Generic implementation of meshless local strong form method

Abstract

The simplicity, generality and efficiency are probably the main attractiveness of the meshless methods that have been under intense developed in recent years. This paper considers one of those methods, namely a relatively simple Meshless Local Strong form Method (MLSM) [1] that generalises several other mesh based and meshless strong form methods, e.g. Finite Difference Method, Local Radial Basis Functions Method, Finite Point Method, Diffuse Approximate Method, etc. MLSM is based on a Weighted Least Squares (WLS) approximants constructed over small local neighbourhood of the considered node. One of the most attractive features of MLSM is its dependency solely on the nodal positions, which enables a rather general formulation that can be directly implemented in a programming language with support for generic abstractions, such as C++11. In another words, the MLSM implementation is not dependent on dimensionality of the domain, on the approximation type, basis pool size, basis types, support size, and nodal positions. In this paper the generic implementation of MLSM is demonstrated by solving various problems in 1D, 2D and 3D on different domain shapes. It is shown that this implementation has little to no execution overhead over e.g. classical Finite Difference Method implementation despite its significant abstraction.