Preconditioning for diffusion problem with small size high resolution inclusions
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Yuri A. Kuznetsov
Abstract
In this paper, we propose and investigate a new preconditioning technique for diffusion problems with multiple small size high contrast inclusions. The inclusions partitioned into two groups. In the first group inclusions the value of diffusion coefficient can be very small, and in the inclusions of the second group it can be very large. The classical P1 finite element discretization is converted in the special algebraic saddle point system. The solution method combines elimination of the DOFs from the first group of inclusions with the Preconditioned Lanczos method with block diagonal preconditioner for the rest of the DOFs. Condition number estimates for the proposed preconditioner are given.
Acknowledgment
The author is grateful to V. K. Kramarenko for his assistance in the preparation of the paper.
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Artikel in diesem Heft
- Frontmatter
- The approach of ‘successive approximations over characteristic interactions’ for inverse problems of nuclear-geophysical technologies
- Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling
- Preconditioning for diffusion problem with small size high resolution inclusions
- Comparative analysis of vector algorithms for statistical modelling of polarized radiative transfer process
Artikel in diesem Heft
- Frontmatter
- The approach of ‘successive approximations over characteristic interactions’ for inverse problems of nuclear-geophysical technologies
- Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling
- Preconditioning for diffusion problem with small size high resolution inclusions
- Comparative analysis of vector algorithms for statistical modelling of polarized radiative transfer process
