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Title: Solving the photon diffusion equation by FEM with Lanczos Algorithm 
Author: Nie, Sixiang
Date: 2003-05
Publisher: University of Hawaii at Manoa
Abstract: In this thesis, finite element method (FEM) with Lanczos algorithm under uniform-grid and multi-grid meshes, denoted as FEML-U and FEML-M algorithms respectively, are introduced to solve the photon diffusion equation. In FEML-U and FEML-M algorithms, an n-dimensional state-space system is established by FEM, and the output of this system is approximated by that of an m-dimensional reduced system, which is generated by Lanczos algorithm. The implementations of FEML-U and FEML-M algorithms simulate the output at detectors of two given organ-size phantoms, and the corresponding simulators are validated. It is shown that the space and time complexities of FEML-U and FEML-M simulators are about O(n) and O(m*n) respectively. Compared to the uniform-grid alternating direction implicit algorithm (ADI-U), it is demonstrated that FEML-U simulations to the given organ-size phantoms are more than 50 times faster. Furthermore, without essentially losing accuracy, FEML-M simulations use at most 30% of space and 75% of time of FEML-U simulations.
Description: xi, 69 leaves
URI: http://hdl.handle.net/10125/6985
Rights: All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.

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