s*****d
发帖数: 1 | 1 call grad = gradient (nabla character in latex),
grad^2 = laplacian
A diffusion equation is
u_t = grad^2 u
= div grad u (1)
Various papers generalize this to oriented diffusion. They all write
u_t = div( g(|grad(u)|) grad u ) (2)
where g() is a function that guides/orients the diffusion, such as
one that fallos off where the edge strength |grad(u)| is high.
My question: is it true that (2) is equivalent to
u_t = g(|grad(u)|) g | x*****d
发帖数: 427 | 2 div 是微分算子，不能跟函数交换，要遵循 Leibniz 法则
div( f grad u) = grad f * grad u + f grad^2 u
【在 s*****d 的大作中提到】
: call grad = gradient (nabla character in latex),
: grad^2 = laplacian
: A diffusion equation is
: u_t = grad^2 u
: = div grad u (1)
: Various papers generalize this to oriented diffusion. They all write
: u_t = div( g(|grad(u)|) grad u ) (2)
: where g() is a function that guides/orients the diffusion, such as
: one that fallos off where the edge strength |grad(u)| is high.
: My question: is it true that (2) is equivalent to
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