报告题目：Space-time localized radial basis function collocation method for solving parabolic and hyperbolic equations without/with variable coffecients
报 告 人:Prof. Ahmed Naji (Faculty of Sciences and Techniques in Tangier)
A radial basis collocation method, to solve parabolic and hyperbolic equations with/without variable coefficients, based on the local space-time domain formulation is developed and presented in this paper. The method is different from those that approximate the time derivative using different formulas such as the implicit, explicit, method of lines, or other numerical methods. Considering a partial differential equation with d spatial dimensions, our technique solves the problem as a (d+1)-dimensional one without distinguishing between space and time variables, and the collocation points have both space and time coordinates. The parabolic equation is solved using the governing domain equation as a condition on the boundary characterized by the final time T. The hyperbolic equation is solved using two different methods. The first one is based on adapting the technique used for solving parabolic equations. The second one is a new technique that looks at the problem as an ill-posed one with incomplete boundary condition data at the final time T of the space-time domain. The accuracy of our proposed method is demonstrated through different examples in one-, two- and three-dimensional spaces on regular and irregular domains. A comparison to Rang-Kutta method is investigated.
Prof. Ahmed Naji started as Assistant professor at Department of Mathematics in Faculty of Sciences and Techniques in Tangier since 1995 and becoming a Full Professor since 2002. Prof. Ahmed Naji held master degree in applied mathematics from Faculty of Sciences in Rabat, Morocco and Master of Philosophy in applied Mathematics and fluid mechanics from Portsmouth University in UK. In 1998 Prof. Ahmed Naji have got PhD degree from Mohammadia School on Engineering in Rabat, Morocco in collaboration with Delaware University in USA under the Fulbright joint research program. Prof. Ahmed Naji has been involved in many scientific researches related to my scientific background. His research interest was focused on numerical methods specially deterministic and stochastic boundary element method to solve free boundary value problems arising in the in fluid flow and solute transport in porous media and specially the localization of interface in the saltwater intrusion into coastal aquifer. Prof. Ahmed Naji has extensive experiences in the area of optimization techniques and their application to engineering problems. Prof. Ahmed Naji have published many articles in the coupling of the optimization techniques and numerical methods with the collaboration of my group of researches in Mohammadia School of Engineering in Rabat, Morocco. The major publication of the group was focused on the problem of saltwater intrusion into coastal aquifer. Currently, He is working on both the theoretical and computational aspects of meshless numerical methods which are based on the use of the radial basic functions. Its coupling with the domain decomposition formulation and its application to fluid flow problem were also studied. Other investigation of the application of the method to environmental problems, specially the transport and dispersion-diffusion of the pollutant into groundwater aquifer was a part of my investigation. Recently, He is also interested in further development of the technique for modelling saltwater intrusion into coastal aquifer.