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Computational Electromagnetics pp 11–18Cite as

Convergence

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Abstract

The usage of computational electromagnetics in engineering and science more or less always originates from a physical situation that features a particular problem. Here, some examples of such situations could be to determine the radiation pattern of an antenna, the transfer function of a frequency selective surface, the scattering from small particles or the influence of a cell phone on its user. The physical problem is then described as a mathematical problem that involves Maxwell’s equations. In a very limited number of cases, the mathematical problem can be solved analytically such that we have an exact solution in closed form. If there exists a solution to the problem that can not be calculated analytically, we can approximate the mathematical problem and pursue an approximate solution. In the context of CEM, such an approximate solution is often referred to as a numerical solution, since it typically involves extensive numerical computations in combination with relatively simple analytical expressions. These simple analytical expressions are normally applied to small subdomains of the original problem-domain, where the subdomain solutions are related to each other such that they collectively correspond to the solution to the original problem. The difference between an approximate solution and the exact solution is referred to as the error. It is desirable that the error can be reduced to an arbitrary low level such that the approximate solution converge to the exact solution, i.e. the accuracy of the numerical solution improves.

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Authors and Affiliations

  1. Department of Signals and Systems, Chalmers University of Technology, Hörsalsvägen 11, SE-41296, Göteborg, Sweden

    Thomas Rylander

  2. Department of Electromagnetics, Chalmers University of Technology, Hörsalsvagen 11, Göteborg, Sweden

    Pär Ingelström

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  1. Thomas Rylander
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  3. Anders Bondeson
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Rylander, T., Ingelström, P., Bondeson, A. (2013). Convergence. In: Computational Electromagnetics. Texts in Applied Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5351-2_2

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