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.