Electro Magnetica Numerica (EM) is a simulator using a Finite-Difference Time-Domain method in the broad sense. To be precise, discretization method of Maxwell equations is Finite Integral Technique (FIT) which is proposed by Thomas Weiland Professor (Technische Universität Darmstadt). The difference between EM and the other FDTD simulator is that EM is using the unstructured grid system. In this report, we will introduce the grid system of its own.
Needless to say, Yee grid is the grid system of FD-TD method. From its simple structure, the structured grids is a convenient grid easy to implement. However, because when the size of the phenomena to be captured among the discretized grids is significantly different in location, it is necessary to use fine grid in whole domain to match the smallest phenomena, large waste will occur . To solve this problem, unstructured grid was introduced and the grid is often used in finite element method (FEM).
The unstructured grid is very flexible to adapt to the complex shapes using tetrahedron element cells. While the orthogonal structure of hexagonal lattice of structured grids is not so flexible compared to the unstructured grid.
On the other hand, it can be said FEM is a drawback compared to FDM, the amount of calculation per grid (cell - element) is larger than that of FDM, but there is a reduction of the cell - element itself by adaptive grid. So FEM is to be in the practical level as a whole.
In the field of numerical electromagnetics, originally, FEM of form that was used with slight modification simulator of structural analysis was the mainstream , but in recent years , FD-TD method is becoming the mainstream with the improvement of computing power. Among them, as a method for adaptive grid basis , Subgrid method has been proposed. This is the technique that define the patch area in part requiring high resolution and overlay fine grid there . A number of techniques have been proposed, but many algorithms have been plagued by numerical instability.
Well, in recent years, a method called the Adaptive Cartesian Grid method has begun to attract attention in the field of computational fluid dynamics . This is how to adapt to where high resolution is required , the same as orthogonal hexagonal lattice structure. It is classified as an unstructured grid as the classification of the data structure.
The technique is simple. We suppose one cell in the computational domain first. Let's call the root cell. It's going to split in half to suit your needs to this cell in order. For example, when it was a two-dimensional problem, one cell will be split into equal child four cells. It becomes the child eight cells when it was three -dimensional .
In general, the data structure is a tree structure. We use the octree for three-dimensional and use quadtree for two-dimensional . Of course, there can be used a data connection as a relationship between cells, which is used in unstructured grid system general.
Conceived by researchers in the United States, such an algorithm has been developed. From the fact that the fluid simulator Cart3D, development has been promoted by Mr. Aftosmis U.S. Langray National Laboratory, began to be licensed by Ansys, the high attention of the industry is suggesting.
The orthogonal adaptive grid which is used in Cart3D is not good consistency with the Leap-Frog discretization method, which is used in the FD-TD method.
Therefore, in the Three Wells Computing, we were focused on the Blocked Adaptive Cartesian Grid method which was proposed early in the adaptive Cartesian grid. This is a method that a lump of cells is in place of the one cell Cart3D. This approach, in recent years, actively research and is being developed by a group of NAKAHASHI at Tohoku University and his colleagues in Japan. By using this method, it is possible of FD-TD scheme to be applied to the lump of cells.
In EM, it is a simulator in the field of the world's first numerical electromagnetics , using the blocked adaptive Cartesian grid . In addition, there is not any numerical instability phenomenon that has been plagued by Subgrid method, nor to verification by the iteration of 100,000 has been confirmed.
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