January 3 - April 21, 2017
Organizers: Susanne C. Brenner, Björn Engquist, Max Gunzburger, Daniel Peterseim, Marc Alexander Schweitzer
Description: Many physical processes in material sciences or geophysics are characterised by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical techniques to adaptively select relevant scales and effectively represent unresolved scales. The program has enhanced the development of corresponding algorithms and the mathematics behind them so that the reliable and efficient numerical simulation of challenging multiscale problems eventually becomes feasible in modern high performance computing environments.
Associated Events: We hosted long-term visitors and organized the following focused activities:
- Winter School on Numerical Analysis of Multiscale Problems (January 9-13)
- Workshop on Numerical Inverse and Stochastic Homogenization (February 13-17)
- Workshop on Non-local Material Models and Concurrent Multiscale Methods (April 3-7)
© HIM
| No. | Author(s) | Title | Preprint | Publication |
| 2017a01 | Gallistl, D.; Peterseim, D. | Numerical stochastic homogenization by quasilocal effective diffusion tensors | 1702.08858 | Communications in Mathematical Sciences. 17(3) (2019), 637-651. https://dx.doi.org/10.4310/CMS.2019.v17.n3.a3 |
| 2017a02 | Carstensen, C.; Gallistl, D.; Gedicke, J. | Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM | 1705.08851 | Numer. Math. 142 (2019), 205–234. https://doi.org/10.1007/s00211-019-01029-7 |
| 2017a03 | Chung, E. T.; Efendiev, Y.; Leung, W. T. | Constraint energy minimizing generalized multiscale finite element method | 1704.03193 | Computer Methods in Applied Mechanics and Engineering. 339 (2018), 298-319. https://doi.org/10.1016/j.cma.2018.04.010 |
| 2017a04 | Gallistl, D.; Henning, P.; Verfürth, B. | Numerical homogenization of H(curl)-problems | 1706.02966 | SIAM Journal on Numerical Analysis. 56(3) (2018), 1187-1986. https://doi.org/10.1137/17M1133932 |
| 2017a05 | Bartels, S.; Buttazzo, G. | Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation | 1708.03762 | Interfaces Free Bound. 21(1) (2019), 1–19. https://doi.org/10.4171/ifb/414 |
| 2017a06 | Nochetto, R. H.; Ntogkas, D.; Zhang, W. | Two-scale method for the Monge-Ampère equation: convergence to the viscosity solution | 1706.06193 | Math. Comp. 88 (2019), 637-664. http://dx.doi.org/10.1090/mcom/3353 |
| 2017a07 | Nochetto, R. H.; Ntogkas, D.; Zhang, W. | Two-scale method for the Monge-Ampère equation: pointwise error estimates | 1706.09113 | IMA Journal of Numerical Analysis. 39(3) (2019), 1085–1109. https://doi.org/10.1093/imanum/dry026 |
| 2017a08 | Nochetto, R. H.; Walker, S. W.; Zhang, W. | The Ericksen model of liquid crystals with colloidal and electric effects | 1708.00925 | Journal of Computational Physics. 352 (2018), 568-601. https://doi.org/10.1016/j.jcp.2017.09.035 |
| 2017a09 | Hutridurga, H.; Venkataraman, C. | Heterogeneity and strong competition in ecology | 1710.06116 | European Journal of Applied Mathematics. 30(4) (2019), 682–706. https://doi.org/10.1017/S0956792518000372 |
| 2017a10 | Schmuck, M.; Pavliotis, G.A.; Kalliadasis, S. | Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality | 1804.09228 | Computational Materials Science. 156 (2019), 441-451. https://doi.org/10.1016/j.commatsci.2018.08.026 |
| 2017a11 | Alaeian, H.; Schedensack, M.; Bartels, C.; Peterseim, Daniel; Weitz, M. | Thermo-optical interactions in a dye-microcavity photon Bose-Einstein condensate | 1710.01706 | New J. Phys. 19 (2019). https://doi.org/10.1088/1367-2630/aa964c |
| 2017a12 | Altmann, R.; Chung, E.; Maier, R.; Peterseim, D.; Pun, S.-M. | Computational multiscale methods for linear heterogeneous poroelasticity | 1801.00615 | Journal of Computational Mathematics. 38 (1), 41-57. https://doi.org/10.4208/jcm.1902-m2018-0186 |
| 2017a13 | Altmann, R.; Henning, P.; Peterseim, D. | Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials | 1803.09950 | Mathematical Models and Methods in Applied Sciences. 30(5) (2020), 917-955. https://doi.org/10.1142/S0218202520500190 |
| 2017a14 | Barrenechea, G. R.; González, C. | A stabilized finite element method for a fictitious domain problem allowing small inclusions | Numerical Methods for Partial Differential Equations. 34(1) (2018), 1-380. https://doi.org/10.1002/num.22190 |
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| 2017a15 | Bartels, S.; Diening, L.; Nochetto, R. H. | Unconditional stability of semi-implicit discretizations of singular flows | 1712.03260 | SIAM Journal on Numerical Analysis. 56(3) (2018), 1187-1986. https://doi.org/10.1137/17M1159166 |
| 2017a16 | Boiveau, T.; Ehrlacher, V.; Ern, A.; Nouy, A. | Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods | 1712.07256 | ESAIM: M2AN. 53(2) (2019), 635 – 658. https://doi.org/10.1051/m2an/2018073 |
| 2017a17 | Brenner, S. C.; Gedicke, J.; Sung, L. | C0 Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints | SIAM Journal on Numerical Analysis. 56(3) (2018), 1187-1986. https://doi.org/10.1137/17M1140649 |
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| 2017a18 | Brown, D. L.; Gedicke, J. | Upscaling Singular Sources in Weighted Sobolev Spaces by Sub-Grid Corrections | 1802.02460 | |
| 2017a19 | Brown, D. L.; Gedicke, J.; Peterseim, D. | Numerical Homogenization of Heterogeneous Fractional Laplacians | 1709.00730 | Multiscale Modeling & Simulation. 16(3) (2018), 1085-1453. https://doi.org/10.1137/17M1147305 |
| 2017a20 | Carstensen, C.; Bringmann, P.; Hellwig, F.; Wriggers, P. | Nonlinear discontinuous Petrov-Galerkin methods | 1710.00529 | Numer. Math. 139 (2018), 529–561. https://doi.org/10.1007/s00211-018-0947-5 |
| 2017a21 | Chung, E.; Efendiev, Y.; Leung, W. T. | Constraint energy minimizing generalized multiscale finite element method in the mixed formulation | 1705.05959 | Comput Geosci. 22 (2018), 677–693. https://doi.org/10.1007/s10596-018-9719-7 |
| 2017a22 | Diehl, P.; Lipton, R.; Schweitzer, M. A. | Numerical verification of a bond-based softening peridynamic model for small displacements: Deducing material parameters from classical linear theory | appeared in Technical report, Institut für Numerische Simulation | |
| 2017a23 | Du, Q.; Tao, Y.; Tian, X.; Yang, J. | Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Greens functions | Journal of Numerical Analysis. 39(2) (2019), 607–625. https://doi.org/10.1093/imanum/dry011 |
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| 2017a24 | Gallistl, D. | Numerical approximation of planar oblique derivative problems in nondivergence form | Math. Comp. 88 (2019), 1091-1119. https://doi.org/10.1090/mcom/3371 |
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| 2017a25 | Gallistl, D.; Peterseim, D. | Computation of quasi-local effective diffusion tensors and connections to the mathematical theory of homogenization | Multiscale Modeling & Simulation. 15(4) (2017), 1325-1864. https://doi.org/10.1137/16M1088533 |
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| 2017a26 | Graham, I. G.; Sauter, S. A. | Stability and error analysis for the Helmholtz equation with variable coefficients | 1803.00966 | Math. Comp. 89(321) (2020), 105-138. https://doi.org/10.1090/mcom/3457 |
| 2017a27 | Graham, I. G.; Spence, E. A.; Zou, J. | Domain Decomposition with local impedance conditions for the Helmholtz equation | 1806.03731 | SIAM Journal on Numerical Analysis. 58(5) (2020), 2435-3123. https://doi.org/10.1137/19M1272512 |
| 2017a28 | Henning, P.; Peterseim, D. | Cranknicolson galerkin approximations to nonlinear schrdinger equations with rough potentials | Mathematical Models and Methods in Applied Sciences. 27(11) (2017), 2147-2184. https://doi.org/10.1142/S0218202517500415 |
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| 2017a29 | Hu, J.; Schedensack, M. | Two low-order nonconforming finite element methods for the Stokes flow in three dimensions | 1710.06682 | IMA Journal of Numerical Analysis. 39(3) (2019), 1447–1470. https://doi.org/10.1093/imanum/dry021 |
| 2017a30 | Jensen, M.; Målqvist, A.; Persson, A. | Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions | 1801.10105 | IMA Journal of Numerical Analysis. 42(1) (2022), 199–228. https://doi.org/10.1093/imanum/draa068 |
| 2017a31 | Jha, P. K.; Lipton, R. | Numerical analysis of nonlocal fracture models in Hölder space | 1701.02818 | SIAM Journal on Numerical Analysis. 56(2) (2018), 635-1185. https://doi.org/10.1137/17M1112236 |
| 2017a32 | Jha, P. K.; Lipton, R. | Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics | 1707.00398 | International Journal for Numerical Methods in Engineering. 114(13) (2018), 1351-1461. https://doi.org/10.1002/nme.5791 |
| 2017a33 | Maier, R.; Peterseim, D. | Explicit Computational Wave Propagation in Micro-Heterogeneous Media | 1803.07898 | Bit Numer Math. 59 (2019), 443–462. https://doi.org/10.1007/s10543-018-0735-8 |
| 2017a34 | Peterseim, D.; Schedensack, M. | Relaxing the CFL condition for the wave equation on adaptive meshes | 1601.04812 | J Sci Comput. 72 (2017), 1196–1213. https://doi.org/10.1007/s10915-017-0394-y |
| 2017a35 | Sauter, S.; Torres, C. | Stability estimate for the Helmholtz equation with rapidly jumping coefficients | 1711.05430 | Angew. Math. Phys. 69(139) (2018). https://doi.org/10.1007/s00033-018-1031-9 |
| 2017a36 | Yang, Y.; Engquist, B. | Analysis of optimal transport and related misfit functions in full-waveform inversion | GEOPHYSICS. 83(1) (2018), 1JF-Z3. https://doi.org/10.1190/geo2017-0264.1 |
| Name | Affiliation |
| Blanca Ayuso de Dios | University of Bologna |
| John Ball | University of Oxford |
| Gabriel R. Barrenechea | University of Strathclyde |
| Soeren Bartels | Albert-Ludwigs-Universität Freiburg |
| Mario Bebendorf | Universität Bayreuth |
| Pavel Blagovestov Bochev | Sandia National Laboratories |
| Thomas Boiveau | Université Paris-Est, CERMICS, ENPC |
| Susanne Brenner | Louisiana State University |
| Donald Brown | University of Nottingham |
| Sean Carney | University of Texas at Austin |
| Carsten Carstensen | Humboldt-Universität zu Berlin |
| Jiun-Shyan Chen | University of California, San Diego |
| Eric Chung | The Chinese University of Hong Kong |
| Nicole Cusimano | Basque Center for Applied Mathematics |
| Marta D'Elia | Sandia National Laboratories |
| Jérôme Daquin | RMIT University |
| Juan Carlos De los Reyes | Escuela Politécnica Nacional |
| Patrick Diehl | Universität Bonn |
| Yalchin Efendiev | Texas A&M University |
| Bjorn Engquist | University of Texas at Austin |
| Alexandre Ern | CERMICS, ENPC |
| Michael Feischl | UNSW Australia |
| Julian Fischer | IST Austria |
| Jan Philip Freese | Karlsruhe Institue of Technology |
| Jan Philip Freese | Karlsruhe Institue of Technology |
| Dietmar Gallistl | Karlsruher Institut für Technologie |
| Joscha Gedicke | Universität Wien |
| Emmanuil Georgoulis | University of Leicester and National Technical University of Athens |
| Ivan Graham | University of Bath |
| Max Gunzburger | Florida State University |
| Wolfgang Hackbusch | MPI Mathematik i.d.N. |
| Friederike Hellwig | Humboldt-Universität zu Berlin |
| Patrick Henning | KTH Royal Institute of Technology |
| Viet Ha Hoang | Nanyang Technological University |
| Harsha Hutridurga | Imperial College London |
| Harsha Hutridurga | Imperial College London |
| Bartosz Jaroszkowski | Sussex University |
| Illia Karabash | Institute of Applied Mathematics and Mechanics of NAS of Ukraine |
| Fotini Karakatsani | University of Chester |
| Vladimir Kazeev | University of Geneva |
| Sebastian Krumscheid | École polytechnique fédérale de Lausanne |
| Omar Lakkis | Free University of Bozen-Bolzano |
| Guanglian Li | Universität Bonn |
| Martin Lind | Karlstad University |
| Robert Lipton | Louisiana State University |
| Dongjie Liu | Shanghai University |
| Roland Maier | Universität Bonn |
| Charalambos Makridakis | University of Sussex |
| Heinrich Mellmann | Humboldt-Universität zu Berlin |
| Olga Mula | Université Paris Dauphine |
| Adrian Muntean | Karlstad University |
| Ricardo Nochetto | University of Maryland |
| Michael Ortiz | Universität Bonn |
| Ivan Oseledets | Skolkovo Institute of Science and Technology |
| Houman Owhadi | Caltech |
| Eun-Hee Park | Kangwon National University |
| Eun-Jae Park | Yonsei University |
| Christoph Paulus | Ircad/Inria |
| Anna Persson | Chalmers University of Technology |
| Daniel Peterseim | Universität Bonn |
| Daniel Peterseim | Universität Augsburg |
| Konstantin Pieper | Florida State University |
| Maxim Rakhuba | Skolkovo Institute of Science and Technology |
| Stefan Sauter | Universität Zürich |
| Mira Schedensack | Humboldt-Universtität zu Berlin |
| Robert Scheichl | University of Bath |
| Markus Schmuck | Maxwell Institute for Mathematical Sciences and School for Mathematical and Computer Sciences |
| Marc Alexander Schweitzer | Universität Bonn |
| Linus Seelinger | Universität Heidelberg |
| Pablo Seleson | Oak Ridge National Laboratory |
| Chi-Wang Shu | Brown University |
| Rob Stevenson | University of Amsterdam |
| Christian Stohrer | Karlsruher Institut für Technologie (KIT) |
| Li-yeng Sung | Louisiana State University |
| Milica Taskovic | The University of Texas at Austin |
| Xiaochuan Tian | Columbia University |
| Céline Torres | University of Zurich |
| Jeremy Trageser | The George Washington University |
| Gantumur Tsogtgerel | McGill University |
| Dora Varga | Universität Bonn |
| Chandrasekhar Venkataraman | University of St Andrews |
| Barbara Verfürth | Universität Münster |
| Gopal Yalla | University of Texas at Austin |
| Jiang Yang | Columbia University |
| Yunan Yang | The University of Texas at Austin |
| Lei Zhang | Shanghai Jiao Tong University |
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