Implementation and experiments with the discontinuous Galerkin method for Maxwell's equations

electromagnetism;computational electromagnetics;numerical method;discontinuous Galerkin;"Maxwells equations"]

Pinto, Heitor D. ; Jin ; Jianming

关键词: electromagnetism;    computational electromagnetics;    numerical method;    discontinuous Galerkin;    "Maxwells equations"];   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/14649/Pinto_Heitor.pdf?sequence=3&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis presents the mathematical derivation and implementation of, andimprovements to, the discontinuous Galerkin method (DGM) for solving Maxwell’s equations.Each step leading to the development of a computer code for this method is explained in detail,and samples codes are included in the Appendix. This work also shows numerical results ofseveral experiments with the method, namely: simulation of simple electromagnetic problemswith a known analytical solution for comparison and error analysis; comparison of different timediscretization schemes, which are not strictly part of DGM; reduction of computation time withthe use of adaptive time steps; and analysis of accuracy of absorbing boundaries in scatteringproblems. A discussion listing advantages and limitations of DGM concludes this work.