Browsing by Author "M. Shearer, Committee Member"

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Advanced Thermosyphon Targets for Production of the 18F Radionuclide.
(2007-03-26) Stokely, Matthew Hughes; M. Shearer, Committee Member; G. Bida, Committee Member; B. Wieland, Committee Member; J. Michael Doster, Committee Chair; M. Bourham, Committee Member
Single phase and boiling batch water targets are the most common designs for the cyclotron production of 18F via the 18O(p,n)18F reaction. Thermosyphon targets have design and operating characteristics which enables higher power operation than conventional boiling targets of like size. Experiments and calculations were performed in order to characterize the performance of a 1.3 cc tantalum [18F]Target. The test target led to the development of a variety of computational techniques as well as experimental methods that will be used in future target design and optimization. Computational methods include several applications of Monte Carlo Radiation Transport as well as Finite Element Analysis. In addition, experimental thermal hydraulic and radiochemical analyses were performed.
Numerical Methods for the Wigner-Poisson Equations
(2005-10-06) Lasater, Matthew; M. Shearer, Committee Member; R. H. Martin, Committee Member; C. T. Kelley, Committee Chair; D. L. Woolard, Committee Member; P. A. Gremaud, Committee Member
This thesis applies modern numerical methods to solve the Wigner-Poisson equations for simulating quantum mechanical electron transport in nanoscale semiconductor devices, in particular, a resonant tunneling diode (RTD). The goal of this dissertation is to provide engineers with a simulation tool that will verify earlier numerical results as well as improve upon the computational efficiency and resolution of older simulations. Iterative methods are applied to the linear and nonlinear problems in these simulations to reduce the computational memory and time required to calculate solutions. Initially the focus of the research involved updating time-integration techniques, but this switched to implementing continuation methods for finding steady-state solutions to the equations as the applied voltage drop across the device varied. This method requires the solution to eigenvalue problems to produce information on the RTD's time-dependent behavior such as the development of current oscillation at a particular applied voltage drop. The continuation algorithms/eigensolving capabilities were provided by Sandia National Laboratories' software library LOCA (Library of Continuation Algorithms). The RTD simulator was parallelized, and a preconditioner was developed to speed-up the iterative linear solver. This allowed us to use finer computational meshes to fully resolve the physics. We also theoretically analyze the steady-state solutions of the Wigner-Poisson equations by noting that the solutions to the steady-state problems are also solutions to a fixed point problem. By analyzing the fixed point map, we are able to prove some regularity of the steady-state solutions as well provide a theoretical explanation for the mesh-independence of the preconditioned linear solver.
Temporal and Pseudo-Temporal Numerical Integration Methods
(2002-10-28) Coffey, Todd Stirling; C. T. Kelley, Committee Member; C. S. Woodward, Committee Member; D. S. McRae, Committee Member; M. Shearer, Committee Member; P. A. Gremaud, Committee Member
Numerical methods for integrating partial differential equations are used in nearly every scientific field. In this dissertation we study two types of numerical integration methods, transient methods and pseudo-transient methods. Transient methods for partial differential equations look for time-accurate solutions that explain the evolution of the equation (although a steady state solution may evolve). Pseudo-transient methods look for steady-state solutions of partial differential equations while paying attention to the transient behavior to aid in stability. In contrast, root-finding methods, e.g. line-search methods, look only for a steady-state solution often not paying attention at all to the transient behavior of the problem. Pseudo-transient continuation is a method for solving steady state solutions of partial differential equations, and is used when traditional line-search methods fail to converge or converge to non-physical solutions. The method is a hybrid between implicit Euler and Newton's method where variable step-sizes are used to transfer from one method to the other. We demonstrate the performance of pseudo-transient continuation both numerically and theoretically on a variety of problems. We extend the global convergence theory, which currently covers a class of ordinary differential equations, to include a class of semi-explicit index-1 differential-algebraic equations. We also studied CVode, a transient code for solving nonlinear partial differential equations. In this work, we explain how CVode was extended to allow for a two-grid nonlinear solver. The two-grid solver coarsens a given mesh and solves the nonlinear problem on the coarse mesh, which is then moved back to the fine mesh for refining. This approach can be less expensive than computing the full nonlinear solution on the fine mesh. We explore some of the theoretical and computational issues involved in implementing this method for a radiative transfer problem as might be seen in stellar fusion.