Solution of Maxwell's Equations by the Singular Integral Equations Method For Three-Dimensional Scattering Problems and Distribution of the Electric Field in a Heart Model

The Singular Integral Equations Method (SIB) used in this article allowed us to solve Maxwell's equations for a three-Dimensional (3D) heart model when a microwave source that radiated pulse modulated microwaves is outside of the heart model. Here we explain the main idea of our SIE method. We first separated the solution of equations from satisfying the boundary conditions. For this purpose, we found the solution of the differential equations having a point source. This fundamental solution is used in our integral representation of a problem. The integral representation automatically satisfied the differential equations but has an unknown density function which must be found from the boundary conditions. The solution of the differential equations, obtained by our SIB method, was rigorous, that is it satisfied the differential equations and all boundary conditions. The false roots did not occur when applying our SIE method. Microwave electric field distributions were analysed at three longitudinal cross-sections of the heart model.