Electromagnetic Scattering Analysis Of Discontinuous Galerkin Time Domain Integral Equation Method

Recently, numerical analysis of transient electromagnetic scattering by time domain integral equation(TDIE) method is becoming more and more popular. Theoretically, due to the continuity of physics, the object must be discretized by conformal meshes if we use the div-conforming basis function. However, many objects are consisted of different materials. It is very difficult to discretize the target with conformal meshes, so employing different discretization sizes at different parts of the target is desired. Therefore, it is meaningful to develop a method which can solve this problem smoothly.In this dissertation, a discontinuous Galerkin method based on time domain volume surface integral equation(DG-TD-VSIE) is described. This method can deal with the non-conformal meshes by using discontinuous Galerkin method with the time domain volume surface integral equation. It is unnecessary to enforce the continuity of physics when using this method, so different basis functions can be used on the independent meshes, which can reduce the consumption of computer memory and improve the accuracy of the result. As a result, DG-TD-VSIE method is more flexible than other TDIE method when analyzing electromagnetic scattering from the complex target in a wide band.In the first part of this dissertation, the theories of time domain integral equation (TDIE) method and discontinuous Galerkin method are introduced. Then, the discontinuous Galerkin method based on time domain volume integral equation (DG-TD-VIE) is derived in detail. After the derivation, we optimize the DG-TD-VIE with continuous Galerkin method, which forms the continuous-discontinuous Galerkin based on time domain volume integral equation (CDG-TD-VIE). Furthermore, the continuous-discontinuous Galerkin method based on time domain volume surface integral equation (CDG-TD-VSIE) is derived after the optimization. Finally, the plane wave time domain (PWTD) technique is introduced into CDG-TD-VSIE method which greatly improves the ability of the latter in solving practical electromagnetic problems.