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Topic: volume integration
Replies: 10   Last Post: Dec 5, 2012 5:57 PM

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Marios Karaoulis

Posts: 86
Registered: 5/10/10
Re: volume integration
Posted: Sep 8, 2011 5:52 PM
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Hi again,

Let's say I have the unx matrix where

1st column is the x-coordinate
2nd column is the y-coordinate
3rd column is the z=coordinate

4th column is the x component of J1
5th column is the y component of J1
6th column is the z component of J1

7th column is the x component of J2
8th column is the y component of J2
9th column is the z component of J2

I create the tetrahedrals
DT=DelaunayTri(unx(:,1),unx(:,2),unx(:,3));
num_tet=length(DT(:,1));

% find volume

% find volume of each tetrahedra
voule_tet=zeros(num_tet,1);
parfor i=1:num_tet

n1=DT(i,1);
n2=DT(i,2);
n3=DT(i,3);
n4=DT(i,4);

P1=[unx(n1,1) unx(n1,2) unx(n1,3)];
P2=[unx(n2,1) unx(n2,2) unx(n2,3)];
P3=[unx(n3,1) unx(n3,2) unx(n3,3)];
P4=[unx(n4,1) unx(n4,2) unx(n4,3)];

V1=P2-P1;
V2=P3-P2;
V3=P4-P3;

volume_tet(i) = abs(det([V1(:) V2(:) V3(:)]))/6;

end


% find integration

jac=zeros(1,num_tet);

parfor k=1:num_tet
% take appropriate solution

n1=DT(k,1);
n2=DT(k,2);
n3=DT(k,3);
n4=DT(k,4);



%take from A (Jx,Jy,Jz) for each 4 points
JA1=[unx(n1,4:6)];
JA2=[unx(n2,4:6)];
JA3=[unx(n3,4:6)];
JA4=[unx(n4,4:6)];


JB1=[unx(n1,7:9)];
JB2=[unx(n2,7:9)];
JB3=[unx(n3,7:9)];
JB4=[unx(n4,7:9)];


jac(1,k)=0.25*volume(k)*(dot(JA1,JB1)+dot(JA2,JB2)+dot(JA3,JB3)+dot(JA4,JB4));



end



Does this look right? Do you have any suggestions how to speed this
up?

Thanks in adnvance



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