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Hybrid Solvers for the Maxwell Equations in Time-Domain
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
2002 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

The most commonly used method for the time-domain Maxwell equations is the Finite-Difference Time-Domain method (FDTD). This is an explicit, second-order accurate method, which is used on a staggered Cartesian grid. The main drawback with the FDTD method is its inability to accurately model curved objects and small geometrical features. This is due to the Cartesian grid, which leads to a staircase approximation of the geometry and small details are not resolved at all.

This thesis presents different ways to circumvent this drawback, but still take advantage of the benefits of the FDTD method. An approach to avoid staircasing errors but still retain the efficiency of the FDTD method is to use a hybrid grid. A few layers of unstructured cells are used close to curved objects and a Cartesian grid is used for the rest of the domain. For the choice of solver on the unstructured grid two different alternatives are compared: an explicit Finite-Volume Time-Domain (FVTD) solver and an implicit Finite-Element Time-Domain (FETD) solver.

The hybrid solvers calculate the scattering from complex objects much more efficiently compared to using FDTD on highly resolved Cartesian grids. For the same accuracy in the solution roughly a factor of 10 in memory requirements and a factor of 20 in execution time are gained.

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this thesis a technique to generalize a well-known subcell model for thin wires, in order to take arbitrarily oriented wires in FETD and FDTD into account, is proposed. The method gives considerable modeling flexibility compared to earlier methods and is proven stable. The results show excellent consistency and very good accuracy on different antenna configurations.

The recursive convolution method is often used to model frequency dispersive materials in FDTD. This method is used to enable modeling of such materials in the unstructured FVTD and FETD solvers. The stability of both solvers is analyzed and their accuracy is demonstrated by computing the radar cross section for homogeneous as well as layered spheres with frequency dependent permittivity.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2002. , p. 155
Series
Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-2516 ; 40
Keywords [en]
Maxwell's equations, time-domain, finite volume methods, finite element methods, hybrid solver, dispersive materials, thin wires
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-2156ISBN: 91-554-5354-6 (print)OAI: oai:DiVA.org:uu-2156DiVA, id: diva2:161811
Public defence
2002-09-06, Room 2347, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2002-05-23 Created: 2002-05-23 Last updated: 2014-09-03Bibliographically approved

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