Fast solvers for degenerated problems
In this paper, finite element discretizations of the degenerated operator -ω<sup>2</sup>(y) u<sub>xx</sub>-ω<sup>2</sup>(x)u<sub>yy</sub>=g in the unit square are investigated, where the weight function satisfies ω(&am...
| Summary: | In this paper, finite element discretizations of the
degenerated operator
-ω<sup>2</sup>(y) u<sub>xx</sub>-ω<sup>2</sup>(x)u<sub>yy</sub>=g
in the unit square are investigated, where the
weight function satisfies ω(ξ)=ξ<sup>α</sup>
with α ≥ 0.
We propose two multi-level methods in order to
solve the resulting system of linear algebraic
equations. The first method is a multi-grid
algorithm with line-smoother.
A proof of the smoothing property is given.
The second method is a BPX-like preconditioner
which we call MTS-BPX preconditioner.
We show that the upper eigenvalue bound of the
MTS-BPX preconditioned system matrix grows
proportionally to the level number. |
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