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

To improve the performance of the low-order linear triangular element for solving transient
wave propagation problems, this paper presents a novel enriched finite element method …

In the earlier paper, it is known that the solution accuracy usually can not be monotonically
increased as the temporal discretization interval decreases when the standard finite element …

In this paper, a novel hybrid collocation scheme based on the generalized finite difference
method (GFDM) and the Burton–Miller singular boundary method (BMSBM) is developed to …

An enriched finite element approach with appropriate enrichment function is proposed for
the transient analyses of wave propagations in nonhomogeneous media. In present method …

This short communication makes the first attempt to apply the generalized finite difference
method (GFDM), a newly-developed meshless collocation method, for the numerical …

This paper presents a novel localized collocation Trefftz method (LCTM) for heat conduction
analysis in two kinds of heterogeneous materials (functionally graded materials and multi …

In this paper, a high-accuracy numerical scheme is developed for long-time dynamic
simulations of 2D and 3D wave propagation phenomena. In the derivation of the present …

This paper presents the localized collocation solver based on fundamental solutions to 3D
elastic wave propagation analysis. In the proposed collocation solver, the approximated …

The traditional finite element method (FEM) could only provide acceptable numerical
solutions for the Helmholtz equation in the relatively small wave number range due to …