The only relevant quality measure for any numerical approximation scheme should be the accuracy relative to its computational cost. Surprisingly, this point of view seems to have gone largely unnoticed in multiscale computations, but it guarantees an unbiased approach to the construction and evaluation of computational schemes.
In this talk, I will focus on atomistic-to-continuum (quasicontinuum) methods for lattice defects. I will first review how the framework of numerical analysis leads to error estimates (accuracy) in terms of the various approximation parameters such as domain size, atomistic region size, finite element mesh, or interface correction. I will then discuss how these estimates can be recast as error estimates in terms of computational cost. Finally, this can be used to optimise the various approximation parameters.
(Joint work with Helen Li, Mitch Luskin, Alex Shapeev and Brian Van Koten)
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