Locally Optimized MIC(0) Preconditioning of Rannacher-Turek FEM Systems
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چکیده
In this paper Rannacher-Turek non-conforming rotated bilinear finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for the iterative solution of the arising linear algebraic system. A locally optimized construction for an M-matrix approximation of the global stiffness matrix is the first step of the proposed algorithm. Then, the preconditioner is obtained by modified incomplete Cholesky factorization (MIC(0)) of the auxiliary M-matrix. Three different approaches for the construction of such matrices are presented. The related spectral condition number estimates are derived. Among the most important contributions of the paper is the clarified role of the skewed meshes for strongly anisotropic problems. A set of numerical tests is presented to illustrate the theoretical investigations. key words: non-conforming FEM, incomplete factorization, element preconditioning, symbolic techniques
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تاریخ انتشار 2007