Parallel FDTD

The use of numerical methods for the solution of large electromagnetic problems is nowadays a common practice. Among the several available techniques, the Finite Difference Time Domain (FDTD) is one of the most frequently adopted algorithms, thanks to its versatility and its ability to deal with complex structures.

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Fig. 1: Example of Variable Mesh.

Unfortunately, the method requires a huge computational effort, so that the study of large simulation domains and the investigation of many practical electromagnetic aspects cannot be afforded by using traditional computers. Also, the needs of high accuracy when the simulation domain is modeled, implies small mesh size, with a non-negligible impact on the memory requirement if a uniform mesh scheme is adopted. The implementation of a variable mesh FDTD (VM-FDTD) algorithm allows a natural and efficient parallel porting, guaranteeing the possibility of managing large memory requirements. In the VM technique, in fact, the discretization is performed in a way so that each grid cell has only one adjacent grid cell for each one of its six faces. Furthermore, along each direction the space step can be arbitrarily varied, within the limits imposed by the stability criterion, allowing very smooth transitions between a fine and a coarse mesh region. In front of the previous advantages, a price in term of memory needs has to be paid: in order to guarantee such properties, in fact, the fine-mesh regions cannot be strictly extended up to the limit of the simulation domain (see Fig 1).
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Fig. 2: Domain border sharing among different processors
The EM fields are updated at each time-step. When the computation updates a field component on the border of the sub-domain, some values belonging to the border of the adjacent sub-domain are required: in order to avoid communications during the computations, every sub-domain can be over-dimensioned and surrounded by the border cells of the other domain (fig.2). This guarantees high speed-ups    and allows the solution of large EM-problems using different space-step-sizes.
 ParallelFDTD3_ENGFig. 3: Human-antenna interaction problem using a Parallel-VM-FDTD Algorithm.  The Fig. 3 only reports the results for one of the many affordable problems by using such a method: the human-antenna interaction problem has been studied using a really fine mesh for the characterization of both source and human-body, and a coarser mesh for the vacuum region; also, smooth transitions from the fine to the coarse regions have been implemented