首页|A Wachspress-Habetler extension to the HSS iteration method in R~(n×n)
A Wachspress-Habetler extension to the HSS iteration method in R~(n×n)
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NETL
NSTL
Elsevier
In the study of implicit iterations for the two dimensional heat and Helmhotz equations, one constructs a splitting of the form A = U + V where U and V are the difference approximations parallel to the x and y axis, respectively. In the commutative case for U and V, several investigations have taken place. For the noncommutative case, a symmetric positive definite matrix F is found, such that UFV = VFU and then, the investigations use this to address the non-commutative nature of U with V. The purpose of this paper is to study the same problem type for the commutativity of H and S in the HSS splitting of A = H + S, where H and S are the symmetric and skew-symmetric parts of A, respectively. Although throughout the literature in C~(n×n), the H of HSS stands for hermitian, we use it in the symmetric matrix case. One then applies this result to the HSS iteration method. Since it is well known that the commutativity of U and V plays an important role in the analysis of ADI methods; especially for the solution of the Helmhotz Equation, one hopes that this commutativity will improve performance of the HSS method. This extension is similar to that of Wachspress and Habetler's variation of the Peaceman-Rachford method. Along the way, suitable conditions are found for A, which yield a symmetric non-zero matrix P = F~(1/2) for which N = PAP is a normal matrix.
Matrix splittingHSS iterative methodNormal matricesWachspress-Habetler type HSS iterative
Thomas Smotzer、John Buoni
展开 >
Department of Mathematics and Statistics, Youngstown State University, Youngstown, OH, USA
NETL
NSTL
Elsevier
