SIAM Journal on Numerical Analysis
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Convergence of the ghost fluid method for elliptic equations with interfaces
Mathematics of Computation
Journal of Computational Physics
A numerical method for solving variable coefficient elliptic equation with interfaces
Journal of Computational Physics
Maximum principle and convergence analysis for the meshfree point collocation method
SIAM Journal on Numerical Analysis
Meshfree Particle Methods
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
A sharp meshfree approximation for derivative discontinuities across arbitrary interfaces is proposed. The interface can be arbitrarily located in a domain in which nodes are distributed uniformly or irregularly. The proposed meshfree approximations consist of two parts, singular and regular. The moving least square meshfree approximation is used together with the local wedge function as basis functions. The approximations for discontinuities are applied in a meshfree point collocation method to obtain solutions of the Poisson problem with a layer delta source on the interface and second order elliptic problems with discontinuous coefficients and/or the singular layer sources along the interface. The numerical calculations show that this method has good performance even on irregular node models.