Objective The present project addresses numerical analysis and algorithmic realization of sparse, adaptive tensor product discretizations of partial differential equations (PDEs) in high dimensions with stochastic data. The aim of the project is to develop mathematically founded adaptive algorithms which are based on sparse tensorization of hierarchic Riesz bases or frames. These will be hierarchic multilevel bases in the physical domain, either Finite Element wavelet type bases or hierarchical, multilevel bases. In the parameter domains corresponding either to random inputs or to phase spaces in transport problems, spectral type representations of ``polynomial chaos'' type shall be employed. Mathematical aim is to analyzed for a classes of elliptic and parabolic PDEs on high or possibly infinite dimensional parameter spaces adaptive, deterministic and dimension independent solution methods with convergence rates superior to those afforded by Monte Carlo Methods, in terms of accuracy vs. complexity. Algorithmic work will address design of data structures with minimal overhead for the efficient realization of the sparse tensor approximations. Applications include space-time adaptive solvers for elliptic, parabolic and certain parametric hyperbolic PDEs, nonlinear approximate spectral representations of nonstationary random fields, scale-resolving solvers of elliptic and parabolic problems with multiple scales with complexity independent of the number of scales, and sparse, adaptive numerical solvers for parametric transport problems. The project will be in collaboration with coworkers in France, Germany, UK, The Netherlands. The project involves mentoring postdocs and predocs who will be actively involved in all aspects of the research, as well as a teaching component. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysis Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2009-AdG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH EU contribution € 1 349 564,00 Address Raemistrasse 101 8092 Zuerich Switzerland See on map Region Schweiz/Suisse/Svizzera Zürich Zürich Activity type Higher or Secondary Education Establishments Administrative Contact Christoph Schwab (Prof.) Principal investigator Christoph Buchs-Schwab (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH Switzerland EU contribution € 1 349 564,00 Address Raemistrasse 101 8092 Zuerich See on map Region Schweiz/Suisse/Svizzera Zürich Zürich Activity type Higher or Secondary Education Establishments Administrative Contact Christoph Schwab (Prof.) Principal investigator Christoph Buchs-Schwab (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
