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This thesis contains results on convergence studies for different stencils of radial basis function generated finite difference (RBF-FD) method applied to solving Black-Scholes equation for pricing European call options. The results experimentally confirm the theoretical convergence rates for smooth payoff functions with stencils of size 3, 5 and 7 in one- dimensional problems, and 9, 13 and 25 in two- dimensional problems. Moreover, it is shown how different terms in the equation can be approximated individually using the proposed method and then combined into a discrete approximation of the entire spatial differential operator. This new version of the RBF-FD method, where each term has been approximated individually, has been compared to the classical method and the outcome did not show any significant performance advantages. Nevertheless, the results also showed that the second order derivative was the hardest one to approximate accurately and this poses an important finding for the future development of the method.

The finite difference time domain (FDTD) method is commonly used for numerical simulations of the electromagnetic wave propagation in time domain. The FDTD method is easy to implement and the computational results are highly relevant to the analytical solution, so that the FDTD method is applied to variety application problems. However, the computational efficiency of the FDTD method is constrained by the upper limit of the temporal discretisation. The Courant Friedrich Lewy (CFL) stability condition limits the time step for the computation of the FDTD method, so that if the spatial discretisation of the computation is set to be small in order to obtain high accurate results, the size of the temporal discretisation need to be satisfy the CFL stability condition. The locally one dimensional FDTD (LOD-FDTD) method is unconditionally stable. The time step and the spatial step can be independently chosen for the computation of the LOD-FDTD method. The arithmetic operations of the LOD-FDTD method is fewer than that of the other implicit FDTD method, such as the Crank Nicolson FDTD (CN-FDTD) method and the alternating direction implicit FDTD (ADI-FDTD) method. Although the implementation of the LOD-FDTD method is simpler than that of the ADI-FDTD method,the numerical error in the computational results of the LOD-FDTD method is equivalent to that in the computational results of the ADI-FDTD method. In this thesis, a new three dimensional (3D) frequency dependent (FD) LOD-FDTD method is proposed. The one pole Debye model is incorporated into the 3D-FD-LOD-FDTD method in order to deal with practical applications. The proposed method is implemented in Fortran 90 and parallelised with OpenMP. A simulation model of the human phantom is developed in the 3D-FD-LOD-FDTD method with fine structures and frequency dependent dielectric properties of the human tissues, and numerical simulation of electromagnetic wave propagation inside the human head is shown.

The aim of the work is to develop an evaluation platform for comunnication on CAN FD bus. This evaluation platform is mainly intended to be used for the application support of the NCV7344 CAN transceiver on given module. The main part of the work is to develop firmware for SAM V71 microcontroller and a control application software for computer. This control application will serve to setup the communication parameters, send and receive data and control communication in the testing network. Attention is also paid to develop and test effectiveness of signal improvement circuits and their impact on bit error rate in real conditions on designed evaluation network.

In this work, a coordinate wise descent algorithm is implemented which serves the purpose of estimating active users in a base station/client wireless communication setup. The implemented algorithm utilizes the sporadic nature of users, which is believed to be the norm with 5G Massive MIMO and Internet of Things, meaning that only a subset of all users are active simultaneously at any given time. This work attempts to estimate the viability of a direct algorithm implementation to test if the performance requirements can be satisfied or if a more sophisticated implementation, such as a parallelized version, needs to be created.The result is an isomorphic ASIC implementation made in a 28 nm FD-SOI process, with proper internal word lengths extracted through simulation. Some techniques to lessen the burden on hardware without losing performance is presented which helps reduce area and increase speed of the implementation. Finally, a parallelized version of the algorithm is proposed, if one should desire to explore an implementation with higher system throughput, at almost no furtherexpense of user estimation error.

京都大学 / 新制・課程博士 / 博士(教育学) / 甲第24824号 / 教博第294号 / 新制||教||219(附属図書館) / 京都大学大学院教育学研究科教育科学専攻 / (主査)准教授 田口, 真奈, 教授 飯吉, 透, 教授 服部, 憲児 / 学位規則第4条第1項該当 / Doctor of Philosophy (Education) / Kyoto University / DGAM