On the superlinear convergence of PCG algorithms: Numerical experiments for convection-diffusion equations. (English) Zbl 1142.65432
Summary: The CGM is studied for nonsymmetric elliptic problems with both Dirichlet and mixed boundary conditions. The mesh independence of the convergence is an important property when symmetric part preconditioning is applied to the FEM discretizations of the boundary value problem. Computations in two dimensions are presented to illustrate the mesh independent superlinear convergence for convection-diffusion equations with both types of boundary conditions. Preconditioning by the leading term plus a zeroth-order term is also investigated in the aspect of superlinear convergence through numerical computations.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
conjugate gradient method; symmetric part preconditioning; mesh independence; superlinear convergence; numerical experimentsReferences:
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