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Volume 21, Issue 2
Explicit Bounds of Eigenvalues for Stiffness Matrices by Quadratic Hierarchical Basis Method

Sang Dong Kim & Byeong Chun Shin

J. Comp. Math., 21 (2003), pp. 113-124.

Published online: 2003-04

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  • Abstract

The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to $Lu := - u'' $ with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like $O(\frac{1}{h})$ where $h$ is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to $O(1)$.

  • Keywords

hierarchical basis, multilevel.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-113, author = { Sang Dong Kim and Byeong Chun Shin }, title = {Explicit Bounds of Eigenvalues for Stiffness Matrices by Quadratic Hierarchical Basis Method}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {2}, pages = {113--124}, abstract = {

The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to $Lu := - u'' $ with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like $O(\frac{1}{h})$ where $h$ is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to $O(1)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8874.html} }
TY - JOUR T1 - Explicit Bounds of Eigenvalues for Stiffness Matrices by Quadratic Hierarchical Basis Method AU - Sang Dong Kim & Byeong Chun Shin JO - Journal of Computational Mathematics VL - 2 SP - 113 EP - 124 PY - 2003 DA - 2003/04 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8874.html KW - hierarchical basis, multilevel. AB -

The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to $Lu := - u'' $ with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like $O(\frac{1}{h})$ where $h$ is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to $O(1)$.

Sang Dong Kim and Byeong Chun Shin . (2003). Explicit Bounds of Eigenvalues for Stiffness Matrices by Quadratic Hierarchical Basis Method. Journal of Computational Mathematics. 21 (2). 113-124. doi:
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