MATH 5620 CLASS PROJECT SUGGESTIONSNUMERICAL ANALYSIS II1. Project guidelines• It is possible to do projects in pairs. Please inform me about this beforeyou choose your project so that we can adjust the workload accordingly.• Two persons (or groups) can do the same project• A short talk (10-20min) where you will present your results to the class willbe part of your project grade (20% talk, 80% write up). The time for yourtalk is flexible, just let me know well in advance if you will need more time.• Please do keep me informed on the progress of your project.• Please do let me know by email when you have chosen a project.• You are strongly encouraged to come discuss the project with me, tomake sure you are on the right track and that we agree on the outcome ofthe project.2. Tentative Schedule• Choose a project by Fri 04/01 (but the earlier the better).• Project reports are due the last day of classes Wed 04/27.• Project presentations are on the last week of classes (04/25–04/27).3. Suggested class projectsThis is by no means an exclusive list. If you are interested in a particularapplication, we can figure out a numerical analysis project based on it. Don’t bethrown off by the name of the method, some of them are very simple. If you needany of the referenced books I own them and would be happy to lend them to you.Also the referenced papers are from journals that our university subscribes to. Letme know if you have problems obtaining them.1. A multigrid method for a 1D elliptic equation [2, 1].2. A domain decomposition method for a 1D elliptic equation.3. Comparison between P1 and P2 elements for solving the Laplace equation in1D.4. Model propagation of fire using the Eikonal equation [4] (longer, better adaptedfor two persons)5. A simple mesh generator: [3].6. Use a finite differences method for the viscous Burger’s equation:ut+ uux= uxx.7. Compare the ADI, LOD and Crank-Nicholson methods for solving the heatequation in 2D on the unit square.8. Implement the Chebyshev Spectral method for solving u00= f(x) [5, 2]9. Two dimensional advection-diffusion equation with a constant velocity field.12 MATH 5620 CLASS PROJECT SUGGESTIONS NUMERICAL ANALYSIS I I10. Use the singular value decomposition to solve an ill-posed linear inverse problem(e.g. deblurring [6]).4. Report and talkWhat I expect is that you identify the problem (why is the method used?), tellme how the method deals with the problem and show a (simple) implementationof the method. You have to convince me in your report that you have understoodthe method. For the talk you would present the method to the class in a way thatyour class mates should be able to understand and show some numerical results.References[1] William L. Briggs, Van Emden Henson, and Steve F. McCormick. A multigridtutorial. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,PA, second edition, 2000.[2] Randall J. LeVeque. Finite difference methods for ordinary and partial dif-ferential equations. Society for Industrial and Applied Mathematics (SIAM),Philadelphia, PA, 2007. Steady-state and time-dependent problems.[3] Per-Olof Persson and Gilbert Strang. A simple mesh generator in Matlab. SIAMRev., 46(2):329–345 (electronic), 2004.[4] J. A. Sethian. Level set methods and fast marching methods, volume 3 of Cam-bridge Monographs on Applied and Computational Mathematics. CambridgeUniversity Press, Cambridge, second edition, 1999. Evolving interfaces in com-putational geometry, fluid mechanics, computer vision, and materials science.[5] Lloyd N. Trefethen. Spectral methods in MATLAB, volume 10 of Software, Envi-ronments, and Tools. Society for Industrial and Applied Mathematics (SIAM),Philadelphia, PA, 2000.[6] Curtis R. Vogel. Computational methods for inverse problems, volume 23 ofFrontiers in Applied Mathematics. Society for Industrial and Applied Mathe-matics (SIAM), Philadelphia, PA, 2002. With a foreword by H. T.