These three methods were subsequently applied to solve electrical propagation in a cardiac tissue slab and a biventricular geometry. The accuracy of RPIMC was evaluated in heat conduction benchmark problems and compared against the Meshless Local Petrov-Galerkin Mixed Collocation (MLPG-MC) method and the Finite Element Method (FEM).
The field function and its gradient are both interpolated (mixed collocation approach) leading to reduced C-continuity requirement compared to strong-form collocation schemes. RPIMC is an efficient purely meshfree method where the solution of the field variable is obtained through collocation. The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. This toolkit aims to provide a basis for the design and implementation of meshfree packages that serves to support the integration of MMs in the engineer's artillery to solve challenging problems. MFREE is designed to be used by both engineering researchers and students in courses on computational mechanics and other topics where MMs can be of interest.
MFREE implements the Moving Least Squares (MLS), the Radial Point Interpolation (RPI) and the Moving Kriging Interpolation (MKI) meshfree approximation schemes, which are widely used in MMs such as the Element-free Galerkin and Meshless Local Petrov Galerkin methods. We chose MATLAB because its user-friendly syntax facilitates understanding of the implementation procedure, which makes it popular in the engineering community. Here we present MFREE, a MATLAB toolkit providing an implementation of several meshfree approximation schemes for 1D, 2D and 3D problems. While there is a vast literature in MMs, commercial or open-source packages based on MMs are still limited and implementing them from scratch may be challenging. However, MMs have not yet reached the maturity of FEM and they are a topic of active research. Meshfree Methods (MMs) are considered an attractive alternative to mesh-based methods such as the Finite Element Method (FEM) due to their efficiency in solving complex problems (e.g.
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