In the course of my professional career, I have transformed distinctive intricate concepts in mathematics, applied physics or technological phenomena into computer languages: C, FORTRAN, MATLAB, and PYTHON. Last, but not least, I am capable of implementing high-performance computing such as Message Passage Interface (MPI) or OpenMP.
It excites me to deal with numbers and implement distinctive algorithms to process them.
In this project, I succeeded in resolving 2D Heat/Diffusion equation via implementing both parallel and sequential algorithms. The entire project was conducted under the supervision of Professor Dr. Vassilios Alexiades, at the Department of Mathematics, the University of Tennessee.
The Partial Differential Equation was discretized via finite difference method and the evolution of diffusion or heat conduction phenomena in the presence/absence of convection transport was explored via implementing both parallel and sequential algorithms.
The results were interpreted in terms of the efficiency of the parallel algorithm by changing the number of the CPUs and allocation of the jobs in the course of parallel algorithms and mainly Message Passage Interface. The findings help to decipher the effect of physical parameters on the diffusion process in physicochemical and biological systems. Moreover, from the computational viewpoint, we could identify the stability of the numerical solution in terms of the discretization and magnitude of the geometrical or physical parameters involved.
*Professor Vassilios Alexiades is an applied mathematician and computational scientist at the Mathematics Department of The University of Tennessee. His works spans across diverse fields, including modeling, analysis, and computation of realistic physical processes in scientific and technological problems arising in biological, materials, energy, and environmental applications, where conservation laws (expressing conservation of energy/mass/momentum) come to play the main role, and mathematically, they are considered as nonlinear systems of Partial Differential Equations.
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QR factorization/decomposition is a method for constructing an orthogonal set of vectors of an initial set of vectors. It is an efficient way to resolve systems of linear equations and in numerical analysis, distinctive decomposition methods are applied to implement efficient matrix algorithms. There are several methods to conduct QR decomposition, and QR decomposition via Gram-Schmidt stands as one of the ubiquitous ones.
In the project under the supervision of Professor Jack Dongarra at the Computer Science Department of the University of Tennessee, I implemented the sequential and parallel algorithms to resolve QR decomposition via the Gram-Schmidt method and compared the different algorithm in terms of efficiency. As a further step, I compared the results with the Scalable Linear Algebra Package (ScaLAPACK) outputs.
My findings demonstrated that ScaLAPACK subroutine outputs reveal the best t performance. Moreover, the parallel algorithm, where I used the Message Passaging Interface (MPI) method, exhibits both better performance and efficiency compared to the sequential algorithm. I utilized the GFlops versus matrix size, Norm-Matrix size, GFlops versus Number of
Processors, and several other measures for confirming our results.
*Professor Jack Dongarra is a Distinguished Professor at the University of Tennessee and founder of several software packages and systems such as Basic Linear AlgebraN Subprograms (BLAS), Linear Algebra Package (LAPACK), Message Passing Interface (MPI) or MATLAB. Professor Jack Dongarra has been selected by the Institute of Electrical and Electronics Engineers Computer Society as its 2020 Computer Pioneer Award winner.
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The emergence of turbulence in the absence of inertial forces has been observed in particular known as Boger fluids polymer solutions, where the high molecular weight polymer is dissolved in a high viscous solvent. However, it is essential to distinguish purely elastic turbulence from thermo-elastic turbulence.
One of my main projects at the University of Tennessee and at the leading computational rheology group of “Material Research And Innovative Laboratory” under the supervision of Professor Dr. Bamin Khomami led to decoupling thermo-elastic instabilities from purely elastic modes in Boger fluid and in Taylor-Couette flow system, which can be extrapolated to several other types of complex fluids.
I applied linear stability analysis combined with pseudo-spectral discretization numerical methods to resolve a complicated set of Navier-Stokes equations in the presence of viscoelastic stresses in conjunction with thermal effects. Distinctive modes of instability were analyzed as a function of the physical properties of the complex fluid and the geometrical features of the flow system. My findings led to an improved understanding of the onset of instability in complex fluids, leading to a thermo-ealstic turbulence, exhibiting a broad range of spatial and temporal scales. Moreover, the reduction in critical Weissenberg number (Wic) is observed as the gap ratio and fluid thermal sensitivity is enhanced.
*Professor Bamin Khomami is a Distinguished Professor and Head of Chemical & Biomolecular Engineering at the University of Tennessee (UT). He is also the director, of Sustainable Energy Education & Research Center (SEERC) while holding the professorship position at the Department of Mechanical, Aerospace & Biomedical Engineering at UT. He is one of the leading scientists in the field of Structure, Dynamics and Rheology of Complex Fluids and Soft Matter and Processing Science of Micro- and Nano-Structured Material.
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