Yee´s macrocells in three dimensions

A concept of Yee´s macrocells in three dimensions is introduced. The macrocell is a reduced order model of Maxwell´s grid equation written for densely subgridded volume slightly larger than a regular Yee´s cell. Problems related to cubic growth of the number of variables and orthogonality loss during the model order reduction process are addressed. It is shown that 3D Yee´s macrocells with high refinement factors can be constructed in seconds. Numerical tests show that macrocells can significantly improve the accuracy at a cost much lower than for subgridding or graded meshing.