Meshfree Methods
Meshfree methods are a class of numerical techniques used in computational physics and engineering to solve partial differential equations without relying on a predefined mesh or grid. They use scattered nodes or particles to discretize the problem domain, making them particularly useful for problems with complex geometries, large deformations, or moving boundaries. These methods include approaches like smoothed particle hydrodynamics (SPH), the element-free Galerkin (EFG) method, and radial basis function (RBF) methods.
Developers should learn meshfree methods when working on simulations involving fluid dynamics, solid mechanics, or multiphysics problems where traditional mesh-based methods like finite element analysis (FEA) struggle, such as in crack propagation, free surface flows, or biological tissue modeling. They are essential in fields like astrophysics, automotive crash testing, and biomedical engineering, where adaptability and handling of discontinuities are critical.