Searching for Neighbor Atoms in Large-Scale

Atomistic Simulations

Wednesday, 10/30/2002

Interatomic Force Calculation in MD Simulation

A neighbor list is maintained for each atom to speed up force calculation.

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Fi = fijj≠i

∑ Searching neighboring atoms

MPM: No Neighbor Particle Finding

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M (n) = m( p)

n

∑ N (n,p)

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F x(n) = m(p)N (n,p)bx

( p)

p

∑

F y(n) = m(p)N (n,p)by

( p)

p

∑

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f x(n) =− V( p) σxx

( p)N,x(n,p) +σ xy

( p)N,y(n,p)

[ ]p

∑

f y(n) =− V( p) σxy

( p)N,x(n,p) +σ yy

( p)N,y(n,p)

[ ]p

∑

Interatomic Force Cut-off Radius

The size of the background grid equals the cut-off radius of the interatomic force.

Searing the Neighbor

Large-scale MD Simulation

Dynamically Update

Atoms List

Put Particles Into Cells

%ncell is the total number of cells%np is the total number of particles%a is the size of a cell%ncelly is the number of cells in y %direction

plist_c=linspace(0,0,ncell);plist_p=linspace(0,0,np);for p=1:np ix=ceil( x_p(p)/a ); iy=ceil( y_p(p)/a ); c=ncelly*(ix-1)+iy; plist_p(p)=plist_c(c); plist_c(c)=p;end

NeighborList

Initial Step

Neighbor List (Atom 1)

Neighbor List (Atom 2)

Neighbor List (Atom 3)

Neighbor List (Atom 4)

Any thing wrong?

Neighbor List (Atom 5)

Any thing wrong?

Neighbor List (Atom 6)

Anything wrong?

Neighbor List (Atom 7)

Neighbor List (Atom 8)

Neighbor List (Atom 9)

Neighbor List (Atom 10)

Neighbor List (Atom 11)

Neighbor List (Atom 12)

Anything wrong?

Put Particles Into Cells

%ncell is the total number of cells%np is the total number of particles%a is the size of a cell%ncelly is the number of cells in y %direction

plist_c=linspace(0,0,ncell);plist_p=linspace(0,0,np);for p=1:np ix=ceil( x_p(p)/a ); iy=ceil( y_p(p)/a ); c=ncelly*(ix-1)+iy; plist_p(p)=plist_c(c); plist_c(c)=p;end