Level Sets Method-numerical

Level Sets Method-numerical - 11/22/2011 1 Level Sets...

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Unformatted text preview: 11/22/2011 1 Level Sets Method Formulation and Numerical Implementation From Curve to Level Sets Method Curve evolution equation (?, ) ? = ¡ 0, = ¢ () In level set notation: So Plug in the curve evolution equation = the unit normal of , 11/22/2011 2 Curve Evolution in Level Set Method • Inward (always on your left-side) normal of u=0 : • So, we can write = − ∇? ∇? Boundary and Initial Conditions 11/22/2011 3 Hamilton-Jacobi Equation Back to the General Level Set Equation • Again, let denote the velocity on the curve (or surface). • Let ? ?, ¡, ¢ = 0 denote the implicit equation (in ¡ and ¢ , at (fixed) time ? ) curve. • Then the level set equation for the curve evolution is ? + ⋅ ∇? = 0 • In the previous example (for £ 2 ), = ( − ∇, ) . 11/22/2011 4 Numerical Discretization • Partition the space (x,y)-plane into grid points: • At time ?...
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This note was uploaded on 01/16/2012 for the course MAP 4371 taught by Professor Xli during the Fall '11 term at University of Central Florida.

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Level Sets Method-numerical - 11/22/2011 1 Level Sets...

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