Meshless Methods
Meshless 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 points to approximate solutions, making them particularly useful for problems with complex geometries, large deformations, or moving boundaries. These methods include approaches like smoothed particle hydrodynamics (SPH), element-free Galerkin methods, and radial basis function methods.
Developers should learn meshless methods when working on simulations involving fluid dynamics, solid mechanics, or heat transfer in scenarios where traditional mesh-based methods (like finite element analysis) are impractical due to mesh distortion or complex domain shapes. They are especially valuable in fields like astrophysics, biomechanics, and material science for modeling phenomena such as explosions, fracture propagation, or biological tissue behavior.