Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
arXiv:1104.1774
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.
33 pages, 4 figures
References in corpus (9)
- Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
- Accuracy of Quasicontinuum Approximations Near Instabilities
- Iterative Methods for the Force-based Quasicontinuum Approximation
- Sharp Stability Estimates for the Force-based Quasicontinuum Method
- An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model
- A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
- The role of the patch test in 2D atomistic-to-continuum coupling methods
- The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain
- Analysis of Energy-Based Blended Quasicontinuum Approximations