LAPLACE OPERATOR.ppt [Lecture seule]

Laplace operator (spatial domain)The Laplace operator is defined by:In the discrete case:wherexy2 2 2xy∂ff2 22∇ f ≡ +2 2∂x∇ f(i,j) ≡∆ f(i,j) +∆ f(i,j)∆ f(i,j) ≡ f(i,j) −f(i−1,j)∆ f(i,j) ≡ f(i,j) −f(i,j−1)∆ f(i,j) ≡ ∆ f(i+ 1,j) −∆ f(i,j)2x x x2y∂∂y[ f(i 1,j) f(i,j) ] [ f(i,j) f(i 1,j) ]≡ + − − − −≡ f(i+ 1,j) + f(i−1,j) −2f(i,j)∆ f(i,j) ≡ f(i,j+ 1) + f(i,j−1) −2f(i,j)