Preconditioning of elliptic problems by approximation in the transform domain
The numerical solution of second-order elliptic boundary value problems is examined. Using finite differences or finite elements, such problems generally are reduced to linear systems of the form \(Ax=b\), where \(A\) is a symmetric and positive definite sparse matrix. The author views the matrix \(A\) as an image and constructs the transform based preconditioner by using the low frequency components of the transformed matrix. The smooth coefficients of the given elliptic operator can be approximated well by the low-rank matrix. Numerical results are reported to show the effectiveness of the methodology.
second-order elliptic boundary value problems
scientific article; zbMATH DE number 1117814