<p>The broad implementation of three-dimensional full-core modeling, with pin-resolved detail, for computational simulation and analysis of nuclear reactors highlights the importance of accuracy and efficiency in simulation codes for accurate and precise analysis. The primary objective of this dissertation is to develop a high-fidelity code capable of solving time-dependent neutron transport problems with 3D whole-core pin-resolved detail in nuclear reactor cores. Additionally, the dissertation explores the optimization of the code's parallelism to enhance its computational efficiency. To reduce the computational intensity associated with the direct 3D calculation of the neutron transport equation, a high-fidelity neutron transport code called PANDAS-MOC is developed using the 2D/1D approach. The 2D radial solution is obtained using the 2D Method of Characteristics (MOC), the axial 1D solution is determined through the Nodal Expansion Method (NEM), and then two solutions are coupled using transverse leakages to find the 3D solution. The convergence of the iterative scheme is accelerated using the multi-level coarse finite different mesh (ML-CMFD) technique. The code's validation and verification are carried out using the C5G7-TD benchmark exercises.</p> <p><br></p> <p>The significant and innovative aspect of this work involves parallelizing and optimizing the PANDAS-MOC code. Three parallel models are developed and evaluated based on the distributed memory and shared memory architecture: MPI parallel model (PMPI), Segment OpenMP threading hybrid model (SGP), and Whole-code OpenMP threading hybrid model (WCP). When computing the steady state of the C5G7 3D core with the same resources, the obtained speedup relationship between the three models is PMPI \(>\) WCP \(>\) SGP, whereas the WCP model only consumed 60\% of the memory of the PMPI model. Furthermore, the hybrid reduction in the ML-CMFD solver and the parallelism design of the MOC sweep are significant issues that decreased the speedup of WCP. Therefore, this study also addresses further optimizations of these two modules.</p> <p><br></p> <p>Concerning the MOC parallelism, two improvements are discussed: No-atomic schedule and Additional Axial Decomposition (AAD) parallelism. The No-atomic schedule evenly distributed the workload among threads and removes the \textit{omp atomic} clause from the code by predefining the MOC calculation sequence for each launched OpenMP thread while ensuring a thread-safe parallel environment. It can significantly reduce the calculation time and improve parallel efficiency. Furthermore, AAD divides the axial layers and OpenMP threads into multiple groups and restricts each thread to work on the layers designated to the same group. </p> <p>Meanwhile, Flag-Save-Update reduction is designed to increase the computational efficiency of the hybrid MPI/OpenMP reduction operations in the ML-CMFD module. It is accomplished by using the global arrays and status flags and establishing a tree configuration of all threads, and it includes no implicit and explicit barriers. In the case of the C5G7 3D core, the parallel efficiency of the MOC solver is about 0.872 when using 32 threads (=\#MPI \(\times\)\#OpenMP), and the Flag-Save-Update reduction yielded better speedup than the traditional hybrid MPI/OpenMP reduction, and its superiority is more obvious as more OpenMP threads are utilized. As a result, the WCP model outperforms the PMPI model for the overall steady-state calculation.</p> <p><br></p> <p>This research also investigates parallelizable preconditioners to accelerate the convergence of the generalized minimal residual method (GMRES) in the CMFD solver. Preconditioners such as Incomplete LU factorization (ILU), Symmetric Successive Over-relaxation (SOR), and Reduced Symmetric Successive Over-Relaxation (RSOR), are implemented in PANDAS-MOC. Except for RSOR, others are unsuitable for hybrid MPI/OpenMP parallel machines due to their inherent sequential nature and dependency on computation order. Their counterparts using the Red-Black ordering algorithm, namely RB-SOR, RB-RSOR, and RB-ILU, are formatted and examined on benchmark reactors such as TWIGL-2D, C5G7-2D, C5G7-3D, and their corresponding subplane models (TWIGL-2D(5S), C5G7-2D(5S), C5G7-3D(5S)), with relaxed convergence criteria (\(10^{-3}\)). Results show that all preconditioners significantly reduce the required number of iterations to converge the GMRES solutions, and RB-SOR is the best one for most reactors. In the case of C5G7-3D(5S), preconditioners exhibit similar sublinear speedup but demonstrate varying runtimes across all tests for both MG-GMRES and 1G-GMRES. However, the speedup results in 1G-GMRES are more than twice as high as those in MG-GMRES. RB-RSOR has an optimal efficiency of 0.6967 at (4,8), while RB-SOR and RB-ILU have optimal efficiencies of 0.6855 and 0.7275 at (32,1), respectively.</p>

A Tomografia de Impedância Elétrica é uma técnica de obtenção de imagens do interior de um corpo, mediante grandezas elétricas medidas em sua superfície. Matematicamente, a técnica determina as distribuições de condutividades e permissividades elétricas num dado modelo do corpo, as quais reproduzem as medidas de correntes e potenciais elétricos em eletrodos fixados ao corpo. Nesse caso, as distribuições de condutividades e permissividades representam a solução de um problema não-linear e mal-posto, o qual é instável e apresenta mínimos locais, requerendo técnicas de inversão específicas. Um sistema de Tomografia de Impedância Elétrica aplicado à obtenção de imagens de valores absolutos possui, atualmente, limitações. São algumas delas a obtenção de distribuições de propriedades suaves e de valores geralmente subestimados, a sensibilidade elevada ao erro de posicionamento dos eletrodos (com relação ao modelo) e ao erro nos valores de parâmetros de contato, a sensibilidade elevada aos ruídos de medição, os tempos elevados de processamento, dentre outros. Com o intuito de abordar as limitações, melhorando o desempenho do sistema de Tomografia de Impedância Elétrica de imagens absolutas, são então propostas e avaliadas ferramentas baseadas no Método de Otimização Topológica no atual trabalho. Mais especificamente, avaliam-se: 1) um método para obtenção de parâmetros de contato em conjunto com uma imagem e um método de regularização baseado no controle explícito da variação espacial da imagem, 2) uma formulação para acomodação de incertezas, 3) uma formulação para correção do posicionamento de eletrodos, 4) uma formulação para projeto de eletrodos e 5) um novo solucionador de sistemas lineares de larga escala. Os resultados mostram a efetividade da maioria das técnicas propostas, e sugerem os novos tópicos de pesquisa em Tomografia de Impedância Elétrica. / Electrical Impedance Tomography images the interior of a body based on electrical quantities measured on the surface of it. Mathematically, the technique finds the electric admittivity distribution in a given body model which reproduces the boundary measurements of electric currents and potentials on electrodes attached to that body. Therefore, the admittivity distribution is the solution of a non-linear and ill-posed problem, which is unstable and have local minima, requiring specific inversion techniques. Electrical Impedance Tomography systems which obtain images corresponding to absolute values present limitations. For instance, the results are usually smooth and underestimated, the sensitivity to errors in the positioning of electrodes and wrong values of contact parameters and the sensitivity to measurement noise are high, the data processing time is high, etc. In this work, techniques based on the Topology Optimization Method intended for improving the performance of the particular Electrical Impedance Tomography system applied to absolute images are proposed and evaluated. More specifically, the following techniques are evaluated: 1) a method intended to obtain contact parameters together with images, and a regularization method based on the explicit control of the spatial variation regarding the image, 2) a formulation applied to handle uncertainties, 3) a formulation applied to correct the position of electrodes, 4) a formulation applied to design electrodes, 5) and a new solver for large-scale linear systems. Results show the effectiveness of most of the proposed techniques, and suggest new research topics in Electrical Impedance Tomography.

A Tomografia de Impedância Elétrica é uma técnica de obtenção de imagens do interior de um corpo, mediante grandezas elétricas medidas em sua superfície. Matematicamente, a técnica determina as distribuições de condutividades e permissividades elétricas num dado modelo do corpo, as quais reproduzem as medidas de correntes e potenciais elétricos em eletrodos fixados ao corpo. Nesse caso, as distribuições de condutividades e permissividades representam a solução de um problema não-linear e mal-posto, o qual é instável e apresenta mínimos locais, requerendo técnicas de inversão específicas. Um sistema de Tomografia de Impedância Elétrica aplicado à obtenção de imagens de valores absolutos possui, atualmente, limitações. São algumas delas a obtenção de distribuições de propriedades suaves e de valores geralmente subestimados, a sensibilidade elevada ao erro de posicionamento dos eletrodos (com relação ao modelo) e ao erro nos valores de parâmetros de contato, a sensibilidade elevada aos ruídos de medição, os tempos elevados de processamento, dentre outros. Com o intuito de abordar as limitações, melhorando o desempenho do sistema de Tomografia de Impedância Elétrica de imagens absolutas, são então propostas e avaliadas ferramentas baseadas no Método de Otimização Topológica no atual trabalho. Mais especificamente, avaliam-se: 1) um método para obtenção de parâmetros de contato em conjunto com uma imagem e um método de regularização baseado no controle explícito da variação espacial da imagem, 2) uma formulação para acomodação de incertezas, 3) uma formulação para correção do posicionamento de eletrodos, 4) uma formulação para projeto de eletrodos e 5) um novo solucionador de sistemas lineares de larga escala. Os resultados mostram a efetividade da maioria das técnicas propostas, e sugerem os novos tópicos de pesquisa em Tomografia de Impedância Elétrica. / Electrical Impedance Tomography images the interior of a body based on electrical quantities measured on the surface of it. Mathematically, the technique finds the electric admittivity distribution in a given body model which reproduces the boundary measurements of electric currents and potentials on electrodes attached to that body. Therefore, the admittivity distribution is the solution of a non-linear and ill-posed problem, which is unstable and have local minima, requiring specific inversion techniques. Electrical Impedance Tomography systems which obtain images corresponding to absolute values present limitations. For instance, the results are usually smooth and underestimated, the sensitivity to errors in the positioning of electrodes and wrong values of contact parameters and the sensitivity to measurement noise are high, the data processing time is high, etc. In this work, techniques based on the Topology Optimization Method intended for improving the performance of the particular Electrical Impedance Tomography system applied to absolute images are proposed and evaluated. More specifically, the following techniques are evaluated: 1) a method intended to obtain contact parameters together with images, and a regularization method based on the explicit control of the spatial variation regarding the image, 2) a formulation applied to handle uncertainties, 3) a formulation applied to correct the position of electrodes, 4) a formulation applied to design electrodes, 5) and a new solver for large-scale linear systems. Results show the effectiveness of most of the proposed techniques, and suggest new research topics in Electrical Impedance Tomography.