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Optimization–Based Coupling of Nonlocal and Local Diffusion Models

Published online by Cambridge University Press:  18 February 2015

Marta D’Elia  and
Pavel B. Bochev
Marta D’Elia
Affiliation:
Sandia National Laboratories, Computer Science Research Institute, P.O. Box 5800, Albuquerque, NM 87185-1320
Pavel B. Bochev
Affiliation:
Sandia National Laboratories, Computer Science Research Institute, P.O. Box 5800, Albuquerque, NM 87185-1320
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Abstract

In this work we introduce an optimization–based method for the coupling of nonlocal and local diffusion problems. Our approach is formulated as a control problem where the states are the solutions of the nonlocal and local equations, the controls are the nonlocal volume constraint and the local boundary condition, and the objective of the optimization is a matching functional for the state variables in the intersection of the nonlocal and local domains. For finite element discretizations we present numerical results in a one–dimensional setting; though preliminary, our tests show the consistency and efficacy of the method, and provide the basis for realistic simulations.

Keywords

diffusionmicrostructuresimulation

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Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1753: Symposium NN – Mathematical and Computational Aspects of Materials Science , 2015 , mrsf14-1753-nn02-07
Copyright
Copyright © Materials Research Society 2015 

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References

REFERENCES

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