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- W3125717784 abstract "The increase in the use of numerical methods to solve electromagnetic scattering problems drives the study of an optimal spatial discretization to obtain a more accurate solution. In this dissertation, the use of curved elements (CE) in the Discontinuous Galerkin Time Domain (DGTD) method is presented as an alternative to common straight side elements (SSE). As can be seen throughout this work, CEs have many advantages in problems involving curved contours because these contours are represented accurately avoiding the use of small SSE and consequently, decreasing the number of nodes on the computational domain, also called degrees of freedom (DOF).Initially, the classical DGTD method with SSE is explained. This is essential because in this part are mentioned most of important characteristics of the method as: the use of the numerical flux to guarantee the connectivity between elements, the orthonormal polynomial basis used to build the semi-discretized form and the Runge Kutta method used for the time integration. Then, it is explained step by step the modifications which must be done to make the curved elements. The process to build the CEs can be divided into three parts: the first one is to identify the elements which are intersected by the curved boundary, the second one is to relocate the nodes of the curved face exactly onto the curved boundary and third, to apply the deformation over the internal nodes of the CEs and update the volume nodes locations. Moreover, the integrals of non-polynomials functions must be taken into consideration due to the jacobian of each curved element is non-constant.In order to validate this formulation, 2D scattering problems were solved. Results showed that the global error decreases when the CEs are used. Moreover, the convergence rate was higher for the CEs than the SSE. Additionally, the use of CEs to solve more complex problems where the amount of CEs increases a lot was presented. Again, the CEs scheme showed a more accurate solution than the SSE with a decrease of number of elements and DOF." @default.
- W3125717784 created "2021-02-01" @default.
- W3125717784 creator A5031164835 @default.
- W3125717784 date "2020-10-21" @default.
- W3125717784 modified "2023-09-23" @default.
- W3125717784 title "A DGTD method using curved elements to solve electromagnetic scattering problems" @default.
- W3125717784 hasPublicationYear "2020" @default.
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