Hodge Decomposition

Hodge Decomposition is a mathematical process that breaks down complex vector fields, like flows or forces on a surface, into three simpler, understandable parts: a gradient part (related to potential or source-like behavior), a curl part (related to swirling or rotational behavior), and a harmonic part (which is both divergence-free and curl-free). This decomposition helps analyze and understand the structure of fields on surfaces, such as in physics or geometry, by separating out the different types of behaviors or patterns present in the original data.