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The new Parallel Krylov Solver package
Jarno Verkaik (Deltares)
Joseph Hughes (USGS)
Edwin Sutanudjaja (UU)
Oliver Schmitz (UU)
Paul van Walsum (Alterra WUR)
Raju Ram (TUD)
1 November, 2016
Contents
• Problem statement and solution
• Short overview of (related) developments
• Concept of domain decomposition
• (Preliminary) results
• Practical usage with iMOD
Cartesius: the Dutch supercomputer
Problem statement and solution
Problem statement:
• In order to support decision makers in solving hydrological problems,
detailed high resolution models are often needed.
• These models typically consist of a large number of computational cells
and have large memory requirements and long run times.
Solution:
• An efficient technique for obtaining realistic run times and memory
requirements is parallel computing, where the problem is divided over
multiple processor cores.
1 November, 2016
Short overview of developments
2010 ----- Deltares develops parallel MT3DMS using Message Passing Interface.
2012 ----- USGS develops parallel U(nstructured)PCG-solver using OpenMP.
2013 ----- Deltares & USGS start working on new Parallel Krylov Solver package
for MODFLOW-2005 based on UPCG (hybrid, combined MPI/OpenMP).
2013 ----- USGS releases MODFLOW-USG (UnStructured Grid) that includes the
PCGU-solver, a derivative solver of UPCG.
2015 ----- Deltares incorporates PKS in MODFLOW-USG. Cases: Indonesia and global.
2016 ----- Deltares incorporates PKS in iMODFLOW, together with Alterra for
MetaSWAP. Main case: Netherlands Hydrological Model.
2017 ----- Deltares releases iMODFLOW with PKS.
2017 ----- Deltares incorporates PKS in iMOD-SEAWAT. Cases: fresh-salt global Deltas.
(2017+---- Deltares & USGS incorporate PKS in new MODFLOW-6.)
1 November, 2016
• Distribute the memory over multiple
(connected) processor cores.
• For this, partitionize the MODFLOW grid:
• iMODFLOW: uniform blocks,
Recursive Coordinate Bisection
• MODFLOW-USG: METIS library
Concept of domain decomposition (1/3)
1 November, 2016
Example
MODFLOW-USG
METIS
Example
iMODFLOW
“uniform”
Example
iMODFLOW
RCB
• Distribute the linear system Ah = b over
the partitions, where h is the groundwater
head to be solved.
• Connect the partitions tightly through MPI,
using an overlap for exchanging data.
• Solve this system in parallel with exactly
the same accuracy as for the serial case.
• Krylov-Schwarz domain decomposition:
• Restricted Additive Schwarz
parallel preconditioner:
• Applied to CG/GCR Krylov methods
• Inaccurate subdomain solve: ILU only
• Dirichlet transmission condition
Concept of domain decomposition (2/3)
1 November, 2016
www.ddm.org
Example structure additive
Schwarz preconditioner M
Concept of domain decomposition (3/3)
1 November, 2016
Results iMODFLOW: NHM (1)
1 November, 2016
• Netherlands Hydrological Model for drought simulation
• iMODFLOW-MetaSWAP-TRANSOL-MOZART-DM
parallel PKS serial
• Simulation period: 2006, daily time-step
• MODFLOW: confined, 7 layers, 7x1300x1200 (~6.5M cells)
• MetaSWAP: ~0.5M cells
Results iMODFLOW: NHM (2)
1 November, 2016
• Maximum measured speedup ~5.
• Maximum theoretical speedup is
limited by surface water (< 1/0.06 16.7).
• Exactly the same heads are computed
with PKS as for the serial case.
Amdahl’s law
Results MODFLOW-USG: global model
1 November, 2016
• PCRGLOB-WB
• Period 1996-jan, transient with daily time-step,
confined, 2 layers, ~4.5M cells, 5 arc-min.
• Run 1: watershed-based input/output
(SIO, 53 watersheds)
• Run 2: Input/output clipped on METIS
partitions (NO_SIO)
Results MODFLOW-USG: Indonesia & synthetic
1 November, 2016
• Indonesia model:
steady-state, confined, 1 layer, ~4M cells,
30 arc-sec.
• Synthetic:
steady-state, confined,
heterogeneous conductivity, 2 layers,
10 km x 10 km, ~112M cells (2x7500x7500)
Synthetic Indonesia
Practical usage with iMOD (Windows)
Easy-to-use in three steps:
1. Install Microsoft MPI:
https://msdn.microsoft.com/en-us/library/bb524831(v=vs.85).aspx
2. Modify your run-file, Dataset 5 (Solver Configuration)
3. Start your parallel job. E.g. starting from the DOS prompt using 4 cores:
mpiexec -n 4 iMODFLOW.exe imodflow.run
1 November, 2016
Enable PKS
Same options as PCG
Partition method, flag for merging IDF output
!!! THANK YOU FOR YOUR ATTENTION !!!
1 November, 2016
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