Wasif Khan
Tutor/Instructor
Department of Mathematics
Faculty of Science and Technology
Bachelor (Mathematics)
Numerical Linear Algebra and Its Applications
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| Official Email |
wasif.khan@vu.edu.pk |
| Contact |
+92 (42) 111 880 880 (Ext: -) |
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Wasif Khan was born on March 5, 1999, in District Lower Dir, Khyber Pakhtunkhwa. He received his early education in his ancestral village, laying a strong foundation for his academic journey. He earned his Bachelor's degree in Mathematics from the University of Peshawar in 2022. Continuing his pursuit of advanced studies, he completed his Master's degree in 2024 from the Abdus Salam School of Mathematical Sciences, Government College University, Lahore. Following the successful completion of his postgraduate studies, Mr. Khan joined the University of Engineering and Technology (UET), Peshawar, Jalozai Campus. Wasif Khan's research interests lie primarily in numerical algebra and its applications, with a particular focus on developing efficient preconditioners for Krylov subspace methods. He is also actively engaged in exploring modern computational techniques, including the application of Physics-Informed Neural Networks (PINNs) for solving differential equations. His work integrates classical numerical methods with contemporary machine learning approaches to address complex problems in scientific computing, such as modeling fluid flow through fractured media and analyzing both linear and nonlinear systems. He has been a part of the Virtual University of Pakistan since April 2025. |
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Category: - |
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COMPARATIVE ANALYSIS OF FINITE DIFFERENCE METHOD (FDM) AND PHYSICS-INFORMED NEURAL NETWORKS (PINNs).
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In this analysis, the solutions of the Linear and Non-Linear models are explored and compared using two distinct methods: the Finite Difference Method (FDM) and the Physics-Informed Neural Networks (PINNs). Initially, the solution is derived employing the principles of FDM, followed by solving the same problem using the methodology of PINNs. Subsequently, a comparative examination of the solution graphs with the exact solution is conducted.
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| Year:
2024 |
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Category: Q2 |
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Optimizing convergence: GMRES preconditioner for Darcy flow problem in a fracture network
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We suggest using a GMRES preconditioner to speed up the convergence of Krylov subspace methods for solving linear equations with a block structure. These types of equations commonly arise in unfitted finite element discretizations of the Darcy flow problem in a fracture network. We have thoroughly examined the spectrum of the preconditioned matrix to demonstrate its effectiveness. Additionally, we have conducted numerical experiments to highlight how well the preconditioners work with flexible-GMRES when solving linear equations from benchmark test problems.
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| Year:
2024 |
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