Conjugate gradient method for dual-dual mixed formulations |
| |
Authors: | Gabriel N. Gatica Norbert Heuer. |
| |
Affiliation: | GI$^2$MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. ; GI$^2$MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. |
| |
Abstract: | We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, the conjugate gradient method with this special inner product can be used as iterative solver. For a model problem, we propose a preconditioner which leads to a bounded number of CG-iterations. Numerical experiments for our model problem confirming the theoretical results are also reported. |
| |
Keywords: | Mixed finite elements dual-dual variational formulation conjugate gradient method |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
|
点击此处可从《Mathematics of Computation》下载全文 |
|