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Radial Basis Function Finite Differences on the GPU

Shell 0.20% C 13.57% C++ 85.61% Objective-C 0.33% Mercury 0.02% MATLAB 0.15% Fortran 0.11%

rbffd_gpu's Introduction

git clone ssh://[email protected]/~efb06/repos/rbffd_gpu.git


Needs :q




cd rbffd_gpu
mkdir build
cd build 
cmake -DUSE_CUDA=off .. 






Casiornis (Cascade.msi.umn.edu): 

Modules: 
  1) local                    5) suacct                   9) vtune/2013/update7      13) impi/4.1.0.030/intel    17) vtk/5.4.2
  2) vars                     6) base                    10) zlib/1.2.8              14) fftw/3.3.3-impi-double  18) metis/5.0.2
  3) user                     7) cuda/5.0                11) bzip2/1.0.6-gnu4.8.0    15) intel/2013/update4
  4) moab                     8) cmake/2.8.11            12) boost/1.53.0            16) mkl/11.0.4.183

source $HOME/../shared/cascade_env.sh
 
cmake -DARMADILLO_ROOT=/home/bollige/shared/intel-soft/ -DFFTW_ROOT=/soft/fftw/intel-impi/3.3.3-double -DUSE_ICC=on -DUSE_CUDA=off ..

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rbffd_gpu's Issues

adams bashforth, ssp-rk4

Try other time schemes for reduced memory use, or increased stability

overlap communication and computation

OpenCL will allow overlap. Need to complete this for

hand coded kernels (easy)
ViennaCL (hard)
CPU (use libnbc to get MPI_ialltoallv support introduced in MPI-v3)

Stokes

The equations I started with for stokes are wrong
Refer to http://www.dealii.org/developer/doxygen/deal.II/step_22.html for a test case we might implement and compare.
The deal.ii package was developed over 10+ years. We wont hope to compare in functionality, but we can definitely borrow their logic for solving PDEs and substitute RBF-FD as the numerical method.

METIS

Introduce metis into the workflow to partition node sets rather than my own domain class

SHould be able to call in the code, but how is the node set distributed initially (all N nodes on all P Processors?)
MIght need to preprocess the grid and load appropriate files at runtime. (change way we load grid to read <grid_name>.)

Node Ordering Tests

Test convergence of GMRES vs Node orderings
- Reorder grid and compute stencils with Matlab (write to disk)
- Load grid and stencils from file
- Assemble matrix
- Solve with GMRES

VCL Cosine Bell

Finish ViennaCL based cosine bell implementation

ILU0 on GPU

Right now the ILU0 is applied on the CPU. We want it to apply on the GPU.

ViennaCL 1.3.1 introduced a GPU kernel to apply ILU factors. Test to make sure that ILU0 works
It was not essential to have this on the GPU since no one has tested this and other preconditioners on RBF-FD matrices.

Support for CVTs

Need to improve support parameter for CVT meshes. The variation in node locations causes very high error.

Using same parameters as MD node sets fails for convergence of 100K, 500K and 1M nodes
Parameters based on conditioning. Perhaps we can compute condition number of stencil and adjust epsilon in a loop when computing weights.
Parameters are also based on sqrt(N). We could translate the sqrt(N) into the radius of minimum enclosing circle for the stencil. The size of the circle could give us a function for maintaining the same conditioning. This assumes the circle has nodes regularly distributed in some way (CVTs would classify if the density function doesnt vary too much).

METIS

Introduce metis into the workflow to partition node sets rather than my own domain class

SHould be able to call in the code, but how is the node set distributed initially (all N nodes on all P Processors?)
MIght need to preprocess the grid and load appropriate files at runtime. (change way we load grid to read <grid_name>.)

spear benchmarks

Repeat benchmarks from keeneland on spear. See the impact of different hardware?

MPI comm is much slower. Spear seems to have issues with hardware. Will need to contact help.

measure gflops and present those numbers in plots in addition to speedup. throughput is more meaningful for others who want to know how the gains are influenced by hardware and how they will appear on their systems.

Weak Scaling

Setup a weak scaling test case on sphere. METIS will be necessary