Green Functions in Finite 数学工具 o Green第一公式 u(r)vou(r Vu·d∑ Vu·Vud 其中f(x)=f(x,02).d7=ddd=,∑是V的 边界面,并且规定外法线方向为正
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êÆóä Green1úª ZZZ V u(r)∇2 v(r)dr = ZZ Σ u∇v · dΣ − ZZZ V ∇u · ∇vdr Ù¥f(r) ≡ f(x, y, z), dr = dxdydz, Σ´V >.¡§ ¿ 5½ { C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 数学工具 o Green第一公式 / u(r)vu(r)dr /1mx-// VuL 其中f(r)≡f(x,y,x),dr= dcddl,∑是V的 边界面,并且规定外法线方向为正
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êÆóä Green1úª ZZZ V u(r)∇2 v(r)dr = ZZ Σ u∇v · dΣ − ZZZ V ∇u · ∇vdr Ù¥f(r) ≡ f(x, y, z), dr = dxdydz, Σ´V >.¡§ ¿ 5½ { C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 数学工具 Green第二公式 / (r)v2u(r)-v(r)v2u(r)dr uVu-Vu·d∑ 尜
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êÆóä Green1úª ZZZ V h u(r)∇2 v(r) − v(r)∇2u(r) i dr = ZZ Σ h u∇v − v∇u i · dΣ C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 基本步骤 V2G(r;r)=--6(r-r)×n(r)
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition Ä Ú½ ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) ×u(r) ∇2u(r) = − 1 ε0 ρ(r) ×G(r; r 0 ) ZZZ V u(r)∇2G(r; r 0 ) − G(r; r 0 )∇2u(r) dr = − 1 ε0 ZZZ V u(r)δ(r − r 0 ) − G(r; r 0 )ρ(r) dr C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 基本步骤 V2G(r;r)=-26(r-r)×v(r) Vdu(r ×G(r;r) lu(r)VG(r r)-G(:)Vu(r) dr G(: r)p(r)d
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition Ä Ú½ ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) ×u(r) ∇2u(r) = − 1 ε0 ρ(r) ×G(r; r 0 ) ZZZ V u(r)∇2G(r; r 0 ) − G(r; r 0 )∇2u(r) dr = − 1 ε0 ZZZ V u(r)δ(r − r 0 ) − G(r; r 0 )ρ(r) dr C. S. Wu 1Êù Green¼ê()