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## Modelling and simulation

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During product development, measurements are expensive due to personal effort or restricted resources such as semi-anechoic chambers. It is straightforward to put this workload into a computer which simulates the measurement setup or even the road reality. It should not be forgotten that a trustworthy simulation needs a model which also requires some effort. Finally, the model needs to be validated which is typically done by measurement. So for a single use, modelling may get more expensive than a direct measurement, but models can be reused in later project phases or for other projects. They can also help to get a deeper understanding. Even a good model stays a model which differs from reality, so a complete substitution of measurements and tests, in particular for compliance, is not realistic. The belief that simulation avoids costs of equipment might be disturbed in some cases by license fees for software. There is a lot of free software around which often uses the same algorithms as commercial packages, but in some cases, commercial products are more comfortable to use and faster to learn. Some packages conceal their algorithms so far, that it is hard to understand in detail how a result has been calculated. Sometimes, the source code of free software is open, in particular for academic use the possibility of modification might be interesting.

Chapter Contents:

• 8.1 Modelling basics
• 8.2 Analytical methods
• 8.3 Semi-analytical methods
• 8.4 Numerical methods
• 8.4.1 Finite difference time domain
• 8.4.2 Monte Carlo methods
• 8.4.3 Finite elements methods
• 8.4.4 Method of moments
• 8.4.5 Fast multi-pole method and multi-level fast multi-pole algorithm
• 8.4.6 Contour integral method
• 8.4.7 Finite integration technique
• 8.4.8 Transmission line matrix method
• 8.4.9 Partial element equivalent circuit method
• 8.4.10 Geometrical optics
• 8.4.11 Geometrical theory of diffraction
• 8.4.12 Uniform theory of diffraction
• 8.4.13 Physical optics
• 8.4.14 Physical theory of diffraction
• 8.4.15 Raytracing
• 8.4.16 Shooting-and-bouncing ray
• 8.5 Stochastic methods
• 8.6 Validation
• 8.6.1 Feature selective validation

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