不均質媒質中のヘルムホルツ波動方程式への境界要素法の適用

抄録

The inhomogeneous term in boundary element method (BEM) analysis is expressed by domain integration. This domain integration reduces the merits of BEM, which are small memory usage and low cost for calculation time.
We show a new approach for transformation of the inhomogeneous term from domain integration into boundary integration, using the Helmholtz equation containing an inhomogeneous wave number (such as in a plasma with spatial density distribution). We attempt the correction from the fundamental solution of a homogeneous medium to that of an inhomogeneous medium by considering the phase distance between source and observation point and amplitude of energy in traveling that distance.
In an inhomogeneous medium, the path of the wavelet is bent by the space distribution of the refraction index, in order to satisfy the Snell law of refraction or Fermat's principle.
The phase distance is calculated by the integration along this bent path. The energy flux density of a traveling wavelet is treated as isotropic in the neighborhood of the source points. However it is not uniform at the observation point because of bent paths. We calculate the energy flux density at the observation point considering the angle of radiation at the source point. These corrections lead to a boundary integral equation without the domain integral.