Finite differences provided the first numerical approach that permitted large-scale
simulations in many applications areas, such as geophysical fluid dynamics. As accuracy …

This book is focused on a powerful numerical methodology for solving PDEs to high
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …

Many applications require that nodes be scattered locally quasi-uniformly within 2-D regions
or on curved surfaces in 3-D space, while obeying some prescribed spatially varying density …

A numerical algorithm based on the local radial basis function collocation method
(LRBFCM) is developed to efficiently compute the derivatives of primary field quantities …

Recent developments have made it possible to overcome grid-based limitations of finite
difference (FD) methods by adopting the kernel-based meshless framework using radial …

Producing reliable acoustic subsurface velocity models still remains the main bottleneck of
the oil and gas industry's traditional imaging sequence. In complex geologic settings, the …

In this paper, we further extend the local radial basis function collocation method (LRBFCM)
for efficient computation of band structures of phononic crystals from 2D to 3D. The proposed …

In this paper, an efficient local radial basis function collocation method (LRBFCM) is
presented for computing the band structures of the two‐dimensional (2D) solid/fluid and …

Finite-difference (FD) methods approximate derivatives through a weighted summation of
function values from neighboring nodes. Traditionally, these neighboring nodes are …

We developed an innovative finite-difference method for elastic wave propagation in the
frequency-domain. The method is a class of mesh-free method which can discretize …