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Alfonso attended San Diego State University where he earned a Bachelor's degree in Mechanical Engineering in 1999. While an undergraduate, Alfonso conducted research in thermodynamics with Peter Salamon and materials science with Larry Thompson. In 2002, he earned a Master's of Science in Computational Science for his work on modeling biological fluid mechanics in arterioles. While working on his thesis, Alfonso was awarded the GAANN fellowship and moved to Los Angeles to study at Claremont |
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Graduate University. At CGU, Alfonso earned a second Master's degree in Applied Mathematics and is currently a Ph.D. candidate in Computational Sciences.
Alfonso is presently finishing his dissertation, A Generalized Multilevel Adaptive Solver for PDEs with Fast Transitions, under the auspices of the CGU Dissertation Grant. This research addresses the tracking of shocks and boundary layers, while minimizing the computational complexity of this task by utilizing a multi-resolution analysis in both space and time. Some of the major contributions of this project are:
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Embedding the MRA into a quadtree-list-structure, thus hiding multilevel details and stability conditions under a key array. |
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Using radial basis functions to compute function values and associated derivatives in a uniform MRA framework. |
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Development of a time-marching algorithm based on space-time RBFs. |
In addition to this research, which amounts to a third of his publications, Alfonso has also published ten other papers in various fields ranging from nano-electronics to artificial intelligence. |