RKPM2D: An Open-Source Implementation of Nodally Integrated Reproducing Kernel Particle Method for Solving Partial Differential Equations

The implemented RKPM2D program is a two-dimensional RKPM-based code developed for the static analysis of two-dimensional linear elasticity problems. The code is developed based on Reproducing Kernel Particle Method (RKPM) with the following features. (1) User-friendly MATLAB program for straightforward meshfree analysis and easy implementation and modification for new functionalities. (2) Subroutine for discretization of two-dimensional domains of arbitrary geometry and nodal representative domain creation through Voronoi diagram partitioning. (3) A complete meshfree Galerkin equation solver with two types of domain integration: stabilized nodal integration, and conventional background Gauss integration. (4) Built-in visualization tools for post-processing of the numerical results. The RKPM2D code is implemented under a MATLAB environment with pre-processing, solver, and post-processing functions fully integrated for supporting reproducible research and serving as an efficient test platform for further development of meshfree methods. Both the MATLAB built-in mesh generator and standard neutral files exported by other mesh generators can be used to obtain the point-based domain discretization for meshfree analysis. A meshfree Galerkin equation solver for 2-dimensional elastostatics, and visualization tools for post-processing are provided. Nitsche’s method is adopted for imposition of essential boundary conditions. Spatial domain integration techniques implemented in the code include the Gauss Integration (GI), the Direct Nodal Integration (DNI), and the Stabilized Conforming Nodal Integration (SCNI). For nodal integration, two different types of stabilization methods are implemented in RKPM2D, including the Modified Stabilized Conforming Nodal Integration (MSCNI) and the Naturally Stabilized Nodal Integration (NSNI).