In this paper we propose a method for the discretization of the parabolic p-Laplacian equation. In particular we use alternately either the backward Euler scheme or the Crank-Nicholson scheme for the time-discretization and the first order Finite Elements Method for space-discretization. To obtain the numerical solution we have to invert a block Toeplitz with Toeplitz blocks matrix. To this aim we use a Conjugate Gradient (CG) algorithm preconditioned by a block circulant with circulant blocks matrix. A Two-Dimensional Discrete Sine-Cosine Fast Transform is applied to invert the block circulant with circulant blocks matrix. The experimental results show how the application of the preconditioner reduces the iterations of the CG of about the 56%-75%.
A Preconditioned Finite Element Method for the p-Laplacian Parabolic Equation
GERACE, Ivan;PUCCI, Patrizia;
2004
Abstract
In this paper we propose a method for the discretization of the parabolic p-Laplacian equation. In particular we use alternately either the backward Euler scheme or the Crank-Nicholson scheme for the time-discretization and the first order Finite Elements Method for space-discretization. To obtain the numerical solution we have to invert a block Toeplitz with Toeplitz blocks matrix. To this aim we use a Conjugate Gradient (CG) algorithm preconditioned by a block circulant with circulant blocks matrix. A Two-Dimensional Discrete Sine-Cosine Fast Transform is applied to invert the block circulant with circulant blocks matrix. The experimental results show how the application of the preconditioner reduces the iterations of the CG of about the 56%-75%.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
