Maxeler@FFH:
Selected FFH Applications
1/12
MAXELER @ FFH
ŠĆEPAN MILJANIĆ,
EPAN@FFH.BG.AC.RS
MILENA PETKOVIĆ,
MILENA@FFH.BG.AC.RS
ALEKSANDAR JOVIĆ,
ALEKSANDAR.JOVIC@FFH.BG.AC.RS
2/12
A Short Survey of FFH Algorithms
Suitable for DataFlow Technology
 Quantum Chemistry
 Chemical Kinetics
 Analysis of Fluids
 Statistical Thermodynamics
 Spectroscopy
3/12
Condition for an Algorithm to be
Suitable for DataFlow
The FFH Viewpoint:
a. BigData
b. Over 95 % of run time in loops
c. Reusability of the data
d.
n/a
e.
n/a
f.
n/a
4/12
Quantum Chemistry
Time-independent Schrödinger equation:
Ĥ  E Goal: optimization of the structure!
 Method of steepest descent – the next point xn+1 is
chosen in the direction of the negative gradient at xn:
xn1  xn  sn  E ( xn )
 Conjugate gradient methods – gradients at the
last two points are taken into account:
xn1  f xn , E ( xn ), E ( xn1 )
 Newton-Raphson method – in addition to the
gradient, the Hessian is computed at each point:
1
xn 1  xn  H ( xn ) E ( xn )
5/12
Chemical Kinetics
System of partial differential equations: used for finding
numerical solutions to sets of coupled chemical reactions.
 Euler method
yn 1  yn  hf ( xn , yn )
 Runge-Kutta algorithm
k1  hf ( xn , yn )
k2  hf ( xn  12 h, yn  12 k1 )
yn1  yn  k2  O(h )
3
 Taylor theorem
dN / dt  a  bN  cN 2  dN 3  ...
6/12
Analysis of Fluids
 Monte-Carlo methods
n
b-a
I
g ( xi )

n i 1
b
I   g ( x)dx
a
 Korteweg–de Vries equation (KdV equation)

2
P
(

,


,

 2n1 x x ,...)dx

dPn 1 n  2
Pn  
  Pi Pn 1i
dx
i 1
 Vlasov equation for classical fluids
 r 1 ( p, r; t )   mP  r 1 ( p, r; t )
7/12
 r 

1


z (r  r ) 1 (r ; t )dr   P  0 ( p)
Statistical Thermodynamics
System of a large number of statistical methods
 Euler-Lagrange equations
d L
dt qi

L
qi
 Boltzmann H-function
H B ( p1 , p2 ,...)   pk ln pk
k
 Schmidt recurrence relation
n p ( N )Z N  e
8/12
 e p

Z N a
1  n p ( N  1)
ZN

Spectroscopy
 Fourier transform

f ( x) 

ˆf ( )e 2ix d

 Taylor Series Expansion
Bz ( x, y , z )    i , j , k x y z
i
j
k
i , j ,k
 Green's function
b
(G f )( x)   G ( x, y) f ( y)d ( y)
a
9/12
Synergy Possibilities: FFH and ETF
 HW @ ETF
 HW @ FFH
 Periodical Joint Meetings
 ETF speed up of concrete FFH calculations
10/12
Why all of this?
11/12
http://www.tcm.phy.cam.ac.uk/~mdt26/qmc_projects/dft/functionals.html
ŠĆEPAN MILJANIĆ,
EPAN@FFH.BG.AC.RS
MILENA PETKOVIĆ,
MILENA@FFH.BG.AC.RS
ALEKSANDAR JOVIĆ,
ALEKSANDAR.JOVIC@FFH.BG.AC.RS
12/12