Raju Ram (COSSE student, double degree with Friedrich-Alexander University of Erlangen- Nurnberg)

Supervisor: Kees Vuik

Site of the project:

Deltares

Princetonlaan 6

3584 CB Utrecht

Supervisor Deltares: Jarno Verkaik

start of the project: October 2016

In March 2017 the Interim Thesis has appeared and a presentation has been given.

The Master project has been finished in August 2017 by the completion of the Masters Thesis and a final presentation has been given.

For working address etc. we refer to our alumnipage.

At Deltares, we are developing large groundwater models for our national and international customers (e.g. water boards, drinking water companies, municipalities, etc.) in order to simulate effects of changes by climate, such as drought, or effects induces by water managers, e.g. increasing pumping wells for drinkwater. The simulation code we use is MODFLOW, and this code is the worldwide standard for groundwater computation.

MODFLOW is a FORTRAN-77 code with extensions to FORTRAN-90 that originally dates from 1988 and is being developed by the United States Geological Survey (USGS). The current core version is MODFLOW-2005. It solves the groundwater equation for Darcy flow on a finite volume grid: if the problem is non-linear (e.g. by Cauchy boundary conditions such as rivers or drains) within each outer iteration a linear system is being solved. Typically the outer iteration is done by Picard iteration and the inner iteration by Conjugate Gradient. Currently, we are developing a new MODFLOW package (module), called Parallel Krylov Solver package together with the USGS and Utrecht University. Last year, we implemented PKS in the new MODFLOW-USG code, that is a spin-off code from MODFLOW that is being developed for unstructured grids. Subdomain partitioning is done with the METIS library in a straightforward manner. Furthermore, MODFLOW-USG can also run for structured grids and partitioning can be chosen as uniform in lateral direction or with the Recursive Bisection Algorithm. The PKS currently supports parallel MPI/OpenMP CG, BiCGSTAB and we are now working on a parallel version of GMRES. It uses an Restrictive Additive Schwarz overlapping parallel preconditioner, with a (preconditioning only) ILU/ICC subdomain solve.

More details on the results for 2015 can be found in: Parallel Solver Report.

For this year we plan to solve issues with the BICGSTAB solver and the rounding errors in the residual we are now encountering. We will also focus more on overlapping computations. Instead of the Indonesia model, we are also working on a parallel version of the global PCRGLOB model, that will consist of 58 subdomains, each representing a hydrologic stream region.

In the project the following steps can be done

- Optimize the interface transmission conditions between the subdomains for largely diagonal dominant groundwater flow, e.g. with optimized Schwarz. Now we have a Dirichlet transmission.
- Add a multi-level parallel preconditioner, e.g. coarse grid / deflation
- Add an iterative subdomain solve, e.g. a stationary method or Krylov subspace
- Optimize METIS of alternative (parallel) graph partitioning algorithm for partitioning of extremely large MODFLOW grids (> 1 billion cells)
- Optimize the CG algorithms to minimize (global) MPI communication; reordering updates