Project description
Modelling complex physical systems at multiple scales
Microstructures with particles of arbitrary shape can create astonishing physical phenomena. Numerical simulation offers scientists the potential to better understand and control these physical systems. However, the computational capability to simulate their complex interplay of effects at many non-separable or even a continuum of characteristic scales exceeds current computing resources by multiple orders of magnitude. Modelling physical phenomena at multiple scales requires a new generation of computational methods that accounts for randomness and disorder in a hierarchical and adaptive fashion. In seeking such a paradigm, the EU-funded RandomMultiScales project aims to design efficient numerical analysis methods to study such multiscale problems. The research conducted is at the intersection between uncertainty quantification and computational physics.
Objective
Geometrically or statistically heterogeneous microstructures and high physical contrast are the key to astonishing physical phenomena such as invisibility cloaking with metamaterials or the localization of quantum waves in disordered media. Due to the complex experimental observation of such processes, numerical simulation has very high potential for their understanding and control. However, the underlying mathematical models of random partial differential equations are characterized by a complex interplay of effects on many non-separable or even a continuum of characteristic scales. The attempt to resolve them in a direct numerical simulation easily exceeds today's computing resources by multiple orders of magnitude. The simulation of physical phenomena from multiscale models, hence, requires a new generation of computational multiscale methods that accounts for randomness and disorder in a hierarchical and adaptive fashion.
This proposal concerns the design and numerical analysis of such methods. The main goals are connected to fundamental mathematical and algorithmic challenges at the intersection of multiscale modeling and simulation, uncertainty quantification and computational physics:
(A) Numerical stochastic homogenization beyond stationarity and ergodicity,
(B) Uncertainty quantification in truly high-dimensional parameter space,
(C) Computational multiscale scattering in random heterogeneous media,
(D) Numerical prediction of Anderson localization and quantum phase transitions.
These objectives base upon recent breakthroughs of deterministic numerical homogenization beyond periodicity and scale separation and its deep links to seemingly unrelated theories ranging all the way from domain decomposition to information games and their Bayesian interpretation. It is this surprising nexus of classical and probabilistic numerics that clears the way to the envisioned new computational paradigm for multiscale problems at randomness and disorder.
Fields of science
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
- natural sciencescomputer and information sciencescomputational sciencemultiphysics
- natural sciencesmathematicsapplied mathematicsnumerical analysis
- natural sciencesmathematicsapplied mathematicsmathematical model
Programme(s)
Funding Scheme
ERC-COG - Consolidator GrantHost institution
86159 Augsburg
Germany