Generalization of Magnetostatic Method of Moments for Thin Layers with Regular Rectangular Grids

R. Szewczyk Industrial Research Institute for Automation and Measurements, Al. Jerozolimskie 202, 02-486 Warsaw, Poland

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Possibilities of the modeling of the flux density distribution in thin films are significantly limited using the finite elements method due to the fast increase of the number of tetrahedral elementary cells with reduction of the thickness. For this reason, method of the moments is very important alternative for finite elements method in the case of thin layers, where layer's thickness should be considered. Method of the moments overcomes this barrier, due to the possibility of operation on uniform: grids with limited number of cells. Moreover, in opposite to the finite elements method, the method of the moments requires solving of the well defined linear equations, instead of the set of ill-posed differential equations. Paper presents the generalization of the method of the moments for thin layers with given thickness. Layers are defined as the 2D rectangular grids. Within the generalization, four key equations describing the influence of rectangular cell's border on the magnetization of cells are stated. On the base of these dependences, the set of 2NM linear equations was determined, where N and M are the numbers of rectangular cells in the rows and columns of regular grid. Finally, the set of linear equations is solved and magnetic flux density distribution in the thin layer is calculated.

DOI: 10.12693/APhysPolA.131.845 PACS numbers: 75.70.Ak, 75.50.Kj