Nonoverlapping domain decomposition method with preconditioner from asymptotic analysis of steady flow in high contrast media

ABSTRACT

We present a nonoverlapping domain decomposition method for steady flow in high contrast heterogeneous media modelled by an elliptic equation with coefficients that have very large amplitude variations on a small spatial scale. The linear system of equations resulting from matching the solution trace and the fluxes through the boundary of the subdomains is ill-conditioned, especially for fine meshes needed to capture the rapid variations of the solution. Our main contribution is to show with analysis and numerical simulations how to use an asymptotic approximation of the Dirichlet to Neumann map of the sub-domain problems to obtain a preconditioner for an efficient domain decomposition algorithm.

Keywords:

• preconditioner
• domain decomposition method
• asymptotic analysis
• high contrast media
• nonoverlapping

2010 Mathematics Subject Classifications:

• 65N08
• 65N20
• 65N55

Acknowledgements

LB acknowledges support from AFOSR award FA9550-18-1-0131 and the U.S.Office of Naval Research award N00014-17-1-2057.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

LB acknowledges support from AFOSR award FA9550-18-1-0131 and the U.S. Office of Naval Research award N00014-17-1-2057.