Metalenz is a spin­off company of Harvard University that works on finding newer and better designs for lenses. To prevent manufacturing designs that might not work, they first want to run computer simulations on their designs. This research focuses on a possible method for these simulations using a test case as design. It turns out that the simulations work, but that they are slow. Therefore, a technique to make the simulations faster, Multi-trace boundary integral equations, is researched. This technique manages to change simulations that take a week to finish into simulations that take a couple of hours to finish. Before Metalenz can start using the simulation techniques, they should be tested for more complicated cases, to make sure they still
work when more factors are at play

In dit project is gewerkt aan een manier om de reflectie van het licht op de textuur van een zonnecel te berekenen. Deze reflectie is berekenend voor de verschillende hoeken van inval en uitval en omgezet in een reflectie matrix. In dit
project is verder gewerkt aan een al bestaand wiskundig model. Dat model was
in staat het door de verstrooiing ontstaande verre veld te berekenen. Dit model maakt gebruik van de methode van momenten, en past deze toe op eerder
ontwikkelde integraal vergelijkingen , die volgen uit de wetten van Maxwel.
Tijdens dit project is dit model aangepast zodat het ook bruikbaar werd voor
het door ons gemodelleerde substraat, van het Asahi-U type. Ook is in dit project gewerkt aan een manier om de bekende data van het Asahi-U substraat om
te zetten naar een wiskundig model .Dit is gedaan door het Asahi-U substraat
om te zetten naar een graaf van knopen en takken, met behulp van het programma GMSH. Vervolgens is gewerkt aan een manier om de berekende data
van het verre veld om te verwerken tot de reflectie matrices. Dit is gedaan met
behulp van een numerieke methode om integralen uit te werken. Tenslotte is de
reflectie matrices opgesteld, waaruit de reflectie van het licht op het substraat
kan worden afgelezen. Deze opgestelde matrix is anders dan de verwachting
niet symmetrisch. De waardes verschillen ook van de waardes die gevonden
zijn met behulp van een empirische meting.

When creating electronic devices, it is essential to model what happens when an electromagnetic field hits the device and it scatters. Conventionally, this can be modelled using the Marching-on-in-Time algorithm. This can become computationally expensive for complex systems. To speed up the algorithm, the Plane-Wave Time-Domain algorithm is combined with the MOT algorithm. To accelerate the process even more, part of the algorithm is implemented using a Graphics Processing Unit, or GPU.

To test if using GPUs for this type of problem is actually beneficial, three experiments are set up. The first one tests the basic operations of addition and multiplication on matrices and vectors of various sizes, to determine if and when the computation time of the GPU is lower than that of a CPU. The second experiment tests the use of Fast Fourier Transform planner functionality and compares the CPU computation time with that of the GPU for the FFT of matrices of various sizes. The third experiment compares an example of the PWTD algorithm on the CPU and the GPU. These experiments are performed on three different devices.

The results from experiment 1 and 2 show that, after a certain point, the GPU is almost always faster, no matter the operation. Experiment 3 shows that the current GPU implementation is currently not as fast as the regular PWTD algorithm, though one of the devices is only 0.003\% slower.

In conclusion, theoretically a decrease in computation time is expected. From experiment 3 it follows that it is not the case yet, though with more optimisation the GPU implementation would almost certainly become faster.

Mankind has always adapted materials to fullfil a need. Recent developments in nano-science allows us to construct objects with varying permittivity and permeability. One possible structure is an invisibility cloak device. This device is put around an object. Any plane wave that enters the cloak should go around this object. The wave exits the cloak as a plane wave, rendering the object on the inside invisible. Since making such a device is quite dicult, it is useful to simulate it first. A relatively new programming language is Julia [1], [2]. Julia has a high performance and this makes it an interesting language to use for these simulations. In this work, the material properties of such a device was calculated. A simulating tactic was developed. This tactic was a hybrid version between the Method of Moments (MoM) and the Finite Elements Method (FEM). Both these methods and the hybrid method were implemented in BEAST.jl [3]
and CompScienceMeshes [4] and were tested using simulations in EMwavesBEP.jl[5]. While the FEM and MoM gave great results, the hybrid algorithm had only a good result for the electric fields. The magnetic elds failed to show the wanted results. The previous determined cloak was simulated using the hybrid algorithm. The cloaking property was clearly visible and the wave
exited as a plane wave. A far field should be calculated to verify this further.