Meshless local Petrov‐Galerkin (MLPG) methods in quantum mechanics

Williams L. Nicomedes, Renato C. Mesquita, Fernando J.S. Moreira, Oszkár Bíró
2011 Compel  
In this work, we apply a meshless method to some problems drawn from the context of quantum mechanics. We investigate eigenvalue problems -the time-independent Schrödinger's equation -and boundary value problems as well, these last illustrated by the Nonlinear Schrödinger equation. Meshless methods require absolutely no meshes, unlike the Finite Element Method (FEM), which turns out to be a great advantage when dealing with three-dimensional problems. In a particular class of meshless methods,
more » ... meshless methods, the MLPG, the shape and test functions belong to different function spaces; the former are constructed via special numerical schemes, whereas there are a number of available options for the latter. The examples have been worked out through MLPG4, also known as Local Boundary Integral Equation Method (LBIE). The accuracy of this method is checked out with results coming from two and three-dimensional analytical problems.
doi:10.1108/03321641111168084 fatcat:yngrbqf3brb5tdiiwyuwtcw4ge