SPH meshfree code

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SPH meshfree code

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SPH Meshfree Code for Curve Fitting

Smoothed Particle Hydrodynamics (SPH) is a meshfree computational method originally developed for fluid dynamics, but its applications have expanded to various fields, including solid mechanics and curve fitting. This MATLAB-based SPH code provides a meshfree approach to solving curve fitting problems, offering flexibility where traditional mesh-based methods may struggle.

The code leverages SPH's particle-based nature to approximate functions and fit curves without relying on predefined grids. Each particle carries information (e.g., position, weight) and interacts with neighboring particles via smoothing kernels, enabling smooth interpolation of data points. The absence of a mesh makes it robust for irregular domains or scattered data.

Key features of this implementation likely include: Kernel functions to define particle influence regions, crucial for accurate approximations. Neighbor search algorithms to efficiently identify interacting particles. Adaptive smoothing lengths to balance resolution and computational cost.

For curve fitting, SPH can handle noisy or non-uniformly distributed data by adjusting kernel radii or particle densities. This approach is particularly useful in scenarios where analytical functions are unknown, and data-driven approximations are needed.

The MATLAB subroutines provided in the archive likely encapsulate core SPH operations—particle initialization, kernel evaluations, and solution updates—making it accessible for researchers exploring meshfree methods in data approximation.