This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific
focus on its theoretical foundations and practical implementations, including various PD …

Numerical solution of hyperbolic differential equations, such as the advection equation,
poses challenges. Classically, this issue has been addressed by using a scheme known as …

This work contributes to nonlocal vector calculus as an indispensable mathematical tool for
the study of nonlocal models that arises in a variety of applications. We define the nonlocal …

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has gained increasing
interest in the pharmaceutical industry. The transport, distribution and absorption of mAbs in …

We present a study on asymptotically compatible Galerkin discretizations for a class of
parametrized nonlinear variational problems. The abstract analytical framework is based on …

Many nonlocal models have adopted Euclidean balls as the nonlocal interaction
neighborhoods. When solving them numerically, it is sometimes convenient to adopt …

Nonlocal models have demonstrated their indispensability in numerical simulations across a
spectrum of critical domains, ranging from analyzing crack and fracture behavior in structural …

Simulating suffusion involves computing both the seepage flow of pore water in soil and the
transport of fine particles with pore water flow. Since the conventional finite element method …

Recent decades have provided a host of examples and applications motivating the study of
nonlocal differential operators. We discuss a class of such operators acting on bounded …

The railgun's armature and rail are in high-speed sliding electrical contact, and there is a
velocity skin effect regarding electromagnetic field distribution. Under this effect, current …