Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures

An efficient localized Trefftz-based collocation scheme for heat conduction analysis in two kinds of heterogeneous materials under temperature loading

A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

A porous wavemaker theory

This paper adopts an efficient localized meshless technique for computing the solution of the nonlinear sinh-Gordon equation (NShGE). The NShGE is one useful description for many natural processes such as solid state physics, surface theory, fluid dynamics, nonlinear optics and dislocation in materials. In the proposed method, at the first step, a second-order accurate formulation is implemented to obtain the temporal discretization. At the second step, a localized collocation meshless technique based on the radial basis function partition of unity is proposed to derive the spatial discretization. A major drawback associated with global collocation techniques is the computational cost due to resulting dense algebraic system. The localized technique tackles the ill-conditioning inherent in global collocation techniques and reduces the associated computational cost. It is shown that the proposed method is stable and second-order convergent with respect to the time variable. Numerical results and comparisons illustrate the high accuracy of the proposed method.

An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory

Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures

In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed.

A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals

This paper presents a recently developed meshless collocation method, the generalized finite difference method (GFDM), to calculate the acoustic bandgaps of 2D liquid phononic crystals with square and triangular lattices. The moving least squares theory and Taylor series expansion are used to construct the GFDM difference formulation for the generalized eigenvalue equations arising from acoustic bandgap analysis. In comparison with the finite element method (COMSOL software), the proposed GFDM can provide similar accurate results with less computational cost for calculating the band structures of the simple/complicated shape scatters in the square/triangular lattice.

Ai-Lun Li

Papers

Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures

A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals

Acoustic Bandgap Calculation of Liquid Phononic Crystals via the Meshless Generalized Finite Difference Method