Send me a message if you are interested in any of my research works. My Research Interests are :
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• Discontinuous Galerkin Methods​ : Unlike traditional Continuous Galerkin (cG) methods that are conforming, the Discontinuous Galerkin (dG) method works over a trial space of functions that are only piecewise continuous, and thus often comprise more inclusive function spaces than the finite-dimensional inner product subspaces utilized in conforming methods. dG schemes are complex in their implementations and have several applications in hyperbolic problems.

 

• Isogeometric Analysis : As a recently developed computational approach, it offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based Computer Aided Design (CAD ) tools. Isogeometric Analysis (IGA) allows models to be designed, tested and adjusted in one go, using a common data set. The fundamental theories have been presented by Hughes et al. (2005) and competes strongly with FEM in several applications especially because it is an High Order scheme. 

 

• Surface Partial Differential Equations : The discretization of PDEs on surfaces started with the use of surface finite elements to compute solutions to the Poisson problem for the Laplace–Beltrami operator on a curved surface proposed and analysed in Dziuk (find paper here). The important concept is the use of triangulated surfaces on which finite element spaces are constructed and then used in variational formulations of surface PDEs using surface gradients. My research interest involves using Isogeometric Analysis (IgA) which have better approximation properties especially with regards to representation of surfaces for discretization. 

 

• Space-Time Methods​ : This approach to ​discretizing time-dependent problems is considered to be a natural way of numerical discretization for problems requiring deforming and moving meshes. The space-time schemes allow for discretization in time and space simultaneously and are also applicable even for unstructured meshes. Here, the time variable is also considered as just another spatial variable. In this sense, the time derivative acts as a strong convection term in the direction of the new spatial variable. In this direction, we use Isogeometric Analysis (IGA) and FEM to present new ideas on solving time-dependent problems.

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• Mathematical Epidemiology : The understanding of the transmission dynamics of infectious diseases has been well-studied and researched in mathematics. These mathematical models have played a major role in increasing the understanding of the underlying mechanisms which influence the spread of diseases and provide guidelines as to how the spread can be controlled. Here, we have studied the transmission dynamics of several epidemiological models including Fractional, stochastic, PDE models.

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• Optimal Control Methods:  Here, so far, we have studied and analyzed the optimal control of Mathematical epidemiology models. By using sensitivity analysis, we are also able to determine the economic value of each strategy used in the control.