This paper presents a summary of various localized collocation schemes and their
engineering applications. The basic concepts of localized collocation methods (LCMs) are …

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 …

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 superconvergent meshfree collocation method with smoothed nodal gradients is
presented. In this method, the first order smoothed gradients of meshfree shape function are …

The reproducing kernel (RK) approximation based direct collocation method (DCM) requires
the complex and time-consuming derivatives calculation of the approximation function, and …

A general arbitrary order recursive gradient formulation is presented for meshfree
approximation. According to this method, an n th order recursive meshfree gradient is …

Increased attention has been paid on numerical modeling of interface problems as its wide
applications in various aspects of science. Motivated by enhancing the application of the …

A stable and highly accurate meshfree scheme based on strong form collocation associated
with radial basis functions and explicit time integration is proposed to solve ill-posed inverse …