A generalized Holland model for wave diffraction by thin wires

february, 2007
Publication type:
International conference with proceedings
Conference on Computational Electromagnetism and Acoustics, Oberwolfach Allemagne
The general context of the problem we are interested in is the simulation of electromagnetic wave diffraction by thin wires. We make two assumptions on such obstacles: we suppose the wires to be perfectly conducting, and suppose their thickness is much smaller than the wavelength of the field. For example, antennas satisfy these hypothesis. We propose to study the model problem of acoustic diffraction by thin obstacles, and we wish to perform such computations using a volumic method with no mesh refinement. To our knowledge there exists only one numerical method matching these previous requirements. It is called the Holland model and was proposed by Holland and Simpson in the engineer literature \cite{Holland}. It is suitable for straigth wires aligned with the axis of a cartesian grid in a FDTD scheme for electromagnetics. This model assumes that the current is constant across any section of the wire and that the field has an electrostatic behavior close to the wire. It is also based on a averaging operator in a region as large as a cell close to the wire. This averaging operator involves a parameter called the lineic inductance that is to be chosen on a empirical basis. This model is widely used in volumic methods, it provides precise results (for a well chosen lineic inductance) and can be easily implemented. Unfortunately it lacks a solid theoretical basis. In particular, there exist only empirical formulas for the lineic inductance. For the model problem of bidimensional acoustic diffraction, we present an augmented finite element method that matches the requirements stated before. From this alternative method, we are able to recover the Holland model. This method then generalizes the Holland model for arbitrary meshes, provides a rigorous setting for it and a theoretical expression of the lineic inductance.
    author={Xavier Claeys and Francis Collino and Marc Duruflé },
    title={A generalized Holland model for wave diffraction by thin wires },
    organization={Conference on Computational Electromagnetism and Acoustics, 
           Oberwolfach Allemagne },
    year={2007 },