Application of the RBF meshless method to the solution of the radiative transport equation

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

“…Recently, a new class of methods, meshless methods [38], has been applied to solve radiative transfer in participating media [31,[39][40][41][42]. The salient feature of meshless methods is that they provide the ways of building approximation space just based on freely scattered nodes without relying on any mesh structure (e.g.…”

Solving PDEs with radial basis functions

“…Since this approach is still in rapid development, the present discussion will not attempt to be comprehensive but only highlight how it has already proved to be highly competitive against previous alternatives. Active application areas not discussed here include elasticity (Kee, Liu and Lu 2008, Tolstykh and Shirobokov 2003), flame propagation (Bayona and Kindelan 2013, Kindelan, Bernal, Gonzalez-Rodriguez and Moscoso 2010), and mechanics (Chinchapatnam, Djidjeli, Nair and Tan 2009, Rodrigues, Roque and Ferreira 2013).…”

Local multiquadric RBF meshless scheme for radiative heat transfer in strongly inhomogeneous media

“…However, these methods have some critical drawbacks, such as, being difficult to be implemented to complex geometries, or often requiring a lot of computation time to achieve high precision even for simple problems. Another kind of methods is based on solving set of discretized partial differential equations of the RTE, including discrete ordinates methods (DOM) [12,13], finite volume method (FVM) [14], finite element method (FEM) [15], spectral element method [16] and meshless or meshfree methods [3,4,[17][18][19][20][21], which have obvious advantages, such as high efficiency and excellent flexibility to deal with multidimensional complex geometries. In recent years, considerable effort has been dedicated to develop these partial differential equation discretization based methods.…”