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Sparse Tensor Approximations of High-Dimensional and stochastic Partial Differential Equations

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.

Field of science

  • /natural sciences/physical sciences/thermodynamics
  • /natural sciences/mathematics/applied mathematics/numerical analysis
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /social sciences/social and economic geography/transport
  • /social sciences/educational sciences/pedagogy/teaching

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
Address
Raemistrasse 101
8092 Zuerich
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 349 564
Principal investigator
Christoph Buchs-Schwab (Prof.)
Administrative Contact
Christoph Schwab (Prof.)

Beneficiaries (1)

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Switzerland
EU contribution
€ 1 349 564
Address
Raemistrasse 101
8092 Zuerich
Activity type
Higher or Secondary Education Establishments
Principal investigator
Christoph Buchs-Schwab (Prof.)
Administrative Contact
Christoph Schwab (Prof.)