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Solving Methods

##
4.6.1 Solver

The analysis by the equation system analyzer leads to a set
of linear equation systems that are usually filled sparsely. To solve these
systems AMIGOS is equipped with a direct and iterative solver taken from
the development libraries [Hal93].
The direct solver uses the Gaussian elimination method
[Lee68]
and should be used for badly conditioned systems. The disadvantage of this
method is the immense amount of memory (*O*(*N*^{2}))
and operation count for inversion (*O*(*N*^{3})) that
is unacceptable for simulations in three dimensions. Therefore it is advisable
to use the implemented iterative solver which is based on the stabilized
biconjugate gradient method (BiCGStab [vdV81])
using an incomplete LU factorization [Saa90]
and an auto scaling algorithm[Fis94b].

**Next:**4.6.2
Time Discretization**Up:**4.6
Solving Methods**Previous:**4.6
Solving Methods
*Mustafa Radi*

*1998-12-11*