  Existing nonlocal diffusion models are predominantly classified into two
categories: bond-based models, which involve a single-fold integral and usually
simulate isotropic diffusion, and state-based models, which contain a
double-fold integral and can additionally prototype anisotropic diffusion.
While bond-based models exhibit computational efficiency, they are somewhat
limited in their modeling capabilities. In this paper, we develop a novel
bond-based nonlocal diffusion model with matrix-valued coefficients in
non-divergence form. Our approach incorporates the coefficients into a
covariance matrix and employs the multivariate Gaussian function with
truncation to define the kernel function, and subsequently model the nonlocal
diffusion process through the bond-based formulation. We successfully establish
the well-posedness of the proposed model along with deriving some of its
properties on maximum principle and mass conservation. Furthermore, an
efficient linear collocation scheme is designed for numerical solution of our
model. Comprehensive experiments in two and three dimensions are conducted to
showcase application of the proposed nonlocal model to both isotropic and
anisotropic diffusion problems and to demonstrate numerical accuracy and
effective asymptotic compatibility of the proposed collocation scheme.
