Work

Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation

Year: 2011

Type: book-chapter

Abstract: Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. However, the development of efficient and reliable iterative solution methods for the force-based approximation presents a challenge due to the non-symmetric and indefinite structure of the linearized force-based quasicontinuum approximation, as well as to its unusual stability properties. In this paper, we present rigorous numerical analysis and computational experiments to systematically study the stability and convergence rate for a variety of linear stationary iterative methods.

Source: Warwick Research Archive Portal (University of Warwick)

DOI: 10.48550/arxiv.1104.1774

Authors: Luskin, Mitchell, Ortner, Christoph

Institutions: University of Minnesota, United Church of Christ, University of Oxford, St. Ann's Episcopal Church

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy

Awards: Numerical Analysis of Quasicontinuum Methods, FRG: Modeling and Computation of Objective Structures in Materials Science and Biology, "NEW; PREDICTIVE SIMULATION AND DESIGN OF MATERIALS BY QUASICONTINUUM AND ACCELERATED DYNAMICS METHODS; PI - MITCHELL LUSKIN"