hp-mesh adaptation for 1-D multigroup neutron diffusion problems
Abstract
In this work, we propose, implement and test two fully automated mesh adaptation methods
for 1-D multigroup eigenproblems. The first method is the standard hp-adaptive refinement
strategy and the second technique is a goal-oriented hp-adaptive refinement strategy. The
hp-strategies deliver optimal guaranteed solutions obtained with exponential convergence rates
with respect to the number of unknowns. The goal-oriented method combines the standard
hp-adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an
adjoint problem in order to compute quantities of interest, such as reaction rates in a sub-domain
or point-wise fluxes or currents. These algorithms are tested for various multigroup 1-D
diffusion problems and the numerical results confirm the optimal, exponential convergence rates
predicted theoretically.
Subject
hp-Mesh adaptationMultigroup
Neutron diffusion
Multi-mesh
Finite element method
Higher order
Citation
Wang, Yaqi (2006). hp-mesh adaptation for 1-D multigroup neutron diffusion problems. Master's thesis, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /4707.