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[Started by Maruoka and Maeda, 2018/10/24] [Updated by Maruoka, 2018/01/25]
If you have question about MEEP and send it to maru@flex.phys.tohoku.ac.jp, I will try to answer it. Coming to my room(room number is 842) is welcomed.
First of all, let's install Anaconda. From The websit of Anaconda, please download the installer of the series of Python3.x . Since the installer is of the file of .sh, execute it as below.
$ bash [download-folder]/Anaconda3-5.2.0-Linux-x86_64.sh
If you find
bash: conda: command not found
then you need to add PATH for ~/anaconda3/bin .
Following command will add path to anaconda3/bin.
setenv PATH $PATH\:<path to anaconda3/bin>
Do not use relative path which does not work correctly.
Then, let's install pymeep (ref )
Execute the command below.
$ conda create -n mp -c chogan -c conda-forge pymeep
All setup is finished.
Activate the system as below.
$ source activate mp
Execute the file as below.Please rename hogehoge.py as what you name it.
(mp) $ python hogehoge.py
You can get sample source from Github.example If you want to deactivate the system, do as below.
(mp) $ source deactivate
In order to install pymeep which support parallel calculation, execute the following command.
$ conda create -n pmp -c chogan -c conda-forge pymeep-parallel
Activate pymeep which support parallel calculation by following command
$ source activate pmp
Programs run with following command.
$ mpirun -np 4 python <script_name>
"-np" indicate how many processors will run. In this case, 4 processors run simultaneously.
Maxwell equation of MEEP is different from ordinal Maxwell equation.
For example,
The Maxwell equation of MEEP is in the last line of below deformation of normal Maxwell equation.
From ordinal Maxwell equation below,
deform it as follows.
Define x',y',z',t',{\omega}',E',H',{\sigma}' as follows.
Substitute new defined parameters, and get Maxwell equation of MEEP as follows.
Here, permittivity of vacuum and permeability of vacuum are 1.
Unit length is a which user can define freely.
During unit time, the light in vacuum travels by unit length, a.
The wavelength of light in vacuum of which frequency is f, is 1/f.
The h5py package can be used for editing HDF5 file in python. Install it by the following command.
apt-get install python-h5py
h5py is already installed on flex and tubes.
On maruoka's WSL,
pip install h5py
doesn't work saying
ImportError: No module named h5py
It is useful to use script below to automatically converting hdf5 to mp4 by pasting this to .bash_profile
function h5mp4(){
mkdir $1
cp $1.h5 $1
cd $1
h5topng $1.h5 -Z -c dkbluered -R -t 0:$2
convert $1*png $1.gif
ffmpeg -i $1.gif -qscale:v 1 $1.mp4
}
For example, if you want to convert hogehoge.h5 which have 1000 number of time indexes, do as follow.
h5mp4 hogehoge 999
It output hogehoge.gif and hogehoge.mp4 automatically.
If you want to know the number of time indexes,do as follow.
h5ls hogehoge.h5
ez Dataset{100, 200, 1000/Inf}
Here, 1000 is the number of time indexes.
We can modify the phase of source by the amplitude.
(set! sources
(list
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ex)
(center 0 0 8)
(size 50 50 0)
)
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ey)
(center 0 0 8)
(size 50 50 0)
(amplitude (exp (* 0+1i 1.570796327)))
)
)
)
(set! sources
(list
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ey)
(center 0 0 8)
(size 50 50 0)
)
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ex)
(center 0 0 8)
(size 50 50 0)
(amplitude (exp (* 0+1i 1.570796327)))
)
)
)
(set! sources
(list
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ex)
(center 0 0 8)
(size 50 50 0)
(amplitude (cos x))
)
(make source
(src (make continuous-src (frequency (/ 1 7))))
(component Ey)
(center 0 0 8)
(size 50 50 0)
(amplitude (sin x))
)
)
)
There are three ways to implement oblique incident light.
TM wave just before total internal reflection.
(define (pw-amp k x0) (lambda (x)
(exp (* 0+1i (vector3-dot k (vector3+ x x0))))))
(define-param theta-deg 48)
(define theta-rad (deg->rad theta-deg))
(define epsilon1 2.25)
(define epsilon2 1.25)
(define-param fcen 0.8) ; pulse center frequency
(define-param df 0.02) ; turn-on bandwidth
(define-param kdir (vector3 (sin theta-rad) 0 (cos theta-rad))) ; direction of k (length is irrelevant)
(define k (vector3-scale (* 2 pi fcen (sqrt epsilon1))
(unit-vector3 kdir))) ; k with correct length
(set! pml-layers (list (make pml (thickness 2)(direction Z))))
(set! k-point (vector3* (* fcen (sqrt epsilon1) ) (vector3 (sin theta-rad) 0 (cos theta-rad))))
(set! geometry
(list
(make block
(center 0 0 -2.5)
(size 10 infinity 5)
(material (make dielectric(epsilon epsilon1)))
)
(make block
(center 0 0 2.5)
(size 10 infinity 5)
(material (make dielectric(epsilon epsilon2)))
)
)
)
(set! sources
(list
(make source
(src (make continuous-src (frequency fcen) (fwidth df)))
(component Ez) (center 0 0 -3) (size 10 0 0)
(amp-func (pw-amp k (vector3 0 0 -3))))))
(define-param T 40) ; run time
(run-until T
(to-appended "ez" (at-every 0.1 output-efield-z))
(to-appended "ex" (at-every 0.1 output-efield-x))
)
plot of Ez
; This example creates an approximate Ez-polarized planewave in vacuum
; propagating at a 45-degree angle, by using a couple of current sources
; with amplitude exp(ikx) corresponding to the desired planewave.
(define-param s 11) ; the size of the computational cell, not including PML
(define-param dpml 1) ; thickness of PML layers
(define sxy (+ s (* 2 dpml))) ; cell size, including PML
(set! geometry-lattice (make lattice (size sxy sxy no-size)))
(set! pml-layers (list (make pml (thickness dpml))))
(set-param! resolution 10)
; pw-amp is a function that returns the amplitude exp(ik(x+x0)) at a
; given point x. (We need the x0 because current amplitude functions
; in Meep are defined relative to the center of the current source,
; whereas we want a fixed origin.) Actually, it is a function of k
; and x0 that returns a function of x ...
(define (pw-amp k x0) (lambda (x)
(exp (* 0+1i (vector3-dot k (vector3+ x x0))))))
(define-param fcen 0.8) ; pulse center frequency
(define-param df 0.02) ; turn-on bandwidth
(define-param kdir (vector3 1 1)) ; direction of k (length is irrelevant)
(define-param n 1) ; refractive index of material containing the source
(define k (vector3-scale (* 2 pi fcen n)
(unit-vector3 kdir))) ; k with correct length
(set! sources
(list
; left
(make source
(src (make continuous-src (frequency fcen) (fwidth df)))
(component Ez) (center (* -0.5 s) 0) (size 0 s)
(amp-func (pw-amp k (vector3 (* -0.5 s) 0))))
; bottom
(make source
(src (make continuous-src (frequency fcen) (fwidth df)))
(component Ez) (center 0 (* -0.5 s)) (size s 0)
(amp-func (pw-amp k (vector3 0 (* -0.5 s)))))
))
(define-param T 400) ; run time
(run-until T (at-end output-efield-z))
plot of Ez
plot of Ez when there is only one source ( why we need two sources )
http://article.gmane.org/gmane.comp.science.electromagnetism.meep.general/3058
(define-param pi 3.14159265)
(define-param dpml 3.0)
(define-param len (+ 20 dpml))
(define-param wid (+ 20 dpml))
(set! geometry-lattice (make lattice (size len wid no-size)))
(define-param beam-waist 2.5) ; beam sigma (gaussian beam width)
(define-param rotation-angle (* (/ 22.5 360) 2 pi)) ; Degrees if you like them
(define-param source-points 60) ; should be a big number
(define-param source-size (* 4 beam-waist)) ; should be bigger than beam-waist
(define-param src_list (list ))
(do
((
r_0
(/ source-size -2)
(+ r_0 (/ source-size (- source-points 1)))
))
((> r_0 (/ source-size 2)))
;for r_0 = -source-size/2 : source- size/source-points : source-size/2
(set! src_list (append src_list
(list (make source
(src (make gaussian-src
(wavelength 1)
(width 3)
))
(amplitude (exp (- 0 (/ (* r_0 r_0) (* 2 beam-waist beam-waist)))))
(component Ez)
(center (* r_0 (sin rotation-angle)) (* r_0 (cos rotation-angle)))
))
))
)
(set! sources src_list)
(set! pml-layers (list (make pml
(thickness dpml)
)))
(set! resolution 10)
(use-output-directory)
(run-until (* 2 len)
(to-appended "ez" (at-every 0.1 output-efield-z))
)
plot of Ez
Electric field of Total Internal Reflection
Code for simulation
(define-param dx 1); cell size in x axis (define-param dy 2); cell size along y axis (define-param fp 1.5) (define-param tpml 0.1); PML thickness (define-param deg 48) (define-param theta (* pi 0.88889)); incident angle of the plane wave (set! theta (* deg (/ pi 180))) (set! resolution 40);define the resolution for simulation domain ;define the lattice (set! geometry-lattice (make lattice (size (+ dx (* 2 tpml)) (+ dy (* 2 tpml)) no-size))) ;define PML thickness (set! pml-layers (list (make pml (thickness tpml)))) ;define the blocks (set! geometry (list (make block (center 0 (* 0.25 dy))(size infinity (+ tpml (* 0.5 dy)) infinity) (material (make dielectric (epsilon 1)))) (make block (center 0 (* -0.25 dy))(size infinity (+ tpml (* 0.5 dy)) infinity) (material (make dielectric (epsilon 2.25)))) )) (set! pml-layers (list (make pml (thickness tpml)))) ;(+ tpml (* 0.5 dy)) ;define the wave vector (define kx (* fp (sqrt 2.25) (sin theta))) ;give the amplitude function (define (f_amp p) (exp (* 0+2i pi kx (vector3-x p)))) (set! k-point (vector3 kx 0 0)) ;define the simulation domain to be complex field (set! force-complex-fields? true) ;define the Gaussian beam (set! sources (list (make source (src (make continuous-src (frequency fp))) (component Ex) (component Ey) (center 0 (* dy -0.50)) (size (+ dx (* 2 tpml)) 0 ) (amp-func f_amp)))) (set! pml-layers (list (make pml (thickness tpml) (direction Y)))) ;extract the data to .png file (run-until 40 (at-beginning output-epsilon) ;(at-end output-efield-y) (to-appended "ey"(at-every 0.05 (in-volume (volume (center 0 0 0)(size dx dy 0))output-efield-y))) (to-appended "ex"(at-every 0.05 (in-volume (volume (center 0 0 0)(size dx dy 0))output-efield-x))) )
If you want to plot electric field vector, you need to plot it from hdf5 file by your code. The ax.quiver function of matplotlib is good idea to plot electric field vector.
To use material library, add
(include "/home/students/maru/meep/scheme/materials.scm")
at the beginning of your program.
This library only works at tube61, 62, 63.
For how to use the material library, check https://meep.readthedocs.io/en/latest/Materials/
You need to specify unit to use material library.
The default is 1000 micro meter.
In order to change the unit to 100 micro meter, add
(set! um-scale (* um-scale 0.1))
You don't need to load materials.py by yourself like scheme.
The default unit length is 1000nm in materials.py.
If you want to use another unit length, you need to rewrite materials.py directory.
After the line where um_scale is defined, change the um_scale in materials.py to the unit length you want.
For example, if you want to use 100nm for unit length, add following line.
um_scale=um_scale*0.1
To modify materials.py, you can check the address of materials.py as follows.
(pmp) maru@tube60:~$ python Python 3.6.6 | packaged by conda-forge | (default, Jul 26 2018, 09:53:17) [GCC 4.8.2 20140120 (Red Hat 4.8.2-15)] on linux Type "help", "copyright", "credits" or "license" for more information. import meep Using MPI version 3.1, 1 processes meep.__file__ '/home/students/maru/anaconda3/envs/pmp/lib/python3.6/site-packages/meep/__init__.py'
In this case, the address of materials.py is
/home/students/maru/anaconda3/envs/pmp/lib/python3.6/site-packages/meep/materials.py
This modification of materials.py has effect only for pmp.
If you want to change the unit length for mp, please change the materials.py of mp also.
Meep support user defined relative permittivity of Drude conductivity.
\epsilon_\infty is approximately the relative permittivity when frequency is very large. f_p is plasma frequency.
Since the relative permittivity of Drude conductivity is expressed in MEEP unit, f_p', gamma', f', we need to derive the relationship to the f_p, gamma, f of SI unit.
From this formula, f_p and gamma of SI unit and f_p' and gamma' of MEEP unit is in the following relationship.
Using f_p', gamma' and epsilon_\infty calculated above,
user_defined_material = mp.Medium(epsilon=epsilon_\infty, E_susceptibilities=[mp.DrudeSusceptibility(frequency=f_p', gamma=gamma', sigma=1)])
will define the material which have f_p', gamma', epsilon_\infty.
In order to use this material, you need to set the option of geometry, materials = user_defined_material.
In the document of PML by one of the the author of MEEP(http://math.mit.edu/~stevenj/18.369/pml.pdf)
With PML, however, the constant factor is very good to start with, so experience shows that a simple quadratic or cubic turn-on of the PML absorption usually produces negligible refections for a PML layer of only half a wavelength or thinner [1,21]. (Increasing the resolution also increases the resolution alos increase the effectiveness of the PML, because it approaches the exact wave equation.)
However, when the light coming at oblique incident angle, PML should be thicker. The reflectivity of PML for incident angle at X can be represented as e^{-2*k*d*cos(X)*G} for some constant G. d is the thickness of PML. k is the wavenumber.(Please check https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=477075 for details). If X approaches to 90 degree, the efficiency of the absorbance of PML becomes really bad.
If you put dielectrics touching to the PML, please confirm you overlap the dielectrics and PML. Otherwise, PML is useless because PML is defined for the boundary of vaccum to absorb the light not for dielectrics. It is implemented by just multiplying tensors on dielectric constants. So you need to overlap PML and dielectrics. (Please check https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=477075 for details).
PML and Dielectrics touch each other but do not overlap
Following error occurs, when you try to use material library at FLEX or Tube60.
ERROR: Unbound variable: E-susceptibilities
Material library only works at tube61, 62, 63. Please go to tube61, 62, 63.
If the version is lower than 1.6, materials.py doesn't work. Check the version of pymeep by
conda list
If you find
pymeep 1.5
then update pymeep from 1.5 to 1.6 as follows.
(mp) maru@flex:~$ conda update -c chogan -c conda-forge pymeep
Solving environment: done
## Package Plan ##
environment location: /home/students/maru/anaconda3/envs/mp
added / updated specs:
- pymeep
The following packages will be downloaded:
package | build
---------------------------|-----------------
libctl-4.1.4 | 1 97 KB chogan
libgdsii-0.2.dev | 0 800 KB chogan
python-3.6.6 | hd21baee_1003 29.0 MB conda-forge
openssl-1.0.2p | h14c3975_1002 3.1 MB conda-forge
mpb-1.7.0 | nomkl_1 74 KB chogan
pymeep-1.7.0 | py36_nomkl_1 3.3 MB chogan
openblas-0.3.5 | h9ac9557_1000 15.8 MB conda-forge
nomkl-3.0 | 0 48 KB
ca-certificates-2018.11.29 | ha4d7672_0 143 KB conda-forge
certifi-2018.11.29 | py36_1000 145 KB conda-forge
------------------------------------------------------------
Total: 52.5 MB
The following NEW packages will be INSTALLED:
libgdsii: 0.2.dev-0 chogan
nomkl: 3.0-0
The following packages will be UPDATED:
ca-certificates: 2018.03.07-0 --> 2018.11.29-ha4d7672_0 conda-forge
certifi: 2018.11.29-py36_0 --> 2018.11.29-py36_1000 conda-forge
libctl: 4.1.2-0 chogan --> 4.1.4-1 chogan
mpb: 1.6.2-4 chogan --> 1.7.0-nomkl_1 chogan [nomkl]
openblas: 0.2.20-8 conda-forge --> 0.3.5-h9ac9557_1000 conda-forge
pymeep: 1.5-py36_nomkl_2 chogan [nomkl] --> 1.7.0-py36_nomkl_1 chogan [nomkl]
The following packages will be DOWNGRADED:
openssl: 1.1.1a-h7b6447c_0 --> 1.0.2p-h14c3975_1002 conda-forge
python: 3.6.8-h0371630_0 --> 3.6.6-hd21baee_1003 conda-forge
Proceed ([y]/n)? y
Downloading and Extracting Packages
libctl-4.1.4 | 97 KB | ########################################################################################### | 100%
libgdsii-0.2.dev | 800 KB | ########################################################################################### | 100%
python-3.6.6 | 29.0 MB | ########################################################################################### | 100%
openssl-1.0.2p | 3.1 MB | ########################################################################################### | 100%
mpb-1.7.0 | 74 KB | ########################################################################################### | 100%
pymeep-1.7.0 | 3.3 MB | ########################################################################################### | 100%
openblas-0.3.5 | 15.8 MB | ########################################################################################### | 100%
nomkl-3.0 | 48 KB | ########################################################################################### | 100%
ca-certificates-2018 | 143 KB | ########################################################################################### | 100%
certifi-2018.11.29 | 145 KB | ########################################################################################### | 100%
Preparing transaction: done
Verifying transaction: done
Executing transaction: done
If you want to use parallel pymeep, then update it also to 1.7.0-py36_nomklh39e3cac_1.
(pmp) maru@tube60:~$ conda update -c chogan -c conda-forge pymeep-parallel
Solving environment: done
## Package Plan ##
environment location: /home/students/maru/anaconda3/envs/pmp
added / updated specs:
- pymeep-parallel
The following packages will be downloaded:
package | build
---------------------------|-----------------
libgcc-ng-7.3.0 | hdf63c60_0 6.1 MB conda-forge
pymeep-parallel-1.7.0 |py36_nomklh39e3cac_1 3.3 MB chogan
------------------------------------------------------------
Total: 9.4 MB
The following NEW packages will be INSTALLED:
libgdsii: 0.2.dev-0 chogan
nomkl: 3.0-0
The following packages will be UPDATED:
ca-certificates: 2018.8.24-ha4d7672_0 conda-forge --> 2018.11.29-ha4d7672_0 conda-forge
certifi: 2018.8.24-py36_1 conda-forge --> 2018.11.29-py36_1000 conda-forge
libctl: 4.1.2-0 chogan --> 4.1.4-1 chogan
libgcc-ng: 7.2.0-hdf63c60_3 conda-forge --> 7.3.0-hdf63c60_0 conda-forge
mpb: 1.6.2-4 chogan --> 1.7.0-nomkl_1 chogan [nomkl]
openssl: 1.0.2p-h470a237_0 conda-forge --> 1.0.2p-h14c3975_1002 conda-forge
pymeep-parallel: 1.5-py36_nomklh39e3cac_4 chogan [nomkl] --> 1.7.0-py36_nomklh39e3cac_1 chogan [nomkl]
Proceed ([y]/n)? y
Downloading and Extracting Packages
libgcc-ng-7.3.0 | 6.1 MB |
################################################################################################################################################################################################## | 100%
pymeep-parallel-1.7. | 3.3 MB |
##################################################################################################################################################### ############################################# | 100%
Preparing transaction: done
Verifying transaction: done
Executing transaction: done
If you find error as below, give permission to working directory and files for writing and edinting.
Working in 3D dimensions.
Computational cell is 20 x 20 x 20 with resolution 10
block, center = (0,0,0)
size (1,3,1)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon diagonal = (1,1,1)
time for set_epsilon = 11.7491 s
-----------
creating output file "./hogehoge.h5"...
on time step 1 (time=0.05), 14.4708 s/step
HDF5-DIAG: Error detected in HDF5 (1.10.2) MPI-process 0:
#000: H5F.c line 445 in H5Fcreate(): unable to create file
major: File accessibilty
minor: Unable to open file
meep: error on line 497 of h5file.cpp: error opening HDF5 output file
application called MPI_Abort(MPI_COMM_WORLD, 1) - process 1
The version of GLIBC at flex is old. Go to t70.
If you connect to flex from remote place (e.g. Sendai Kosen) , you sometimes come across following error.
(pmp) maeda@tube60:/abinitio2/maeda/pymeep/Rectangle/drude/Omote$ mpirun -np 5
python after-Rec-drude-Au.py 45
Working in 3D dimensions.
Computational cell is 20 x 20 x 20 with resolution 10
block, center = (0,0,0)
size (1,3,1)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon diagonal = (1,1,1)
time for set_epsilon = 5.05642 s
lorentzian susceptibility: frequency=3.47141, gamma=2.01155
lorentzian susceptibility: frequency=2.39466, gamma=0.701702
lorentzian susceptibility: frequency=0.66944, gamma=0.278261
lorentzian susceptibility: frequency=0.33472, gamma=0.19438
drude susceptibility: frequency=1e-10, gamma=0.0427474
-----------
creating output file "./after-Rec-drude-Au-ex-surface-45deg.h5"...
creating output file "./after-Rec-drude-Au-ey-surface-45deg.h5"...
creating output file "./after-Rec-drude-Au-ez-inner-45deg.h5"...
creating output file "./after-Rec-drude-Au-ez-outer-45deg.h5"...
Fatal error in PMPI_Waitall: Other MPI error, error stack:
PMPI_Waitall(405)...............: MPI_Waitall(count=92, req_array=0x9adaad0,
status_array=0xc9e3670) failed
MPIR_Waitall_impl(221)..........: fail failed
PMPIDI_CH3I_Progress(623).......: fail failed
pkt_RTS_handler(317)............: fail failed
do_cts(662).....................: fail failed
MPID_nem_lmt_dcp_start_recv(302): fail failed
dcp_recv(165)...................: Internal MPI error! Cannot read from remote
process
Two workarounds have been identified for this issue:
1) Enable ptrace for non-root users with:
echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
2) Or, use:
I_MPI_SHM_LMT=shm
Fatal error in PMPI_Waitall: Other MPI error, error stack:
PMPI_Waitall(405)...............: MPI_Waitall(count=85, req_array=0xa328890,
status_array=0xd21c7f0) failed
MPIR_Waitall_impl(221)..........: fail failed
PMPIDI_CH3I_Progress(658).......: fail failed
MPID_nem_handle_pkt(1439).......: fail failed
pkt_RTS_handler(317)............: fail failed
do_cts(662).....................: fail failed
MPID_nem_lmt_dcp_start_recv(302): fail failed
dcp_recv(165)...................: Internal MPI error! Cannot read from remote
process
Two workarounds have been identified for this issue:
1) Enable ptrace for non-root users with:
echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
2) Or, use:
I_MPI_SHM_LMT=shm
Fatal error in PMPI_Waitall: Other MPI error, error stack:
PMPI_Waitall(405)...............: MPI_Waitall(count=85, req_array=0x9c2b8f0,
status_array=0xcc31ed0) failed
MPIR_Waitall_impl(221)..........: fail failed
PMPIDI_CH3I_Progress(658).......: fail failed
MPID_nem_handle_pkt(1439).......: fail failed
pkt_RTS_handler(317)............: fail failed
do_cts(662).....................: fail failed
MPID_nem_lmt_dcp_start_recv(302): fail failed
dcp_recv(165)...................: Internal MPI error! Cannot read from remote
process
Two workarounds have been identified for this issue:
1) Enable ptrace for non-root users with:
echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
2) Or, use:
I_MPI_SHM_LMT=shm
Following command will resolve this error when you connect from Sendai Kosen.
export I_MPI_SHM_LMT=shm
