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3.2.1 Boundary Conditions Dirichlet Problem ur()=on =- Fo(arier Neumann Problem r(a) a mz=m1如mF|- a(x)drx∈r Neumann Problem generates Hypersingular Integral 3.2.2 Dirichlet Problem 2nd Kind SLIDE 13 dur(E) (x) 3.2.3 Radiation Condition SLIDE 14 nr‖-‖ d→O(引-2) Add Extra Term to slow decay 0 4 Greens Theorem Approach 4.1 Green's Second Identity SLIDE 15 Aluon-uomarl Easy to implement any boundary conditions3.2.1 Boundary Conditions Slide 12 Dirichlet Problem uΓ(x) = Γ ∂ ∂nx 1 x − x σ(x )dΓ x ∈ Γ Neumann Problem ∂uΓ(x) ∂nx = ∂ ∂nx Γ ∂ ∂nx 1 x − x σ(x )dΓ x ∈ Γ Neumann Problem generates Hypersingular Integral 3.2.2 Dirichlet Problem 2nd Kind! Slide 13 ∂uΓ(x) ∂nx = 2πσ(x ) + Γ ∂ ∂nx 1 x − x σ(x )dΓ 3.2.3 Radiation Condition Slide 14 limx→∞u(x) = Γ ∂ ∂nx 1 x − x σ(x )dΓ → O(x−2) Add Extra Term to slow decay u(x) = Γ ∂ ∂nx 1 x − x σ(x )dΓ + αG(x∗) x∗ Ω 4 Green’s Theorem Approach 4.1 Green’s Second Identity Slide 15 Ω u∇2w − w∇2u dΩ = Γ w ∂u ∂n − u ∂w ∂n dΓ Now let w = 1 x−x 2πu(x) = Γ 1 x − x ∂u ∂n − u ∂ ∂nx 1 x − x dΓ Easy to implement any boundary conditions! 4