In the past two decades, meshfree methods have emerged into a new class of computational
methods with considerable success. In addition, a significant amount of progress has been …

Physics-informed neural network architectures have emerged as a powerful tool for
developing flexible PDE solvers that easily assimilate data. When applied to problems in …

We compare isogeometric collocation with isogeometric Galerkin and standard C 0 finite
element methods with respect to the cost of forming the matrix and residual vector, the cost …

Since most approximation functions in meshfree methods are rational functions which do not
possess the Kronecker delta property, how to achieve exact integration and accurately …

Meshfree direct collocation method (DCM) based on strong form suffers low accuracy and
instability compared with Galerkin-based meshfree methods. Meshfree weighted least …

A theoretical framework for the accuracy analysis of meshfree collocation methods is
presented with a particular focus on the effects of boundary conditions. In the proposed …

The back propagation (BP) is one of the most widely used algorithms in the feedforward
neural network (FNN), but selecting the non-optimal weights and thresholds may induce the …

This paper is the first investigation establishing the link between the meshfree state-based
peridynamics method and other meshfree methods, in particular with the moving least …

Isogeometric collocation methods have been proposed recently and their accuracy and
efficiency demonstrated for elastostatics and explicit dynamics. This paper addresses two …

The static and dynamic problems of thin functionally graded shells (FGSs) with in-plane
material inhomogeneity are investigated in this work. Governing equations are derived …