Math 690N

Advanced Numerical Methods 

Tentative Course Plan

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Part I Domain Decomposition Method (DDM) --- by Steven Hou

Week 1—Week 7,   08/22-10/06

Part II Level Set Method (LSM) --- by Hailiang Liu

Week 8   10-14  October
10/11 --- Implicit surfaces, representation of interfaces
10/13 --- geometry and level set tools

Week 9  17-21  October
10/18 --- Signed distance function, adding dynamics
10/20 --- Motion involving mean curvature

Week  10  24-28  October
10/25 --- Motion in Normal direction and extrapolation
10/27 ---  Reconstruction of Distance function 

Week 11 31-04  October--November
11/01 --- HJ equations + Algorithms
11/03 ---  Codimension-two objects

Week 12 07-11 November
11/08--- Efficient schemes
11/10 --- Extension of physical quantities

Week 13  14-18  November
11/15 --- Applications---Geometry
11/17 ---  Image Enhancement and Noise removal

22-26 November   *** Thanksgiving Break ***

Week 14  28 November ---02 December
11/29 --- Computer Vision
12/01 --- Computation of multi-valued solutions

Week 15 05 - 09  December
12/06 --- High frequency waves
12/08 --- Semi-classical limit

Final Week  12-- 16   December  TBA.