  Extreme and isolated eigenvalues are known to be harmful to the convergence
of an iterative solver. These eigenvalues can be produced by strong
heterogeneity in the underlying physics. We can improve the quality of the
spectrum by "deflating" the harmful eigenvalues. In this work, deflation is
applied to linear systems in reservoir simulation. In particular, large, sudden
differences in the permeability produce extreme eigenvalues. The number and
magnitude of these eigenvalues is linked to the number and magnitude of the
permeability jumps. Two deflation methods are discussed. Firstly, we state that
harmonic Ritz eigenvector deflation, which computes the deflation vectors from
the information produced by the linear solver, is unfeasible in modern
reservoir simulation due to high costs and lack of parallelism. Secondly, we
test a physics-based subdomain-levelset deflation algorithm that constructs the
deflation vectors a priori. Numerical experiments show that both methods can
improve the performance of the linear solver. We highlight the fact that
subdomain-levelset deflation is particularly suitable for a parallel
implementation. For cases with well-defined permeability jumps of a factor 104
or higher, parallel physics-based deflation has potential in commercial
applications. In particular, the good scalability of parallel
subdomain-levelset deflation combined with the robust parallel preconditioner
for deflated system suggests the use of this method as an alternative for AMG.
