Poisson eq and conjugate gradient method

February 25, 1999, 03:38

Hi,

I got some problems trying to simulate a Poisson equation in 2D with periodic boundary condition (for testing purpose). I use finite element discretization with bilinear functions on a regular mesh and I solve the equation with a conjugate gradient iterative solver. The solver doesn't seem to converge quickly. Is it expected and well known?

I am also looking for a preconditioner. Is it possible to find one which can be use on a element level without building the global matrix (and which is efficient of course)?

Thanks for help

Gary

February 25, 1999, 08:40

Oups I forgot to say that I impose a nodal value inside the domain.

March 19, 1999, 00:24

If the matrix (Ax=b) you finally have to solve is symmetric and positive definite, it will converge at any intial values of x0 (initially assumed approximate solution vector). And for a preconditioner, I think, Jacobi or SSOR can be used. And IC-CG, ILU-CG, MILU-CG have been reported to give more fast convergence. But the convergence rates depend on the matrix type you have to solve. So, at first, check the matrix you have to solve.

February 25, 1999, 03:38	Poisson eq and conjugate gradient method	#1
Gary Dantinne Guest Posts: n/a	Hi, I got some problems trying to simulate a Poisson equation in 2D with periodic boundary condition (for testing purpose). I use finite element discretization with bilinear functions on a regular mesh and I solve the equation with a conjugate gradient iterative solver. The solver doesn't seem to converge quickly. Is it expected and well known? I am also looking for a preconditioner. Is it possible to find one which can be use on a element level without building the global matrix (and which is efficient of course)? Thanks for help Gary

February 25, 1999, 08:40	Re: Poisson eq and conjugate gradient method	#2
Gary Dantinne Guest Posts: n/a	Oups I forgot to say that I impose a nodal value inside the domain.

March 19, 1999, 00:24	Re: Poisson eq and conjugate gradient method	#3
timea Guest Posts: n/a	If the matrix (Ax=b) you finally have to solve is symmetric and positive definite, it will converge at any intial values of x0 (initially assumed approximate solution vector). And for a preconditioner, I think, Jacobi or SSOR can be used. And IC-CG, ILU-CG, MILU-CG have been reported to give more fast convergence. But the convergence rates depend on the matrix type you have to solve. So, at first, check the matrix you have to solve.