2011/04/10 by Mitchell Luskin, Christoph Ortner, Luskin, Mitchell +1
Engineering · Materials Science · Physics and Astronomy · #FOS: Mathematics #Force Microscopy Techniques and Applications #Mechanical and Optical Resonators #Nonlocal and gradient elasticity in micro/nano structures #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1104.1774
openalex publication_date 2011/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Force-based multiphysics coupling methods have become popular since they\nprovide a simple and efficient coupling mechanism, avoiding the difficulties in\nformulating and implementing a consistent coupling energy. They are also the\nonly known pointwise consistent methods for coupling a general atomistic model\nto a finite element continuum model. However, the development of efficient and\nreliable iterative solution methods for the force-based approximation presents\na challenge due to the non-symmetric and indefinite structure of the linearized\nforce-based quasicontinuum approximation, as well as to its unusual stability\nproperties. In this paper, we present rigorous numerical analysis and\ncomputational experiments to systematically study the stability and convergence\nrate for a variety of linear stationary iterative methods.\n