Research| Multiscale Modeling

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The objective of multiscale modeling is to predict the response of complex systems at all relevant spatial and temporal scales at a cost that is sub-linear with respect to the full micro-scale solver. We are currently developing a class of multiscale methods known as global-local or computational homogenization techniques with applications to various areas:

> Computational Mechanics of Molecular Crystals

> Computational Radiation Material Science

> Multiscale modeling of composites

Recent projects

The Self-consistent Multiscale Method (SMM) is a novel modeling paradigm that ensures self-consistency of the macro- and micro-scale coupling within the framework of matrix-free global-local multiscale model. The matrix-free approach naturally lends to very efficient parallelization, as the macroscopic computation is fully decoupled from one element to the other.

The explicit global-local multiscale model usages the global-local approach at the spatial scale while taking advantage of the explicit computation at the temporal scale. The explicit time integration algorithms lend themselves to efficient parallelization resulting an efficient computation of very large and highly nonlinear problems. Hence, instead of perceiving multiscale modeling and parallelization as two separate processes, we are interested in developing an integrated parallel multiscale method that is designed to take advantage of the specific architecture of these explicit time integration algorithms on massively parallel machines.

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Sponsors

> Office of Naval Research (ONR)

> Defense Threat Reduction Agency (DTRA)

> Army Research Office (ARO)

Investigators

Suvranu De, DSc.

Rahul, MS

Amir Zamiri, PhD

Ranajay Ghosh, PhD

Shree Krishna, PhD

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Journal articles

Rahul, De S. A preconditioned Newton-Krylov (GMRES) solver for the Jacobian-free computation of global-local multiscale methods In preparation.

Rahul, De S. An efficient coarse-grained parallel algorithm for global-local multiscale computations on massively parallel systems, Accepted.

Macri M, De S. An octree partition of unity method (OCTPUM) with enrichments for multiscale modeling of heterogeneous media, Computers and Structures 2008; 86: 780-795.

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Conference articles

Rahul, De S. Efficient implementation of hierarchical multiscale methods on massively parallel systems, 10th US National Congress on Computational mechanics (USNCCM X), 2009

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