TY - JOUR
T1 - Correlation Between Mesh Geometry and Stiffness Matrix Conditioning for Nonlocal Diffusion Models
AU - Jibum Kim
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 312
EP - 328
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.270114.280914a
UR - https://global-sci.org/intro/article_detail/eajam/10840.html
KW - Peridynamics, condition number, finite element method.
AB - <p style="text-align: justify;">Nonlocal diffusion models involve integral equations that account for nonlocal
interactions and do not explicitly employ differential operators in the space variables.
Due to the nonlocality, they might look different from classical partial differential equation
(PDE) models, but their local limit reduces to partial differential equations. The
effect of mesh element anisotropy, mesh refinement and kernel functions on the conditioning
of the stiffness matrix for a nonlocal diffusion model on 2D geometric domains is
considered, and the results compared with those obtained from typical local PDE models.
Numerical experiments show that the condition number is bounded by $c\delta^{−2}$ (where $c$ is a constant) for an integrable kernel function, and is not affected by the choice of the
basis function. In contrast to local PDE models, mesh anisotropy and refinement affect
the condition number very little.</p>