A Multilevel in Space and Energy Solver for Multigroup Diffusion and Coarse Mesh Finite Difference Eigenvalue Problems

In reactor physics, the efficient solution of the multigroup neutron diffusion eigenvalue problem is desired for various applications. The diffusion problem is a lower-order but reasonably accurate approximation to the higher-fidelity multigroup neutron transport eigenvalue problem. In cases where the full-fidelity of the transport solution is needed, the solution of the diffusion problem can be used to accelerate the convergence of transport solvers via methods such as Coarse Mesh Finite Difference (CMFD). The diffusion problem can have O(108) unknowns, and, despite being orders of magnitude smaller than a typical transport problem, obtaining its solution is still not a trivial task. In the Michigan Parallel Characteristics Transport (MPACT) code, the lack of an efficient CMFD solver has resulted in a computational bottleneck at the CMFD step. Solving the CMFD system can comprise 50% or more of the overall runtime in MPACT when the de facto default CMFD solver is used; addressing this bottleneck is the motivation for our work. The primary focus of this thesis is the theory, development, implementation, and testing of a new Multilevel-in-Space-and-Energy Diffusion (MSED) method for efficiently solving multigroup diffusion and CMFD eigenvalue problems. As its name suggests, MSED efficiently converges multigroup diffusion and CMFD problems by leveraging lower-order systems with coarsened energy and/or spatial grids. The efficiency of MSED is verified via various Fourier analyses of its components and via testing in a 1-D diffusion code. In the later chapters of this thesis, the MSED method is tested on a variety of reactor problems in MPACT. Compared to the default CMFD solver, our implementation of MSED in MPACT has resulted in an ~8-12x reduction in the CMFD runtime required by MPACT for single statepoint calculations on 3-D, full-core, 51-group reactor models. The number of transport sweeps is also typically reduced by the use of MSED, which is able to better converge the CMFD system than the default CMFD solver. This leads to a further savings in overall runtime that is not captured by the differences in CMFD runtime.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146075/1/bcyee_1.pd

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also