# 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.

Using HOBF allows the geometry to be meshed with larger triangles while obtaining the same solution accuracy. These larger and coarser mesh elements imply that fewer mesh elements are used to discretise a model. The fewer mesh elements imply that fewer unknowns have to be solved during the computation process and that problems can be solved with less memory. In very large models, the solution time will also be reduced.

Feko uses hierarchical basis functions to increase the order of any triangle as necessary. Small geometric details of a model will still 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.

^{1}uniform theory of diffraction

^{2}ray launching geometrical optics