# Higher Order Basis Functions (HOBF)

Higher order basis functions (HOBF) use higher order polynomial basis functions to model the currents on any particular mesh element.

- Method of moments (MoM) (including hybridisation with UTD and RL-GO)
- Multilevel fast multipole method (MLFMM)

Using HOBF allows the geometry to be meshed with larger triangles while obtaining the same solution accuracy. These larger and coarser mesh elements reduce the total number of mesh elements. In most cases the total unknowns are reduced. This leads to a reduction in solution time and memory.

Feko uses hierarchical basis functions to increase the basis function order of any triangle as required. Small geometric details of a model will be meshed with electrically small mesh elements, while larger details are meshed with coarser mesh elements. When the Solver automatically performs order selection for the model, higher order basis functions are applied to electrically large mesh elements, while lower order basis functions are applied to electrically smaller mesh elements. With this adaptive scheme, the Solver automatically ensures high fidelity MoM solutions, using as little memory as possible and fastest possible solution times.