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Numerical approximation to Helmholtz equation using a spectral method

Z. Mahani, A. Hakim, A. Ziyyat


This paper presents a numerical approximation of an electromagnetic field in its far zone from a knowledge of the field distribution in the near zone. This technic is based on using a spectral method to resolve the Helmholtz equation in an hybrid coordinate system: Cartesian for the vectorial Helmholtz equation and spherical for the scalar Helmholtz equation. Because of the truncation error, the spherical coordinate system is the appropriate one for non-directive antennas and gives a closed surface around the antenna under test. In this study, we focus on the precision and rapidity of the transformation to fulfill the industrial requirements. The used approach is based on near field technic, usually used to evaluate the radiation pattern of an antenna measurement.


Near Fields Technic, Modal Decomposition, Helmholtz Equation, Spherical Wave Function.

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