# Category : Science and Education

Archive : MATLAB.ZIP

Filename : PDE

//Parameters

rho //radius of cylindrical inclusion

n //number of terms in solution

m //number of boundary points

//initialize operation counts

flop = <0,0>;

//initialize variables

m1 = round(m/3);

m2 = m - m1;

pi = 4.0*atan(1.0);

//generate points in Cartesian coordinates

//right hand edge

for i = 1:m1, x(i) = 1; y(i) = (1-rho)*(i-1)/(m1-1);

//top edge

for i = m2+1:m, x(i) = (1-rho)*(m-i)/(m-m2-1); y(i) = 1;

//circular edge

for i = m1+1:m2, t = (pi/2)*(i-m1)/(m2-m1+1); ...

x(i) = 1-rho*sin(t); y(i) = 1-rho*cos(t);

//convert to polar coordinates

for i = 1:m-1, th(i) = atan(y(i)/x(i)); ...

r(i) = sqrt(x(i)**2+y(i)**2);

th(m) = pi/2; r(m) = 1;

//generate matrix

//Dirichlet conditions

for i = 1:m2, for j = 1:n, k = 2*j-1; ...

a(i,j) = r(i)**k*cos(k*th(i));

//Neumann conditions

for i = m2+1:m, for j = 1:n, k = 2*j-1; ...

a(i,j) = k*r(i)**(k-1)*sin((k-1)*th(i));

//generate right hand side

for i = 1:m2, b(i) = 1;

for i = m2+1:m, b(i) = 0;

//solve for coefficients

c = A\b

//compute effective conductivity

c(2:2:n) = -c(2:2:n);

sigma = sum(c)

//output total operation count

ops = flop(2)

Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/