Master of Science in Mathematics
Department of Mathematical Sciences
Date of Award
Dr. Hashim bin Zubair
Committee Member 1
Dr. Mehfooz ur Rehman, NESCOM, Islamabad
Committee Member 2
Dr. Abdul Hanan Sheikh, QUEST, Nawabshah
Committee Member 3
Dr. Junaid Alam Khan, Institute of Business Administration, Karachi
Geometry, Mathematics, Mathematical Analysis
Multigrid method belong to the class of methods that are used for numerical solution of discretized differential equations with superior performance. Multigrid methods were specifically designed for the solution of discretized elliptic Partial Differential Equations earlier. The method was later broaden in different ways to handle other Equations earlier. The method was later broaden in different ways to handle other PDE problems, including nonlinear ones, as well as problems not modeled by PDEs. Multigrid methods use relaxation schemes to damp the high frequency eigenvalues, we use a modified relaxation scheme RUB-Jacobi as our core relaxation scheme. The discussion is broaden to the variable coarsening and comparing them with the standard ones. To achieve accuracy complete Local Fourier Analysis have been established for two Dimensions for a tripling case. In the end complete performance analysis is given with the help of suitable experiments. These experiments are extended to d dimension.
Ashraf, M. S. (2015). Geometric mutigrid method with variable grid coarsening parameters, optimal parameters, analysis, and experimentation (Unpublished master's thesis). Institute of Business Administration, Pakistan. Retrieved from https://ir.iba.edu.pk/etd/53
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