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UBC Theses and Dissertations

An experimental study of the incomplete Cholesky factorization for the anisotropic diffusion equation Beauchamp, Austin


We consider the numerical solution of large and sparse linear systems arising from a finite difference discretization of the anisotropic diffusion equation. We study preconditioned conjugate gradient as an iterative solver, with the incomplete Cholesky factorization as a preconditioner. The incomplete Cholesky factor is created using two different dynamic dropping parameters: a drop tolerance to control the magnitude of included values, and a fill factor to control the memory allocation/usage of the factor. For large matrices, we show that certain drop tolerances will achieve optimal results with a controllable amount of memory usage. Our numerical experiments are based on a fast C code that has been written as part of this research project, and which uses an asymptotically optimal version of the Cholesky factorization as its base. We illustrate our findings on linear systems of dimensions up to ten million degrees of freedom.

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