Basic Information
Multigrid Methods For Problems With Many Variables, Especially Numerical Solution of Elliptic Partial Differential Equations. The Motivation and Applications Are From Various Fields of Scientific Computing, Including Image Processing and Analysis. Basic Concepts, Local and Global Processing, Discretization,1d Model Problem and Its Direct and Iterative Solution, Convergence Analysis, 2d Model Problem, Survey of Classical Relaxation Methods. Error-smoothing By Relaxation, Grid-refinement Algorithm, Two-grid and Multigrid Algorithm, Fourier Analysis of Convergence, Ellipticity and H-ellipticity, Nonlinear And Anisotropic Problems, Advanced Techniques, Algebraic Approach, Applications. Learning Outcomes# After Completing The Course, The Student Wil Be Able To# 1. Discern Between Global and Local Processing. 2. Define and Discern Between Discretization Errors, Algebraic Errors And Rounding Errors. 3. Discern Between Smoothing and Reduction of Algebraic Error. 4. Adapt (by Programming) a Given Multigrid Code to Various Problems And Components, Including Nonlinear Problems. 5. Define and Compute The Smoothing Factor and H-ellipticity Measure, Using Fourier Analysi. 6. Solve Example Problems With Multigrid and Analyze The Efficiency Of The Solver.
Faculty: Computer Science
|Graduate Studies
Pre-required courses
234107 - Numerical Analysis 1 or 234125 - Numerical Algorithms