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Title: Atomistic-to-continuum coupling
Author: Wu, Huan
ISNI:       0000 0004 7227 7084
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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The present thesis is on error analysis of atomistic-to-continuum (A/C) coupling models for crystal defects, which is a class of multi-scale coupling models that combine atomistic interactions around the defect cores and continuum elasticity models at far-fields This thesis consists of two parts. The first part presents a sharp error analysis of an A/C model in 2D with high-order finite element methods, whereas in the past the analysis for employing FEM has been restricted to first-order. The second part discusses a new A/C coupling scheme employing a boundary element method to improve the description of the far-field. In the first part we formulate a \patch test consistent" atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method in the material bulk. We prove a sharp error estimate in the energy-norm, which demonstrates that this scheme is (quasi-)optimal amongst energy-based sharp-interface a/c schemes that employ the Cauchy{Born continuum model. Our analysis also shows that employing a continuum discretization with order greater than two does not yield qualitative improvements to the rate of convergence. In the second part we formulate a new A/C coupling scheme that employs a boundary element method to obtain an improved far- field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect embedded in a homogeneous crystal. The error analysis shows that it is possible to entirely bypass the FEM region while maintaining an optimal convergence rate. The thesis is accompanied by an introduction to atomistic-to-continuum coupling and literature review on various coupling methods and the general framework for error analysis.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics