{"id":23,"date":"2020-10-14T13:05:56","date_gmt":"2020-10-14T13:05:56","guid":{"rendered":"http:\/\/blogs.uakron.edu\/aaristot\/?page_id=23"},"modified":"2023-11-25T13:56:58","modified_gmt":"2023-11-25T13:56:58","slug":"research","status":"publish","type":"page","link":"https:\/\/blogs.uakron.edu\/aaristot\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n
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My research interests are focused on the development<\/em>, theoretical analysis<\/em> and implementation<\/em> of efficient algorithms in view of their application to the simulation of problems of practical interest. My specialty is on Discontinuous Galerkin Finite Element Methods<\/a> (DG-FE) methods for the numerical solution of partial differential equation (PDE) problems and applications. Specifically, I am interested in the development and analysis of high order numerical schemes that accurately and efficiently resolve the solution\u00a0to non linear equations like Cahn-Hilliard<\/a> type equations, arising in models describing biological growth e.g. cancerous tumors<\/em> and phase separation. Adaptive mesh refinement<\/a>, (theoretical) error analysis and energy stability via convex splitting are also being addressed in my work. For the solution of the resulting algebraic (nonlinear)\u00a0systems efficient solvers based on multigrid<\/a> are designed. Recently the development and application of machine learning methods<\/em> for the numerical solution of partial differential equations is an interesting aspect of my work.<\/figure>\r\n<\/div>\n\n\n\n

The development of hybrid discrete cellular automata systems<\/em> (HD-CA) by coupling linear and non-linear reaction diffusion partial differential equations with discrete (stochastic) cellular automata<\/a> systems is also a part of my work. I utilize hybrid discrete systems to derive constitutive relationships and study phenomena in biology specifically biofilm, cancer, tissue engineering, virus dynamics modeling<\/em>, and evolutionary game theory<\/em>.<\/p>\n\n\n\n

I am looking for motivated students with love for mathematics that are interested in doing research. Ask me for more details!!<\/strong><\/em><\/p>\n\n\n\n

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External Funding<\/h2>\r\n