Efficient solvers for incompressible fluid flows in geosciences

Abstract

Saddle point problems involving large systems of linear equations arise in a wide variety of applications in computational science and engineering. A variety of solvers have been developed for these type of problems typically with specific applications in mind. We focus on saddle point problems as they arise from incompressible fluid flow problems in geosciences. They are characterized through a spatially variable viscosity when modeling temperature dependencies (for example, in Earth mantel convection models) or moving material interfaces (for example, in subduction zones simulation and numerical volcano models). We overview some of the iterative techniques used and discuss suitable preconditioning techniques. We discuss the implementation of the schemes using the python module Escript and compare the efficiency of these schemes when applied to convection models on a parallel computer. References

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