乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T16:33:49Z","timestamp":1732034029993},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,3,1]],"date-time":"2011-03-01T00:00:00Z","timestamp":1298937600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Visual Sci."],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1007\/s00791-011-0165-5","type":"journal-article","created":{"date-parts":[[2011,11,22]],"date-time":"2011-11-22T13:17:37Z","timestamp":1321967857000},"page":"91-103","source":"Crossref","is-referenced-by-count":18,"title":["A POD framework to determine robust controls in PDE optimization"],"prefix":"10.1007","volume":"14","author":[{"given":"A.","family":"Borz\u00ec","sequence":"first","affiliation":[]},{"given":"G.","family":"von Winckel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,11,23]]},"reference":[{"key":"165_CR1","first-page":"1311","volume":"11","author":"J.A. Atwell","year":"2001","unstructured":"Atwell J.A., Borggaard J.T., King B.B.: Reduced order controllers for Burgers\u2019 equation with a nonlinear observer. Int. J. Appl. Math. Comput. 11, 1311\u20131330 (2001)","journal-title":"Int. J. Appl. Math. Comput."},{"issue":"3","key":"165_CR2","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1137\/050645142","volume":"45","author":"I. Babu\u0161ka","year":"2007","unstructured":"Babu\u0161ka I., Nobile F., Tempone R.: A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Num. Anal. 45(3), 1005\u20131034 (2007)","journal-title":"SIAM J. Num. Anal."},{"key":"165_CR3","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1137\/S0036142902418680","volume":"42","author":"I.M. Babuska","year":"2004","unstructured":"Babuska I.M., Tempone R., Zouraris G.E.: Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42, 800\u2013825 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"165_CR4","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00791-010-0134-4","volume":"13","author":"A. Borz\u00ec","year":"2010","unstructured":"Borz\u00ec A.: Multigrid and sparse-grid schemes for elliptic control problems with random coefficients. Comput. Vis. Sci. 13, 153\u2013160 (2010)","journal-title":"Comput. Vis. Sci."},{"key":"165_CR5","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1137\/060671590","volume":"51","author":"A. Borz\u00ec","year":"2009","unstructured":"Borz\u00ec A., Schulz V.: Multigrid methods for PDE optimization. SIAM Rev. 51, 361\u2013395 (2009)","journal-title":"SIAM Rev."},{"key":"165_CR6","doi-asserted-by":"crossref","first-page":"2172","DOI":"10.1137\/070711311","volume":"31","author":"A. Borz\u00ec","year":"2009","unstructured":"Borz\u00ec A., von Winckel G.: Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients. SIAM J. Sci. Comp. 31, 2172\u20132192 (2009)","journal-title":"SIAM J. Sci. Comp."},{"key":"165_CR7","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1002\/gamm.201010017","volume":"33","author":"A. Borz\u00ec","year":"2010","unstructured":"Borz\u00ec A., Schulz V., Schillings C., von Winckel G.: On the treatment of distributed uncertainties in PDE-constrained optimization. GAMM Mitteilungen 33, 230\u2013246 (2010)","journal-title":"GAMM Mitteilungen"},{"key":"165_CR8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1017\/S0962492904000182","volume":"13","author":"H.-J. Bungartz","year":"2004","unstructured":"Bungartz H.-J., Griebel M.: Sparse grids. Acta Numer. 13, 147\u2013269 (2004)","journal-title":"Acta Numer."},{"key":"165_CR9","doi-asserted-by":"crossref","unstructured":"Demmel, J.W.: Applied Numerical Linear Algebra. SIAM (1997)","DOI":"10.1137\/1.9781611971446"},{"key":"165_CR10","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1016\/j.jcp.2006.12.014","volume":"225","author":"B. Ganapathysubramanian","year":"2007","unstructured":"Ganapathysubramanian B., Zabaras N.: Sparse grid collocation schemes for stochastic natural convection problems. J. Comput. Phys. 225, 652\u2013685 (2007)","journal-title":"J. Comput. Phys."},{"key":"165_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3094-6","volume-title":"Stochastic finite elements: a spectral approach","author":"R.G. Ghanem","year":"1991","unstructured":"Ghanem R.G., Spanos P.D.: Stochastic finite elements: a spectral approach. Springer, New York (1991)"},{"key":"165_CR12","unstructured":"Graham, I.G., Kuo, F.Y., Nuyens, D., Scheichl, R., Sloan, I.H.: Quasi-monte carlo methods for computing flow in random porous media. Bath Institute For Complex Systems. Preprint 04\/10 (2010)"},{"key":"165_CR13","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/13873954.2010.514703","volume":"17","author":"B. Haasdonk","year":"2011","unstructured":"Haasdonk B., Ohlberger M.: Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline\/online decomposition. Math. Comp. Model. Dyn. Syst. 17, 145\u2013161 (2011)","journal-title":"Math. Comp. Model. Dyn. Syst."},{"key":"165_CR14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718614","volume-title":"Lagrange Multiplier Approach to Variational Problems and Applications","author":"K. Ito","year":"2008","unstructured":"Ito K., Kunisch K.: Lagrange Multiplier Approach to Variational Problems and Applications. SIAM, Philadelphia (2008)"},{"key":"165_CR15","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11071-005-2803-2","volume":"41","author":"G. Kerschen","year":"2005","unstructured":"Kerschen G., Golival J.-C., Vakakis A.F., Bergman L.A.: The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn. 41, 147\u2013169 (2005)","journal-title":"Nonlinear Dyn."},{"key":"165_CR16","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1145\/1114268.1114275","volume":"31","author":"A. Klimke","year":"2005","unstructured":"Klimke A., Wohlmuth B.: Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Trans. Math. Softw. 31, 561\u2013579 (2005)","journal-title":"ACM Trans. Math. Softw."},{"key":"165_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/m2an:2007054","volume":"42","author":"K. Kunisch","year":"2008","unstructured":"Kunisch K., Volkwein S.: Proper orthogonal decomposition for optimality systems. ESAIM Math. Model. Numer. Anal. 42, 1\u201323 (2008)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"165_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of Systems Governed by Partial Differential Equations","author":"J.L. Lions","year":"1971","unstructured":"Lions J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin (1971)"},{"key":"165_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6257-2","volume-title":"Probability Theory, vols. I & II","author":"M. Loeve","year":"1978","unstructured":"Loeve M.: Probability Theory, vols. I & II, 4th edn. Springer, New York (1978)","edition":"4"},{"key":"165_CR20","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.jcp.2006.10.010","volume":"224","author":"Y.M. Marzouk","year":"2007","unstructured":"Marzouk Y.M., Najm H.N., Rahn L.A.: Stochastic spectral methods for efficient Bayesian solution of inverse problems. J. Comput. Phys. 224, 560\u2013586 (2007)","journal-title":"J. Comput. Phys."},{"key":"165_CR21","doi-asserted-by":"crossref","unstructured":"Nguyen, N.C., Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation. In: Biegler, L. Biros, G., Ghattas, O., Heinkenschloss, M., Keyes, D., Mallick, B., Marzouk, Y. Tenorio, L., van Bloemen Waanders, B., Willcox, K. (eds.) Large Scale Inverse Problems and Quantification of Uncertainty, Chap. 8, pp. 151\u2013173. Wiley, UK (Series in Computational Statistics) (2010)","DOI":"10.1002\/9780470685853.ch8"},{"key":"165_CR22","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1137\/060663660","volume":"46","author":"F. Nobile","year":"2008","unstructured":"Nobile F., Tempone R., Webster C.: A sparse grid stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 46, 2309\u20132345 (2008)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"165_CR23","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1081\/SAP-200044467","volume":"23","author":"B. \u00d8ksendal","year":"2005","unstructured":"\u00d8ksendal B.: Optimal control of stochastic partial differential equations. Stoch. Anal. Appl. 23(1), 165\u2013179 (2005)","journal-title":"Stoch. Anal. Appl."},{"key":"165_CR24","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/nla.568","volume":"15","author":"E. Rosseel","year":"2008","unstructured":"Rosseel E., Boonen T., Vandewalle S.: Algebraic multigrid for stationary and time-dependent partial differential equations with stochastic coefficients. Numer. Linear Algebra Appl. 15, 141\u2013163 (2008)","journal-title":"Numer. Linear Algebra Appl."},{"key":"165_CR25","doi-asserted-by":"crossref","first-page":"646","DOI":"10.2514\/1.37955","volume":"47","author":"V. Schulz","year":"2009","unstructured":"Schulz V., Schillings C.: On the nature and treatment of uncertainties in aerodynamic design. AIAA J. 47, 646\u2013654 (2009)","journal-title":"AIAA J."},{"key":"165_CR26","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s00607-003-0024-4","volume":"71","author":"Ch. Schwab","year":"2003","unstructured":"Schwab Ch., Todor R.A.: Sparse finite elements for stochastic elliptic problems higher order moments. Computing 71, 43\u201363 (2003)","journal-title":"Computing"},{"key":"165_CR27","volume-title":"Random Fields: Analysis and Synthesis","author":"E. Vanmarcke","year":"1983","unstructured":"Vanmarcke E.: Random Fields: Analysis and Synthesis. MIT Press, USA (1983)"},{"issue":"3","key":"165_CR28","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1137\/040615201","volume":"27","author":"D. Xiu","year":"2005","unstructured":"Xiu D., Hesthaven J.S.: High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comp. 27(3), 1118\u20131139 (2005)","journal-title":"SIAM J. Sci. Comp."}],"container-title":["Computing and Visualization in Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-011-0165-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00791-011-0165-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-011-0165-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T23:03:00Z","timestamp":1560985380000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00791-011-0165-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["165"],"URL":"https:\/\/doi.org\/10.1007\/s00791-011-0165-5","relation":{},"ISSN":["1432-9360","1433-0369"],"issn-type":[{"value":"1432-9360","type":"print"},{"value":"1433-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}