On the formulations of the boundary integral equations for scattering by homogeneous bodies

The accuracy and efficiency of different combination forms of integral equations has been well studied for homogenous bodies in the literature. However, the effect of the combination coefficients on accuracy and efficiency has little investigated for these different combination formulations so far. This paper gives a systematic and numerical study on this problem, i.e. how and why the combination coefficients affect the accuracy and efficiency in the different combination formulations. A general principle of choosing combination coefficients is also presented in this paper. An optimized combination coefficient is proposed for the JMCFIE, which has been confirmed to be a good combination formulation for homogenous bodies. Numerical experiments confirm that the optimized JMCFIE (O-JMCFIE) has fast convergence over the conventional JMCFIE (C-JMCFIE) when maintaining the same accuracy.