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Book synopsis

This work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the calculation of the numerical flux at an interface between neighbouring elements, and a second-order leap-frog time integration scheme. Next, to reduce the computational costs of the method, we propose a hp-like DGTD method which combines local h-refinement and p-enrichment. Then, we report on a detailed numerical evaluation of the DGTD methods using several propagation problems. Finally, in order to improve the accuracy and rate of convergence of the DGTD methods previously studied, we study a family of high-order explicit leap-frog time schemes. These time schemes ensure the stability under some CFL-like condition. We also establish rigorously the convergence of the semi-discrete approximation to Maxwell's equations and we provide bounds on the global divergence error.

Book details

Book category Książki po angielsku Literature & literary studies Literature: history & criticism Literary studies: general

• Full title: High-Order Discontinuous Galerkin Methods for the Maxwell Equations
• Author: Hassan Fahs
• Language: English
• Binding: Paperback
• Number of pages: 208
• EAN: 9786131500206
• ISBN: 6131500207
• ID: 06935635
• Publisher: Omniscriptum
• Weight: 313 g
• Dimensions: 229 × 152 × 12 mm
• Date of publishing: 28. February 2018

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