Finite volume element (FVE) discretization and multilevel solution of the axisymmetric heat equation
By:  Eric T. Litaker
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1994
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 111
Description: The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed
Notes: Thesis advisor(s): David R. Canright,  V.E. Henson.

"December 1994."

Thesis (M.S. in Mathematics) Naval Postgraduate School, December 1994.

Includes bibliographical references.

Approved for public release; distribution unlimited.

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US Marine Corps (USMC) author.