The C++/C/Fortran wrapper for flexibly periodic FMM and operator data generator to be used with PVFMM.
The flexibly periodic KIFMM algorithm is described in:
Wen Yan & Michael Shelley, Flexibly imposing periodicity in kernel independent FMM: A Multipole-To-Local operator approach Journal of Computional Physics, Volume 355, 2018, Pages 214-232, 10.1016/j.jcp.2017.11.012.
The flexibly periodic Stokeslet Image algorithm is described in:
Wen Yan & Michael Shelley, Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall arXiv:1803.02424
Please cite them if you find it useful.
Dependency: The C++ template library Eigen is necessary to compile the test driver main.cpp. The wrapper class itself (FMMWrapper.h/.cpp) does not rely on Eigen.
Go to folders in M2LLaplace or M2LStokes and modify the Makefile to use the correct c++ compiler and the correct path to Eigen library header files.
After compilation, type:
XXX.X p > ./M2LYYYaD3Dpbwhere XXX.X is the name of the executable, YYY is the name of the kernel (Stokes, LaplaceCharge, LaplaceDipole, etc), p is the discretization number for KIFMM, 'a' is periodic dimension, and 'b' is the point number for the equiv surface. 'b' controls the tradeoff between accuracy and cost. 'b=10' gives single precision and 'p=16' gives double precision, roughly. For exmaple, M2L2D3Dp8 means doubly periodic in 3D space with p=8. See FMMWrapper.cpp for details.
For example
localhost:periodicfmm wyan$ cd ./M2LStokes/2D3D/
localhost:2D3D wyan$ ./Stokes2D3D.X 8 > ./M2LStokes2D3Dp8The executable also solves a tiny test problem to check the accuracy after the M2L operator is calculated. At the end of the above execution process, you should see something like:
localhost:2D3D wyan$ tail ./M2LStokes2D3Dp8
-4.527578312263358384e-11
Usample M2L total: 1.567028182748916532e+00
1.769944468765771717e-10
-4.527578312263358384e-11
Usample Ewald: 1.567028149573803653e+00
-4.150067072042485956e-19
0.000000000000000000e+00
error 3.317511287903585071e-08
1.769944472915838697e-10
-4.527578312263358384e-11Copy those M2LYYYaD3Dpb files for Stokes kernel to the subfolder /pdata/ in $PVFMM_DIR, remove any extra lines to make sure the M2L files start with "i j value" lines like:
localhost:2D3D wyan$ head ./M2LStokes2D3Dp8
0 0 -8.963371808378797212e+00
0 1 -1.614059953274547965e+01
0 2 2.183755414811182050e+01
0 3 6.150120972933304841e+00The correct folder structure should look like:
localhost:2D3D wyan$ cd $PVFMM_DIR
localhost:pvfmm wyan$ ls ./pdata/M2LStokes*
./pdata/M2LStokes1D3Dp10 ./pdata/M2LStokes2D3Dp10 ./pdata/M2LStokes3D3Dp10
./pdata/M2LStokes1D3Dp12 ./pdata/M2LStokes2D3Dp12 ./pdata/M2LStokes3D3Dp12
./pdata/M2LStokes1D3Dp14 ./pdata/M2LStokes2D3Dp14 ./pdata/M2LStokes3D3Dp14
./pdata/M2LStokes1D3Dp16 ./pdata/M2LStokes2D3Dp16 ./pdata/M2LStokes3D3Dp16
./pdata/M2LStokes1D3Dp6 ./pdata/M2LStokes2D3Dp6 ./pdata/M2LStokes3D3Dp6
./pdata/M2LStokes1D3Dp8 ./pdata/M2LStokes2D3Dp8 ./pdata/M2LStokes3D3Dp8The wrapper files are located in the folder 'FMM':
PeriodicFMM/ $ ls ./FMM
FMMWrapper.cpp FMMWrapper.h FMMWrapper.o FMMWrapperWall2D.cpp FMMWrapperWall2D.h LaplaceCustomKernel.hpp
PeriodicFMM/ $ The test-driving routines are located in the folder 'ModuleTest'
PeriodicFMM/ $ ls ./ModuleTest/
StokesFMM3D StokesFMMWall2D MakefileInc.mk
PeriodicFMM/ $ Modify the file MakefileInc.mk properly.
To run the demo and tests for Stokes 3D periodic FMM:
PeriodicFMM/ $ cd ModuleTest/StokesFMM3D/
StokesFMM3D/ $ make
make: 'TestStokes3D.X' is up to date.
StokesFMM3D/ $ TestStokes3D.X --helpto get command line options.
To run the demo and tests for Stokes 3D periodic FMM above a wall:
PeriodicFMM/ $ cd ModuleTest/StokesFMMWall2D/
StokesFMMWall2D/ $ make
make: 'TestStokesWall2D.X' is up to date.
StokesFMMWall2D/ $ ./TestStokesWall2D.X --helpto get command line options.
This test driver demonstrates how to use the wrapper FMM class and can perform tests for FreeSpace, SP, DP, TP in 3D space, for random & chebyshev points, with OpenMP & MPI.
This wrapper only works with the new_BC branch of my fork of PVFMM.