Using the nodal method in ventilation analysis

I am developing a script to find the internal pressures of 3 separate zones using the exterior pressures, using the Jacobi matrix and iterations.

However, I am receiving this error message: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN , with inaccurate results for the interior pressures.

This is my code:

clear all

%External Pressures

Pe1=-600;

Pe2=70;

Pe3=58;

E=0.01; %Error margin

Ke1=1.3;

Ke2=0.61;

Ke3=1.525;

K12=2.54;

K32=1.86;

Cde1=0.65;

Cde2=0.61;

Cde3=0.61;

Cd12=0.62;

Cd32=0.62;

Ae1=2;

Ae2=1;

Ae3=2.5;

A12=4;

A32=3;

P1=200;

P2=60;

P3=80;

N=4;

P=zeros(N,N);

P(1,1)=P1;

P(1,2)=P2;

P(1,3)=P3;

fP1=-Ke1*abs(Pe1-P1^0.5)-(K12*abs(P2-P1)^0.5);

fP2=Ke2*abs(Pe2-P2)^0.5+K12*abs(P1-P2)^0.5+K32*abs(P3-P2)^0.5;

fP3=-Ke3*abs(Pe3-P3)^0.5-K32*abs(P2-P3)^0.5;

fP=[fP1,fP2,fP3];

df1p1=(-0.5*(Ke1*(abs(Pe1-P1)))^-0.5)-(0.5*(K12*(abs(P2-P1)))^-0.5);

df1p2=-(0.5*(K12*(abs(P2-P1)))^-0.5);

df1p3=(0);

df2p1=(-0.5*(K12*(abs(P1-P2)))^-0.5);

df2p2=(-0.5*(Ke2*(abs(Pe2-P2)))^-0.5)-(0.5*(K12*(abs(P1-P2)))^-0.5)-(0.5*(K32*(abs(P3-P2)))^-0.5);

df2p3=(-0.5*(K32*(abs(P3-P2)))^-0.5);

df3p1=(0);

df3p2=(-0.5*(K32*(abs(P2-P3)))^-0.5);

df3p3=(-0.5*(Ke3*(abs(Pe3-P3)))^-0.5)-(0.5*(K32*(abs(P2-P3)))^-0.5);

%Jacobian Matrix

J=[df1p1,df1p2,df1p3;df2p1,df2p2,df2p3;df3p1,df3p2,df3p3];

J_inv=inv(J);

for j=2:N-1

for i=1:N-1

if abs(P(i+1)-P(i))>E

P(i+1,j)=P(i,j)-(J_inv(i,j)*fP(i));

end

end

end

%calculating the air exchange rate

m12=Cd12*A12*sqrt(2*1.225*(abs(P2-P1)));

m32=Cd32*A32*sqrt(2*1.225*(abs(P3-P2)));

me1=Cde1*Ae1*sqrt(2*1.225*(abs(Pe1-P1)));

me2=Cde2*Ae2*sqrt(2*1.225*(abs(Pe2-P2)));

me3=Cde3*Ae3*sqrt(2*1.225*(abs(Pe3-P3)));

Answer 1

[Alan Stevens]

Try removing

J_inv=inv(J);

and replacing

(J_inv(i,j)*fP(i))

by

J(i,j)\fP(i)