Numerical Analysis Seminar

Seminar information archive ~04/01Next seminarFuture seminars 04/02~

Date, time & place Tuesday 16:30 - 18:00 056Room #056 (Graduate School of Math. Sci. Bldg.)


16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Mitchell Luskin (University of Minnesota)
Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)
[ Abstract ]
The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.
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