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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 42710 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Shishegar, Amir Ahmad
- Abstract:
- Always, there has been a great interest toward electromagnetic wave propagation and new ways for simulation of the problem. Level set methods provide a powerful mathematical framework for propagating surfaces (in 3-D) or curves (in 2-D). The contours of the moving objects are viewed as the zero level sets of a function and propagated in a Eulerian point of view by means of a Hamilton–Jacobi partial differential equation expressing the conservation of the level sets under a given velocity field. Level set methods have been applied in a wide range of domains, such as physics, chemistry, fluid dynamics, combustion, image processing… In this thesis, we introduce a new numerical procedure for simulations in geometrical optics that, based on the recent development of Eulerian phase-space formulations of the model, can deliver very accurate, uniformly resolved solutions which can be made to converge with arbitrarily high orders in general geometrical configurations. A fully 2–D code is then prepared using MATLAB. The code is validated by comparing its results with [8]. In the next step, we will see that the Maxwell’s equations can be written in the form of transport and Hamilton-Jacobi equations in Cartesian coordinates. Thus the same numerical methods such as DGFEM, could be applied for maxwell’s equations. So we will use DGFEM procedure again to simulate wave propagation in Cartesian coordinates. The algorithm and its code is validated by comparing its result with analytical examples. After this, we show that the Maxwell’s equations can be looked as transport and Hamilton-Jacobi equations in cylindrical and spherical coordinates too. So we follow the DGFEM procedure again. Validation is provided by comparing its result with analytical examples. At the end, we will show some ways of antenna modeling as a current source in solving procedure. This could be valuable achievement for the numerical scheme
- Keywords:
- Level Set Method ; Hamilton-Jacobi Equation ; Discontinuous Galerkin Finite Element Method (DGFEM)
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