lec25 - SMA-HPC 2002 MIT SMA-HPC 2002 MIT SMA-HPC 2002 MIT...

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SMA-HPC ©2002 MIT 3-D Laplace’s Equation First Kind Issues z Spike Function=1 on a disk 22 0 1 xy R σ= +≤ 2 00 0 1 2 ) 1 ( i R disk c dS rd R xx d r x r π θ σ = = ∫∫ 0 2 () 1 disk dS R x = Singular Kernel Case Smooth Kernel Case Smooth kernel 0 faster as 0, more singular R →→ 0 0 R +> The singular Kernel Saves the day
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SMA-HPC ©2002 MIT Convergence Analysis 3-D Laplace’s Equation Quick review of FEM Convergence for Laplace 2 uf i n ∇= Partial Differential Equation form 0 uo n is the volume domain is the problem surface Γ “Nearly” Equivalent weak form Introduced an abstract notation for the equation u must satisfy ( ) 1 for (,) ) ll ( a uv d x f v d x v H auv lv ΩΩ ∇∇ = ∫∫ 142 4 31 42 43 () = ( ) 1 for all vH
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SMA-HPC ©2002 MIT Convergence Analysis 3-D Laplace’s Equation Quick review of FEM Convergence for Laplace is a weighted sum of basis funct o in s n u The basis functions define a space 1 Introduce an approximate soluti n o n n ii i u
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This note was uploaded on 11/08/2011 for the course AERO 16.872 taught by Professor Danielhastings during the Fall '03 term at MIT.

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lec25 - SMA-HPC 2002 MIT SMA-HPC 2002 MIT SMA-HPC 2002 MIT...

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