Electro Magnetica (EM) is categorized as FD-TD type electromagnetic simulator. EM is based on the conventional FD-TD method, whoes lattice is staggared and the time-marching scheme is Leap-Frog scheme. The FD-TD is already confirmed its effectiveness in the electromagnetic domain. So many algorithms and numerical models are established in many research are so you could obtain good models to solve your problems.

図1 直交適合格子の構造

We stated EM is based on the FD-TD method, however, the method discretizing the space is an special method, very different from the conventional Yee lattice. The method is called "Blocked Adaptive Cartesian Grid" method. This method has mainly been developed in the Computational Fluid Dynamics domain since '80 as one of the derivatives from the Adaptive Cartesian Grid (ACG) method[1][2]. This method is categorized as unstructured grid. Basically the unstructured grid is not applicable to the conventional FD-TD method, we overcome the diffculty by adopting the Blocked cell[1] which was originally proposed by Powerll et.al.

ACG method starts with a single root cell which corresponds to the whole simulation area and refines the grid cells by equi-deviding the parent cells as their necessities. Figure 1 shows the data structure and corresponding grid cell distribution in two dimensional case. The case shows quad-tree structure but it will be octet-tree structure in the three dimension.

In Fig.1, the filled circle indicates the leaf node in the tree structure and has the corresponding grid cell. The nodes and the grid cells with number from 1 to 6 are corresponding each other. The grid cell indicates the smallest unit in discretized space, the field values such as electric field are located in the cells in generall.

The resultant grid cells are parallelpiped hexahedrons and are very different from the grid cells in the structured grid. This is the because the method is categorized as the unstructured grid but it is not straight forward to apply to FD-TD scheme.

To solve the difficulty, we adopted the blocked cell instead of a single cell for each node in the tree structure. We re-descritize the blocked cell with Yee grid inside to merge the FD-TD and the AGC method[3].

The left figure shows the actual window view of EM. In the left side part of the window the interface to set parameters for simulation is placed. 3D view window to show the result is placed in the right part of the window and there is logging window under the 3D view window.

EM is very flexible in grid generation competing with the unstructured grid method by adopting the Blocked AGC method, also has very accurate and memory effective by adopting the FD-TD method. This make EM the only one simulator. Please take a look at the examples performed by EM simulator in the showcase. The full-functioned demo program is available for Windows and MacOS X platform you can try to solve your own problem with the software. The questions/suggestions about EM or electromagnetic problems are welcome and please consider putting lines in the Forum.

Screen Shot of EM
Screenshot of EM


  • [1] Powell,  K., Solution of the Euler and Magnetohydrodynamic Equations on Solution Adaptive Cartesian Grids, von Karman Institute for Fluid Dynamics, Lecture Series 1994-05, Rhode-Saint-Genese, Belguim, Mar. 1996.
  • [2] Aftosmis, M.J., Berger, M.J., Melton, J.E., Robust and efficient Cartesian mesh generation for component-based geometry, AIAA Paper 97-1725-CP, Jun., 1995.
  • [3] ABE, H., Blocked Adaptive Cartesian Grid FD-TD Method for Electromagnetic Field with Complex Geometies, Int'l Conf. MST, JST, 2011

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