PyMOR – generic algorithms and interfaces for model order reduction. (English) Zbl 1352.65453


65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
65Y20 Complexity and performance of numerical algorithms
35L03 Initial value problems for first-order hyperbolic equations
35J20 Variational methods for second-order elliptic equations
68N01 General topics in the theory of software
Full Text: DOI arXiv


[1] F. Ballarin, G. Rozza, and A. Sartori, RBniCS – reduced order modelling in FEniCS, ScienceOpen Posters, (2015), .
[2] W. Bangerth, R. Hartmann, and G. Kanschat, deal.II – a general purpose object oriented finite element library, ACM Trans. Math. Software, 33 (2007), 24, . · Zbl 1365.65248
[3] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander, A generic grid interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE, Computing, 82 (2008), pp. 121–138, . · Zbl 1151.65088
[4] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander, A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework, Computing, 82 (2008), pp. 103–119, . · Zbl 1151.65089
[5] B. A. Belson, J. H. Tu, and C. W. Rowley, Algorithm 945: Modred–a parallelized model reduction library, ACM Trans. Math. Software, 40 (2014), 30, . · Zbl 1369.65199
[6] P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods, SIAM J. Math. Anal., 43 (2011), pp. 1457–1472, . · Zbl 1229.65193
[7] A. Buhr, C. Engwer, M. Ohlberger, and S. Rave, A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations, in Proceedings of the 11th World Congress on Computational Mechanics, X. Oliver, E. Onate, and A. Huerta, eds., CIMNE, Barcelona, 2014, pp. 4094–4102.
[8] A. Buhr, C. Engwer, M. Ohlberger, and S. Rave, Arbilomod, a simulation technique designed for arbitrary local modifications, arXiv e-prints, 2015, . · Zbl 1369.65160
[9] S. Chaturantabut and D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput., 32 (2010), pp. 2737–2764, . · Zbl 1217.65169
[10] C. Daversin, S. Veys, C. Trophime, and C. Prud’homme, A reduced basis framework: Application to large scale non-linear multi-physics problems, ESAIM: Proceedings and Surveys, 43 (2013), pp. 225–254, . · Zbl 1325.65152
[11] R. DeVore, G. Petrova, and P. Wojtaszczyk, Greedy algorithms for reduced bases in Banach spaces, Constr. Approx., 37 (2013), pp. 455–466, . · Zbl 1276.41021
[12] M. Drohmann, B. Haasdonk, S. Kaulmann, and M. Ohlberger, A software framework for reduced basis methods using dune-rb and rbmatlab, in Advances in DUNE, A. Dedner, B. Flemisch, and R. Klöfkorn, eds., Springer, Berlin, Heidelberg, 2012, pp. 77–88, .
[13] M. Drohmann, B. Haasdonk, and M. Ohlberger, Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation, SIAM J. Sci. Comput., 34 (2012), pp. A937–A969, . · Zbl 1259.65133
[14] B. Haasdonk, Convergence rates of the pod-greedy method, ESAIM Math. Model. Numer. Anal., 47 (2013), pp. 859–873, . · Zbl 1277.65074
[15] B. Haasdonk, Reduced basis methods for parametrized PDEs—A tutorial introduction for stationary and instationary problems, chapter to appear in Model Reduction and Approximation: Theory and Algorithms, P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, SIAM, Philadelphia.
[16] B. Haasdonk, M. Dihlmann, and M. Ohlberger, A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space, Math. Comput. Model. Dyn. Syst., 17 (2011), pp. 423–442, . · Zbl 1302.65221
[17] B. Haasdonk, M. Ohlberger, and G. Rozza, A reduced basis method for evolution schemes with parameter-dependent explicit operators, Electron. Trans. Numer. Anal., 32 (2008), pp. 145–161. · Zbl 1391.76413
[18] J. S. Hesthaven, G. Rozza, and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, SpringerBriefs in Mathematics, Springer, Cham, 2016, . · Zbl 1329.65203
[19] S. F. Johnsen, Z. A. Taylor, M. J. Clarkson, J. Hipwell, M. Modat, B. Eiben, L. Han, Y. Hu, T. Mertzanidou, D. J. Hawkes, S. Ourselin, Niftysim: A gpu-based nonlinear finite element package for simulation of soft tissue biomechanics, Int. J. Comput. Assist. Radiol. Surg., 10 (2015), pp. 1077–1095, .
[20] E. Jones, T. Oliphant, P. Peterson, et al., SciPy: Open Source Scientific Tools for Python, (2001–2015).
[21] D. J. Knezevic and J. W. Peterson, A high-performance parallel implementation of the certified reduced basis method, Comput. Methods Appl. Mech. Engrg., 200 (2011), pp. 1455–1466, . · Zbl 1228.76109
[22] A. Logg, K.-A. Mardal, G. N. Wells, eds., Automated Solution of Differential Equations by the Finite Element Method, Springer, Heidelberg, 2012, .
[23] A. Logg and G. N. Wells, Dolfin: Automated finite element computing, ACM Trans. Math. Software, 37 (2010), 20, . · Zbl 1364.65254
[24] M. Ohlberger, S. Rave, and F. Schindler, Model reduction for multiscale lithium-ion battery simulation, in ENUMATH 2015, Ankara, Turkey, Lect. Notes Comput. Sci. Eng., Springer, 2016. · Zbl 1355.78031
[25] M. Ohlberger, S. Rave, S. Schmidt, and S. Zhang, A model reduction framework for efficient simulation of li-ion batteries, in Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, J. Fuhrmann, M. Ohlberger, and C. Rohde, eds., Springer, Cham, 2014, pp. 695–702, . · Zbl 1327.78021
[26] M. Ohlberger and F. Schindler, Error control for the localized reduced basis multiscale method with adaptive on-line enrichment, SIAM J. Sci. Comput., 37 (2015), pp. A2865–A2895, . · Zbl 1329.65255
[27] T. E. Oliphant, Python for scientific computing, Comput. Sci. Eng., 9 (2007), pp. 10–20, .
[28] A. T. Patera and G. Rozza, Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations, version \textup1.0, copyright MIT 2006–2007, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering.
[29] F. Pérez and B. E. Granger, IPython: A system for interactive scientific computing, Comput. Sci. Eng., 9 (2007), pp. 21–29, .
[30] A. Quarteroni, A. Manzoni, and F. Negri, Reduced Basis Methods for Partial Differential Equations, La Matematica per il 3+2, Springer, Cham, 2016. · Zbl 1337.65113
[31] F. Schindler and R. Milk, \tt dune-gdt, (2015), .
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