C - Mathematical theory and computational techniques for multiscale materials modeling

Symposium organizers

William Curtin (EPFL, Switzerland)
Carlos Javier Garcia-Cervera (University of California Santa Barbara, USA)
James Kermode (University of Warwick, UK)
Frédéric Legoll (Ecole des Ponts ParisTech, France) - point of contact
Xiantao Li (Pennsylvania State University, USA)
Alexei Lozinski (Université de Franche-Comté, France)
Mitchell Luskin (University of Minnesota, USA)
Christoph Ortner (University of Warwick, UK)

Symposium description

The mechanics of solids furnishes a wealth of mathematical problems that require a variety of techniques from a number of disciplines. The aim of this symposium is to address some of them, at different space and time scales.

At the atomistic scale, many emerging problems present new challenges for mathematical modeling and analysis, as well as new computational challenges. For instance, the recent increases in the capabilities of nanoscale experimental measurement techniques have triggered the need for mathematically rigorous multiscale models that can make quantitative predictions. We will focus on novel methodological approaches for complex material behavior modeling, and on analytical and computational tools for the model reduction of atomistic-level descriptions. Particularly of interest will be systems where (i) strong bidirectional coupling between length scales leads to a requirement for non-uniform precision and/or (ii) reaching experimental time scales requires advanced rare event/sampling techniques.

At the continuum scale, heterogeneous materials also present computational challenges. The properties of the materials are varying on a small characteristic length scale (think e.g. of composite materials, of polycrystals, …). When the geometry of the microstructure satisfies some assumptions (such as periodicity, or stationarity), homogenization theory can be used. Numerical homogenization techniques have been proposed to address the case when such geometry assumptions cannot be made. Several families of approaches have been introduced. Some of these multiscale approaches have close connections to domain decomposition (DD) methods. Conversely, DD methods targeted to multiscale problems have also been recently proposed. We will discuss the recent variants of the methods, to understand how they compare one to another, and identify open problems.

The topics to be covered include:

  • Efficient methods for DFT calculations
  • The automated construction of interatomic potentials
  • State-of-the-art concurrent modeling approaches such as QM/MM, quasi-continuum, lattice Green’s functions and electronic embedding
  • Multiscale diffusion methods, diffusive molecular dynamics (DMD), coarse-grained molecular dynamics
  • Heat conduction in low-dimensional nano-scale systems
  • State-of-the-art numerical homogenization techniques, including MsFEM, LOD and HMM
  • The relation between numerical homogenization techniques and domain-decomposition techniques

The symposium will also highlights methodological similarities between questions posed at different scales: the relation between domain-decomposition techniques and concurrent atomistic-to-continuum approaches, the design of appropriate boundary conditions when the fine-scale model is only solved locally,...

Invited speakers 

  • Assyr Abdulle (EPFL, Switzerland)
    Model order reduction techniques for numerical homogenization

  • Eric Cancès (Ecole des Ponts ParisTech, France)
    Error estimators for first-principle molecular simulation

  • Ludovic Chamoin (ENS Cachan, France)
    Multiscale computations with MsFEM: a posteriori error estimation, adaptive strategy, and coupling with PGD model reduction

  • Eric Chung (Chinese University of Hong Kong)
    Adaptive GMsFEM and its applications

  • Gabor Csanyi (University of Cambridge, UK)
    Coarse graining interatomic potentials with machine learning

  • Maria Emelianenko (George Mason University, USA)
    Kinetic modeling of materials coarsening: From individual grains to network statistics

  • Guillaume Enchéry (IFPEN, France)
    A parallel implementation of the mixed multiscale finite element method for the simulation of two-phase flows in porous media

  • Vikram Gavini (University of Michigan, USA)
    Large-scale real-space electronic structure calculations

  • Katie Newhall (UNC Chapel Hill, USA)
    Reversal-time scaling in low-damping ferromagnetic models

  • Art Voter (LANL, USA)
    Local hyperdynamics

Key dates

  • Abstract submission deadline (oral):
    February 15th, 2016
  • Abstract acceptance notification:
    April 1st, 2016
  • Abstract submission deadline (poster):
    May 31st, 2016
  • Application deadline for student and post-doc grants:
    July, 18th 2016
  • Early registration deadline:
    September 5th, 2016
  • Image competition deadline
    September 15th, 2016
  • Registration deadline:
    October 7th, 2016