AMR-FDTD: a dynamically adaptive mesh refinement scheme for the finite-difference time-domain technique

A fast computational electromagnetic (EM) simulator is invaluable, especially for trouble-shooting high-speed printed circuit boards (PCBs) and packages. An AMR-FDTD (adaptive mesh refinement finite-difference time-domain) technique is proposed for the simulation of large complex structures. The root mesh is refined hierarchically and forms a tree structure. The ratio between the cell sizes of adjacent levels is fixed. The mesh tree is re-created after fixed time steps. The ratio between the time steps of adjacent levels is the same. At each time step of the root mesh, the fields of the upper level are updated first, and then lower levels are updated. In each level of the mesh, PEC, ABC and source conditions are enforced. Except for grid points on perfect electrical conductors (PEC) and absorbing boundary conditions (ABC), the boundary value of a child mesh is interpolated from its upper level mesh. The lower level mesh is updated multiple times until it catches up its upper level mesh. After the entire tree is updated, from bottom up, each lower level mesh updates the fields of its upper level mesh.