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The adoption of the 3-D version of finite-difference time-domain (FDTD) allows us to handle a large number of scattering objects without sacrificing the accuracy of the solution. We have developed a 3-D FDTD solver for the scattering of electromagnetic waves from a 3-D object. The algorithm uses an operator splitting technique in the frequency domain to separate the object from the free space, leading to a pure absorbing boundary condition. The scattered fields are then computed by a multigrid method, and the 3-D EM fields are advanced in time using a 1-D FDTD scheme. The solver handles a 3-D object with a size of up to 20003 voxels, and it can model scattering from over 10^10 voxels in 2-D and over 10^11 voxels in 3-D. It is not possible to handle objects with a size of more than 10^10 voxels in 1-D. The solver was used to analyze a full-wave simulation of an anechoic chamber. A high-frequency source is placed in the chamber, and a spatial and angular analysis is performed to study the quality of the solution. The solution is accurate enough to model antennas used for communication, imaging, and radar, and for the modelling of space and airborne platforms.
The work was performed within the framework of the EU-funded project BENTWIND. The project addresses the development of a high-performance software package that can be used for the analysis of full-wave electromagnetic scattering, both from stationary and moving objects. To maximize the performance of the software, a memory-efficient and scalable numerical solver is necessary. While the numerical solver will be extended for the 3-D case, our work has focused on the improvement of the raw waveform simulation. We have presented a solution to the problem of three-dimensional E-field simulation with anisotropic material properties. This method is based on the fact that the integral form of Maxwell's equations is a linear problem and the E-field can be projected onto a scalar function. The scalar function is a solution to the scalar Helmholtz equation, which is a second order partial differential equation. To find the solution to the Helmholtz equation, we used the finite element method with orthogonal polynomials as basis functions. Our method is more efficient than other approaches, since no matrix manipulations are required.
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