Analysis of extrapolation cascadic multigrid method (EXCMG)

Abstract

Based on an asymptotic expansion of finite element, a new extrapolation formula and extrapolation cascadic multigrid method (EXCMG) are proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of triple grids, the error of the new initial value is analyzed in detail. A larger scale computation is completed in PC.

Cascadic multigrid methods combined with sixth order compact scheme for poisson equation

“…Based on a new extrapolation interpolation formula, Chen [10][11][12][13] proposed the following extrapolation cascadic multigrid method (EXCMG), in which new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. Numerical results show the advantage of EXCMG in comparison with CMG (see [12]).…”

“…Using the similar idea in [11], we design a new extrapolation interpolation formula based on the sixth order compact difference scheme (2.2), and also two extrapolation cascadic multigrid algorithms for solving the (2.3).…”

“…In order to obtain a better initial value, the quadratic interpolation and classical extrapolation are used by Li [9], instead of linear interpolation. In recent years, a new extrapolation formula and an extrapolation cascadic multigrid method (EXCMG) are proposed by Chen [10][11][12][13], in which new extrapolaiton and quadratic interpolation are used to provide a better initial value on the refined grid.…”

“…Based on Chen's works [10][11][12][13], we propose a new extrapolation interpolation operator with a sixth order compact different scheme. By using the new operator, we can obtain a better approximate value on fine grid level.…”

Time-Extrapolation Algorithm (TEA) for Linear Parabolic Problem

“…In recent years, we have proposed an extrapolation cascadic multi-grid method (EXCMG) [3,6] and a new extrapolation formula, which use a linear combination of the solutions on previous 2 level coarse meshes to provide a good initial value of finite element solution on nextlevel fine mesh. This method is of high accuracy and converges for both the function and its derivative.…”