74 citations · 200 across the 12 of their papers we have counts for
13 papers
Trajectory-Based RBF Collocation Method via Closest-Point Embedding for Surface Advection-Diffusion Equations
Xiaobin Li, Leevan Ling, Yizhong Sun
We introduce a Trajectory-Based RBF Collocation (TBRBF) method for solving surface advection-diffusion equations on smooth, compact manifolds. TBRBF decouples advection and diffusi…
Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces
Wen Hu, Zhuojia Fu, Leevan Ling
This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions.…
Realistic pattern formations on surfaces by adding arbitrary roughness
Siqing Li, Leevan Ling, Steven J. Ruuth +1
We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, so…
A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations
Zhengjie Sun, Leevan Ling
We propose a meshless conservative Galerkin method for solving Hamiltonian wave equations. We first discretize the equation in space using radial basis functions in a Galerkin-type…
Exploring Oversampling in RBF Least-Squares Collocation Method of Lines for Surface Diffusion
Meng Chen, Leevan Ling
This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, build…
A stochastic extended Rippa's algorithm for LpOCV
Leevan Ling, Francesco Marchetti
In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm […
A kernel-based least-squares collocation method for surface diffusion
Meng Chen, Ka Chun Cheung, Leevan Ling
There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more co…
Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity
Siqing LI, Leevan Ling, Xin Liu +3
Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the converge…
Kernel-based collocation methods for heat transport on evolving surfaces
Meng Chen, Leevan Ling
We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on…
A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
A. Petras, L. Ling, C. Piret +1
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs…
A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels
Pankaj K Mishra, Gregory E Fasshauer, Mrinal K Sen +1
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 basis fu…
An RBF-FD closest point method for solving PDEs on surfaces
Argyrios Petras, Leevan Ling, Steven J. Ruuth
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J…
--Convergence of least-squares kernel collocation methods
Ka-Chun Cheung, Leevan Ling, Robert Schaback
The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems…