributors: Nobile, Fabio [Politecnico di Milano, Italy]

File Description: Medium: ED; Size: 56 p.

Access URL: http://www.osti.gov/scitech/servlets/purl/934852

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Authors: Babuška, Ivo Nobile, Fabio Tempone, Raul et al.

Contributors: Babuška, Ivo Nobile, Fabio Tempone, Raul et al.

Subject Terms: stochastic collocation method, partial differential equations with random inputs, finite elements, uncertainty quantification, convergence rates, multivariate polynomial approximation, Smolyak approximation, anisotropic sparse approximation

File Description: application/pdf

Relation: A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2010, 52 (2):317 SIAM Review; SIAM Review; http://hdl.handle.net/10754/555664

Availability: http://hdl.handle.net/10754/555664
https://doi.org/10.1137/100786356

A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data

Authors: Lang, Jens Scheichl, Robert Silvester, David

Source: Lang, J, Scheichl, R & Silvester, D 2020, 'A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data', Journal of Computational Physics, vol. 419, 109692. https://doi.org/10.1016/j.jcp.2020.109692

Subject Terms: Adaptivity, High-dimensional approximation, Multilevel methods, Sparse grids, Stochastic collocation, Uncertainty quantification

File Description: application/pdf

Availability: https://research.manchester.ac.uk/en/publications/c08deffa-734b-475f-a4f8-ac606656201f
https://doi.org/10.1016/j.jcp.2020.109692
https://pure.manchester.ac.uk/ws/files/172960384/AMLUQ_LSS2020_final.pdf
http://www.scopus.com/inward/record.url?scp=85087588525&partnerID=8YFLogxK

ADAPTIVE SMOLYAK PSEUDOSPECTRAL APPROXIMATIONS.

Authors: CONRAD, PATRICK R. MARZOUK, YOUSSEF M.

Source: SIAM Journal on Scientific Computing; 2013, Vol. 35 Issue 6, pA2643-A2670, 28p

Subject Terms: ALGORITHMS, POLYNOMIAL approximation, SPARSE graphs, ORTHOGONAL polynomials, APPROXIMATION theory, CHEMICAL kinetics

An Improved Probabilistic Collocation Method for Uncertainty Quantification of Oil–Water Transport through Fractured Porous Media: Effect of Uncertain Gravity Imbibition.

Authors: Sharafi, Mohammad Sadegh Ahmadi, Mohammad Kazemi, Alireza

Source: Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ); Apr2025, Vol. 50 Issue 7, p5135-5156, 22p

Subject Terms: MONTE Carlo method, COLLOCATION methods, POROUS materials, POLYNOMIAL chaos, POINT set theory

A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.

Authors: Wodraszka, Robert Carrington, Tucker

Source: Journal of Chemical Physics; 4/21/2019, Vol. 150 Issue 15, pN.PAG-N.PAG, 12p, 2 Graphs

Subject Terms: POTENTIAL energy surfaces, SCHRODINGER equation, POINT set theory, COLLOCATION methods, PHYSICAL & theoretical chemistry

Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature.

Authors: Simmons, Jesse Carrington Jr., Tucker

Source: Journal of Chemical Physics; 4/14/2023, Vol. 158 Issue 14, p1-12, 12p

Subject Terms: COLLOCATION methods, VIBRATIONAL spectra, POLYATOMIC molecules, POTENTIAL energy surfaces, QUADRATURE domains, MOLECULAR spectra

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

Authors: R. Ahlfeld B. Belkouchi F. Montomoli

Source: Journal of Computational Physics. 320:1-16

Subject Terms: Anisotropic Smolyak Grid, Technology, INTERPOLATION, Sparse Gaussian Quadrature, SAMBA, 01 natural sciences, 09 Engineering, SYSTEMS, DRIVEN UNCERTAINTY QUANTIFICATION, Interdisciplinary Applications, 0101 mathematics, 01 Mathematical Sciences, Science & Technology, 02 Physical Sciences, Mathematical, Physics, Applied Mathematics, SIMULATIONS, Physics, Mathematical, Physical Sciences, Computer Science, Computer Science, Interdisciplinary Applications, Uncertainty Quantification, Non-Intrusive Polynomial Chaos, Arbitrary Polynomial Chaos, STORAGE

Access URL: http://spiral.imperial.ac.uk/bitstream/10044/1/32946/4/1-s2.0-S0021999116301516-main.pdf
http://hdl.handle.net/10044/1/32946

A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces.

Authors: Wodraszka, Robert Carrington, Tucker

Source: Journal of Chemical Physics; 3/21/2021, Vol. 154 Issue 11, p1-10, 10p

Subject Terms: POTENTIAL energy surfaces, COLLOCATION methods, ENERGY function, POTENTIAL functions, POTENTIAL energy

Computing vibrational energy levels of CH4 with a Smolyak collocation method.

Authors: Avila, Gustavo Carrington Jr., Tucker

Source: Journal of Chemical Physics; 2017, Vol. 147 Issue 14, p1-10, 10p

Subject Terms: VIBRATIONAL redistribution (Molecular physics), COLLOCATION methods, KINETIC energy, HIERARCHICAL clustering (Cluster analysis), UNIVARIATE analysis

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials.

Authors: Wu, Jinglai Luo, Zhen Zhang, Nong et al.

Source: Engineering Optimization; Sep2015, Vol. 47 Issue 9, p1264-1288, 25p

Subject Terms: STATISTICAL sampling, CHEBYSHEV approximation, COLLOCATION methods, HYPERCUBES, TENSOR algebra