liege caliste bigdft
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8/6/2019 Liege Caliste Bigdft
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
3rd International ABINIT Developer Workshop
LIÈGE - BELGIUM
Introducing wavelet basis sets inside ABINIT via
the BigDFT project
Damien Caliste & Luigi Genovese
PCPM - UCL / L_Sim - CEA Grenoble
30 January 2007
EU Nest Adventure - BigDFT project www.abinit.org
8/6/2019 Liege Caliste Bigdft
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Outline
1 Poisson Solver for free BCInterpolating scaling functions
SeparabilityPerformances
2 Computing Hartree’s potential in ABINIT for isolatedsystems
The 02poisson interfaceComputing potentials in real spaceEffects on sample potentials
3 Inclusion of a wavelet basis set into ABINIT, the BigDFTproject
A quick view into BigDFT machineryInterface between BigDFT and ABINITConvergence and results
4 Summary and outlook
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Poisson Solver with interpolating scaling functions
Calculation of the self-consistent potential
Poisson Equation for isolated systems∇2V H (r) = −4πρ(r) =⇒ V H (r) =
Z Ω
K (|r− r|)ρ(r)d r
The kernel K (r) = 1/r with Ω = R3
This equation is usually solved using plane waves. Theirdelocalization results in problems for isolated systems.How to remove long-distance interactions?
Most commonly used methods (Hockney, Martina-Tuckerman)
Modify the kernel operator K = K short + K long
Does not implement well short-distance behaviour
We must consider a size that is larger than the size ofthe original system
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Using a localized function set
Interpolating Scaling Functions (from wavelet theory)
Localized in real and Fourier space
Undergo multi-scale relations
The expansion coefficients coincide with the values on a(uniform) grid
Separable basis functions φj(r) = φ j x (x )φ j y
(y )φ j z (z )
Optimal for isolated systems
The potential is obtained via a discrete convolution
V (i) =
∑jK i−j ρ(j)
K i =Z
K (|r|)Φi(r)d r =Z
1
r φi x
(x )φi y (y )φi z
(z )d r
Given K i, we can calculate convolution using zero-padded
FFT (O (N log(N ) scaling)EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Gaussian tensor product decomposition
The calculation of the kernel K i can be improved thanks toseparability of the basis
Approximation with gaussians(Beylkin et al.)
1
r ∑
k
ωk e −p k r 2
with very high accuracy89 terms, p k , ωk suitably chosen.The sum in gaussians allows us to write the tensordecomposition of the kernel:
The computational cost is reduced N 3 → 89×N
K j =89
∑k =1
ωk K j x (p k )K j y
(p k )K j z (p k )
K j (p ) = R φ0(x )e −p (x − j )2dx
EU Nest Adventure - BigDFT project www.abinit.org
8/6/2019 Liege Caliste Bigdft
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
Separability
Performances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Features
Very fast with moderate memory occupation:
Elapsed Time on a Cray XT3,1283 grid
np 1 2 4 8 16 32 64
s .92 .55 .27 .16 .11 .08 .09
More precise than other existing Poisson Solvers:
1e-11
1e-10
1e-09
1e-08
1e-07
1e-06
1e-05
1e-04
0.001
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
M a x
E r r o r
Grid step
HockneyTuckerman
8th14th20th30th40th50th60th
100th
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Overview
In summary, we have developed a technique
Free boundary conditions
Very high accuracy
Good computational performance, easy to parallelize
Based on a real space grid, can be used independently
Allows for MultiResolution Analysis (adaptivity)
Paper published
L. Genovese, T. Deutsch, A. Neelov,S. Goedecker, G. Beylkin
Efficient solution of Poisson’s equation with free boundary conditions , [arXiv: cond-mat/0605371],J. Chem. Phys. 125, 074105 (2006)
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
The 02poisson interface
ABINIT BigDFT
included from 02poisson directory
PSolver_hartree()
Branching into rhohxc_coll() between hartre() andPSolver_hartree()
if (dtset%icoultrtmt == 1) thencall PSolver_hartree(dtset, 1, nfft, ngfft, rhor, rprimd, vhartr)elsecall hartre(cplex,gmet,gsqcut,izero,mpi_enreg,nfft,ngfft,qphon,rhog,vhartr)
end if
Two new input variablesicoultrtmt that controls the computation of Coulomb’spotential ;nscforder which commands the degree ofinterpolating scaling functions used in the kernel.
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT inABINIT
Outlines
Structure
Results
Outlook
Realspace potentials within E total
With icoultrtmt == 1, all local potentials are computed inrealspace.
Real space Reciprocal space
E kin
E hart PSolver_hartree() hartre()
E psp _ nl
E psp _ loc branched inside mklocl()
mklocl_realspace()† mklocl_recipspace()
E ewald simple ion/ion interaction
∑λ,κ ;λ=κ
Z λionZ κ ion
τλ−τκ ionion_realspace() ewald()
† Computation of E psp _ loc in real space requires a description of
pseudo-potentials in RS, currently implemented for GTH and HGH
only.
EU Nest Adventure - BigDFT project www.abinit.org
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
Better estimated potentials for isolated systems
The local part from pseudo-potentials
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
-20 -15 -10 -5 0 5 10 15 20
I o n i c p o t e n t i a l ( H a
r t r e e . B o h r -
1 )
Distance in [111] axis (Bohr)
Centered SiH4
molecule: calculation of the ionic potential (Ec=20Ht)
Gaussian charges on originPeriodic conditions, box size = 10BohrPeriodic conditions, box size = 20BohrPeriodic conditions, box size = 30Bohr
Isolated conditions
the potentials are correct in the boundary regions ;
the 1r
behavior is valid whatever the supercell size.
EU Nest Adventure - BigDFT project www.abinit.org
B i d i l f i l d
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
Better estimated potentials for isolated systems
The Hartree’s potential
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
H a r t r e e
p o t e n t i a l ( H
a r t r e e . B o h r
- 1 )
Distance in demi [111] axis (Bohr)
Centered SiH4
molecule: calculation of the Hartree potential (Ec=20Ht)
Gaussian charges on originDot charges on origin
Periodic conditions, box size = 10BohrPeriodic conditions, box size = 20BohrPeriodic conditions, box size = 30Bohr
Isolated conditions
the potentials are correct in the boundary regions ;
the 1r
behavior is valid whatever the supercell size.
EU Nest Adventure - BigDFT project www.abinit.org
E i till ff t d b b i
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
E total is still affected by box size
Total energy of a silane molecule
-6.23
-6.22
-6.21
-6.2
-6.19
-6.18
-6.17
-6.16
6 8 10 12 14 16 18 20
E n e r g y ( H a r t r e e )
Supercell size (size len th in Bohr)
Periodic (Ec=50Ht)Real space (Hartree and ionic) (Ec=50Ht)
Total energy is not significantly modified by accurate potential treatment.
the kinetic part of the energy is strongly dependent onthe periodicity of the super-cell ;
a full real-space is mandatory for isolated and/orinhomogeneous systems.
EU Nest Adventure - BigDFT project www.abinit.org
A i k i i t Bi DFT hi
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
A quick view into BigDFT machinery
Every steps of electronic calculations are treated in realspace on a systematic basis set.
Pseudo-potentials are described by separable functions(GTH and HGH) ;Wave-functions are expanded on a Daubechies’ waveletbasis set (i.e. a set of coefficients on a real spaceadaptative grid).
New tools have been developped to handle theSchrödinger’s equation.
A real space laplacian, using filters on wavelets ;Storage and matricial computation of wave-functions ona two-resolution grid ;
A real space preconditionner for wavelets.
The ground state is computed in a direct minimisationloop, using either the steepest descent algorithm or aDIIS scheme.
EU Nest Adventure - BigDFT project www.abinit.org
I t f b t Bi DFT d ABINIT
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
Interface between BigDFT and ABINIT
All informations have been gathered into Fortran types.
Data storage
wvl_wf_type - stores the decomposition of wave-functions ;
wvl_keyArrays_type - description of the two-resolution grid ;
wvl_projectors_type - stores the projector parts ofpseudo-potentials.
Most of the main routines have been branched and call theBigDFT library (using a module interface).
New interface routines
src/08seqpar/wvl_vtorho() - the main part within theminimisation loop (build the Hamiltonian, compute the gradient andcreate new wave-functions using steepest descent or DIIS) ;
src/05common/wvl_mkrho() - compute density fromwave-functions ;
src/04wvl_wfs - contains basic routines to create, free, manipulatewave-functions on a two-grid wavelet basis set ;
EU Nest Adventure - BigDFT project www.abinit.org
New input variables
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
New input variables
Main specific variables to control the basis set
wvl_hgrid the grid size
wvl_frmult the expansionaround atoms for fine grid
wvl_crmult the expansionaround atoms for coarsegrid
All wavelet specific input variable are prefixed by wvl_ .
Other relevant variablesusewvl to enable a wavelet computation ;
nwfshist for the DIIS history.
EU Nest Adventure - BigDFT project www.abinit.org
An accurate total energy
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
An accurate total energy
The main convergence parameter iswvl_hgrid and an usual value for organicmolecule is 0.35Bohr.
[Convergence of E total versus wvl_hgrid for a silane]
1e-06
1e-04
0.01
0.2 0.3 0.4 0.5 0.6 0.7
Total energy for a silane molecule
-6.24
-6.22
-6.2
-6.18
-6.16
-6.14
-6.12
6 8 10 12 14 16 18 20
E n e r g y ( H a r t r e e )
Supercell size (size length in Bohr)
Ec=10HtEc=15HtEc=25HtEc=35Ht
Wavelet computed value (hgrid = 0.5)
E wvltotal = E
pwtotal with a converged cut-off.
EU Nest Adventure - BigDFT project www.abinit.org
Summary and Outlook
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BigDFT - anew ABINIT
library
PSolverdescription
Interpolets
SeparabilityPerformances
PSolver inABINIT
02poisson
Real space
Results
BigDFT in
ABINITOutlines
Structure
Results
Outlook
Summary and Outlook
The standalone code created in the frame of the Europeanproject BigDFT, has been included in ABINIT for developper
usage. It is characterised by:a systematic real space basis set ;
an accurate ground state computation.
The next development will import the capability to
run on parallel with a split on bands (mature in BigDFT) ;
compute forces for geometry optimisation (mature inBigDFT) ;
use a scheme to improve accurancy without increasingthe basis-set (recently introduced in BigDFT).
A simple linear scaling approach is under development in theBigDFT project and schedule for inclusion in ABINIT in 5.4series.
Wavelet computations for end-users will be presented during
next autumn in a CECAM tutorial.EU Nest Adventure - BigDFT project www.abinit.org
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