Galerkin-based meshless methods for photon transport in the biological tissue

Meshless Galerkin methods using radial basis functions

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

Simple Test Functions in Meshless Local Petrov - Galerkin Methods

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tes...

Kernel–Based Meshless Methods

2 Kernels 1 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Positive Definiteness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 General Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Inner Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Dualit...

A meshless discrete Galerkin method for solving the universe evolution differential equations based on the moving least squares approximation

In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...

Kernel Based Meshless Methods