STAHDPDE
Sparse Tensor Approximations of High-Dimensional and stochastic Partial Differential Equations
| Coordinatore |
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Non specificata |
| Totale costo | 1˙349˙564 € |
| EC contributo | 1˙349˙564 € |
| Programma | 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) |
| Code Call | ERC- |
| Anno di inizio | 2010 |
| Periodo (anno-mese-giorno) | 2010-01-01 - 2014-12-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZURICH
Organization address
address: Raemistrasse 101 contact info |
CH (ZUERICH) | hostInstitution | 1˙349˙564.00 |
| 2 |
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZURICH
Organization address
address: Raemistrasse 101 contact info |
CH (ZUERICH) | hostInstitution | 1˙349˙564.00 |
Mappa
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Obiettivo del progetto (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.'