Research

I am interested in iterative solvers and preconditioners for large, sparse linear systems of equations that arise in the discretization of partial differential equations. Specifically, I am interested in multigrid methods that can be applied when geometric coarsening is challenging or impossible, i.e., in flow simulations in complex pore-scale rock geometries.

My work is centered around the development, implementation, and performance evaluation of p-multigrid methods, their combination with other multigrid methods and iterative solvers, and their application to pore-scale flow simulations for hydrocarbon recovery.

My other interest include numerical methods for partial differential equations (mostly elliptic and parabolic PDEs) and the applications of mathematics in oil and gas exploration and production.

I am also interested in the application of software engineering techniques in the design and development of scientific software.

CPHIS

I implemented several p-multigrid methods in a software package called CPHIS, which is available as open source software here.

CPHIS can be used as a stand-alone linear solver or as a hybrid parallel (MPI+OpenMP) solver with Trilinos' Tpetra package. CPHIS' modular design allows for the easy integration of other linear algebra and solver frameworks, such as PETSc, MueLu, or AMGX, with little coding effort.