University of Twente Student Theses
Krylov subspace time domain computations of monochromatic sources for multi-frequency optical response
Hanse, A.M. (2017) Krylov subspace time domain computations of monochromatic sources for multi-frequency optical response.
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| Abstract: | The study of correlations of speckle patterns of scattering media from incident beams with different angle, frequency and spatial location provides insight in the behavior of light transmission in scattering media. This insight can be exploited for numerous applications such as real-time imaging of biological tissue. Multi-frequency studies of speckle correlations can provide information about the nature and strength of disorder in a material. Currently the main method of calculating speckle patterns for multiple frequencies is broad band pulse excitation using the finite-difference-time-domain (FDTD) method. However, to achieve a reasonable accuracy multiple computations with narrower pulses of partially overlapping frequency spectra have to be done. In these computations the spatial part of the source is constant and only the temporal part of the source is different for every run. In Krylov subspace exponential time integration methods the system is projected on a smaller system of ODEs, this projection is made independent of the temporal part of the source. In this research we present three different Krylov subspace methods to efficiently solve Maxwell’s equations in a scattering medium for monochromatic sources to calculate a multi-frequency response. Two of these methods are shown to be efficient, they perform better than the implicit trapezoidal rule (ITR) scheme. The first of these methods simulates Maxwell’s equations in one big time step and exploits the fact that the projection to a system of smaller ODEs is made independent of the temporal part of the source. The memory requirements of this method are very high but it is the fastest method for finding multi-frequency solutions. In the second method, the solution is rewritten as a time periodic asymptotic solution plus a correction term. The latter is a solution to a homogeneous problem which can be solved by a Krylov subspace method efficiently. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics MSc (60348) |
| Link to this item: | https://purl.utwente.nl/essays/72241 |
| Export this item as: | BibTeX EndNote HTML Citation Reference Manager |
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