May - August 2011
Organizers: Michael Griebel, Wolfgang Hackbusch, Markus Hegland, Christoph Schwab
Description: Partial differential equations related to high-dimensional parameter spaces are a major challenge in science, engineering and finance. Here, the well-known curse of high dimension prevents an efficient treatment by standard numerical discretization for most of the problems. The resulting enormous computational challenges cannot be met merely by larger computers, but require fundamentally new mathematical and algorithmic ideas. These can only be envisioned by an interdisciplinary attempt which involves modeling, analysis, stochastics and numerics. To this end, we brought together leading experts from these areas.
Associated Events:
- Workshop 1: Sparse Grids and Applications
- Workshop 2: Manifold Learning
- Workshop 3: Theoretical Aspects of High-Dimensional Problems and Information-Based Complexity
- Workshop 4: Tensor Approximation in High Dimension
- Workshop 5: High-Dimensional Aspects of Stochastic PDEs
- Summer School on H-matrices
- Summer School on Hierarchical Tensor Approximation
© HIM
| No. | Author(s) | Title | Preprint | Publication |
| 2011b01 | Chkifa, A.; Cohen, A.; DeVore, R.; Schwab, C. | Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs | ESAIM Math. Model. Numer. Anal. 47(1) (2013), 253–280. https://doi.org/10.1051/m2an/2012027 |
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| 2011b02 | Grella, K.; Schwab, C. | Sparse discrete ordinates method in radiative transfer | Comput. Methods Appl. Math.11(3) (2011), 305–326. https://doi.org/10.2478/cmam-2011-0017 |
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| 2011b03 | Griebel, M.; Oswald, P. | Greedy and randomized versions of the multiplicative Schwarz method | Linear Algebra Appl. 437(7) (2012), 1596–1610. https://doi.org/10.1016/j.laa.2012.04.052 |
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| 2011b04 | Oseledets, I. | DMRG approach to fast linear algebra in the TT-format | Comput. Methods Appl. Math. 11(3) (2011), 382–393. https://doi.org/10.2478/cmam-2011-0021 |
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| 2011b05 | Wasilkowski, G. W. | Liberating the dimension for L2-approximation | J. Complexity. 28(3) (2012), 304–319. https://doi.org/10.1016/j.jco.2011.12.002 |
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| 2011b06 | Chernov, A.; Schwab, C. | First order k-th moment finite element analysis of nonlinear operator equations with stochastic data | Math. Comp. 82(284) (2013), 1859–1888. https://doi.org/10.1090/S0025-5718-2013-02692-0 |
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| 2011b07 | Oseledets, I.; Tyrtyshnikov, E.; Zamarashkin, N. | Tensor-train ranks for matrices and their inverses | Comput. Methods Appl. Math. 11(3) (2011), 394–403. https://doi.org/10.2478/cmam-2011-0022 |
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| 2011b08 | Kuo, F. Y.; Schwab, C.; Sloan, I. H. | Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients | link | SIAM J. Numer. Anal. 50(6) (2012), 3351–3374. https://doi.org/10.1137/110845537 |
| 2011b09 | Dahlke, S.; Oswald, P.; Raasch, T. | A note on quarkonial systems and multilevel partition of unity methods | Math. Nachr. 286(5-6) (2013), 600–613. https://doi.org/10.1002/mana.201100246 |
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| 2011b10 | Chernov, A.; Schwab, C. | Sparse space-time Galerkin BEM for the nonstationary heat equation | pdf (revised version) | ZAMM Z. Angew. Math. Mech. 93(6-7) (2013), 403–413. https://doi.org/10.1002/zamm.201100192 |
| 2011b11 | Hegland, M.; Wasilkowski, G. W. | On tractability of approximation in special function spaces | 1201.4886 | J. Complexity. 29(1) (2013), 76–91. https://doi.org/10.1016/j.jco.2012.10.002 |
| 2011b12 | Dung, D.; Ullrich, T. | n-Widths and ε-dimensions for high-dimensional sparse approximations | ||
| 2011b13 | Kressner, D.; Tobler, C. | Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems | Comput. Methods Appl. Math. 11(3) (2011), 363–381. https://doi.org/10.2478/cmam-2011-0020 |
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| 2011b14 | Schilling, R. L.; Partzsch, L. | Brownian motion: An introduction to stochastic processes | De Gruyter Grad. De Gruyter, Berlin, 2014. xvi+408 pp. MR3234570 |
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| 2011b15 | Schilling, R. L.; Wang, J. | Some theorems on Feller processes: transience, local times and ultracontractivity | 1108.3246 | Trans. Amer. Math. Soc. 365(6) (2013), 3255–3286. https://doi.org/10.1090/S0002-9947-2012-05738-2 |
| 2011b16 | Khoromskaia, V.; Khoromskij, B. N.; Schneider, R. | QTT representation of the Hartree and exchange operators in electronic structure calculations | link | Comput. Methods Appl. Math. 11(3) (2011), 327–341. https://doi.org/10.2478/cmam-2011-0018 |
| 2011b17 | Lifshits, M. A.; Papageorgiou, A.; Woźniakowski, H. | Average case tractability of non-homogeneous tensor product problems | 1112.4251 | J. Complexity. 28(5-6) (2012), 539–561. https://doi.org/10.1016/j.jco.2012.05.003 |
| 2011b18 | Lifshits, M. A.; Papageorgiou, A.; Woźniakowski, H. | Tractability of multi-parametric Euler and Wiener integrated processes | 1112.4248 | Probab. Math. Statist. 32(1) (2012), 131–165. https://www.math.uni.wroc.pl/~pms/publications.php?nr=32.1 |
| 2011b19 | Schwab, C.; Süli, E. | Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions | Stoch. Partial Differ. Equ. Anal. Comput. 1(1) (2013), 204–239. https://doi.org/10.1007/s40072-013-0002-6 |
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| 2011b20 | Kazeev, V. A.; Khoromskij, B. N.; Tyrtyshnikov, E. E. | Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity | link | SIAM J. Sci. Comput. 35(3) (2013), A1511–A1536. https://doi.org/10.1137/110844830 |
| 2011b21 | Nistor, V.; Schwab, C. | High-order Galerkin approximations for parametric second-order elliptic partial differential equations | link | Math. Models Methods Appl. Sci. 23(9) (2013), 1729–1760. https://doi.org/10.1142/S0218202513500218 |
| 2011b22 | Dick, J.; Nuyens, D.; Pillichshammer, F. | Lattice rules for nonperiodic smooth integrands | 1211.3799 | Numer. Math. 126(2) (2014), 259–291. https://doi.org/10.1007/s00211-013-0566-0 |
| 2011b23 | Hegland, M.; Leopardi, P. | Sparse grid quadrature on products of spheres | 1202.5710 | Numer. Algorithms. 70(3) (2015), 485–517. https://doi.org/10.1007/s11075-015-9958-9 |
| 2011b24 | Dick, J.; Gnewuch, M. | Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence | 1210.4223 | Found. Comput. Math. 14(5) (2014), 1027–1077. https://doi.org/10.1007/s10208-014-9198-8 |
Name |
Affiliation |
| Alon Arad | Australian National University |
| Dung Dinh | Vietnam National University |
| Simon Foucart | Drexel University |
| Jochen Garcke | TU Berlin |
| Michael Griebel | Universität Bonn |
| Wolfgang Hackbusch | Max-Planck-Institut für Mathematik Leipzig |
| Markus Hegland | Australian National University |
| Viet Ha Hoang | Nanyang Technological University |
| John Jakeman | Australian National University |
| Vladimir Kazeev | Russian Academy of Sciences |
| Venera Khoromskaia | Max-Planck-Institut für Mathematik in den Naturwissenschaften |
| Boris Khoromskij | Max-Planck-Institut für Mathematik in den Naturwissenschaften |
| Daniel Kressner | ETH Zürich |
| Frances Kuo | University of New South Wales |
| Elizabeth Lam | University of Toronto |
| Mikhail Lifshits | St. Petersburg State University |
| Per Lötstedt | Uppsala University |
| Martin Mohlenkamp | Ohio State University |
| Ekaterina Muravleva | Max Planck Institute for Mathematics in the Sciences |
| James Nichols | University of New South Wales (UNSW) |
| Victor Nistor | Penn State University |
| Erich Novak | Universität Jena |
| Erich Novak | Universität Jena |
| Dirk Nuyens | Katholieke Universiteit Leuven |
| Ivan Oseledets | Russian Academy of Sciences |
| Peter Oswald | Jacobs University Bremen |
| Vladimir Pestov | University of Ottawa |
| Daniel Rudolf | Friedrich-Schiller-Universität Jena |
| René Leander Schilling | TU Dresden |
| Reinhold Schneider | TU Berlin |
| Christoph Schwab | ETH Zürich |
| Ian H. Sloan | University of New South Wales |
| Vikram Sunkara | Australian National University |
| Endre Süli | Oxford University |
| Evgeny Tyrtyshnikov | Russian Academy of Sciences |
| Mario Ullrich | Friedrich-Schiller-Universität Jena |
| Grzegorz (Greg) W. Wasilkowski | University of Kentucky |
| Holger Wendland | University of Oxford |
| Henryk Wozniakowski | Columbia University |
This list does not include people who only participated in the workshops or summer schools.
© HIM