Computational efficiency of meshfree methods with local-coordinates algorithm

TLDR: In this paper, a mesh-free method with uniform nodal distribution and local coordinates shape function was proposed to reduce the computational time dependency on the number of nodes by 36% and reduce the complexity of analysis of problems requiring very fine nodal distributions.

Abstract: In this study, meshfree methods with uniform nodal distribution and local-coordinates shape functions are investigated. The proposed meshfree method can be used with various shape functions and is tested on a test patch with a Laplace governing equation and both essential and Neumann boundary conditions. It is shown to reduce the computational time dependency on the number of nodes by 36%. This reduction of dependency is significant as it reduces the computational time by several orders for analysis of problems requiring very fine nodal distribution. The meshfree method with uniform nodal distribution and local coordinates shape function reduces and converges to the perfectly uniform nodal distribution with finer nodal distributions. The technique is illustrated on a rectangular Kirchhoff-Love plate to show the practical use of the technique for allowing higher order shape function and finer nodal distribution to be used with multiple overlapping boundary conditions as well as on an electromagnetic problem to explain the uses of this technique on solving multiple similar problem cases with slight changes in geometry of boundary nodes. Overall, the present methodology provides a simple way to increase the computational efficiency of meshfree methods in range of an order while retaining many of its benefits.