Do I need MathLink to run finite-difference fast enough for Manipulate?

• To: mathgroup at smc.vnet.net
• Subject: [mg115705] Do I need MathLink to run finite-difference fast enough for Manipulate?
• From: "James" <icorone at hotmail.com>
• Date: Wed, 19 Jan 2011 05:23:20 -0500 (EST)

```Hello guys,

I would like to create a Manipulate for a finite-difference on a system
of PDEs using a 100x100 array that is processed about 10,000 times.  Is
it possible to code this in native Mathematica, for example using
Compile, fast enough to be reasonably used by Manipulate (under 3 or 4
seconds)?  The C++ code is below and with the Compiler set to optimize
speed, it runs in approximately 1.5 seconds.  However, if I attempt to
just code it in Mathematica using arrays, it takes much too long to
execute.

Can someone help me decide if the only reasonable option is to use

Thanks Guys.  Here's the C++ code.  The variables u, v, and lap
are all 100x100 arrays.

startt=clock();

for(p=1;p<=10000;p++){

lap[0][0]=(u[0][1]-4*u[0][0]+u[0][M-1]+u[1][0]+u[N-1][0]);

for(j=1;j<=M-2;j++)
{
lap[0][j]=(u[0][j+1]-4*u[0][j]+u[0][j-1]+u[1][j]+u[N-1][j]);
}

lap[0][M-1]=(u[0][0]-4*u[0][M-1]+u[0][M-2]+u[1][M-1]+u[N-1][M-1]);

for(i=1;i<=N-2;i++)
{
lap[i][0]=(u[i][1]-4*u[i][0]+u[i][M-1]+u[i+1][0]+u[i-1][0]);
}

for(i=1;i<=N-2;i++)
{

lap[i][M-1]=(u[i][0]-4*u[i][M-1]+u[i][M-2]+u[i+1][M-1]+u[i-1][M-1]);
}

lap[N-1][0]=(u[N-1][1]-4*u[N-1][0]+u[N-1][M-1]+u[0][0]+u[N-2][0]);

lap[N-1][M-1]=(u[N-1][0]-4*u[N-1][M-1]+u[N-1][M-2]+u[0][M-1]+u[N-2][M-1]);

for(j=1;j<=M-2;j++)
{

lap[N-1][j]=(u[N-1][j+1]-4*u[N-1][j]+u[N-1][j-1]+u[0][j]+u[N-2][j]);
}

for(i=1;i<=N-2;i++)
for(j=1;j<=M-2;j++)
{
lap[i][j]=(u[i][j+1]-4*u[i][j]+u[i][j-1]+u[i+1][j]+u[i-1][j]);
}

for(i=0;i<M;i++)
for(j=0;j<N;j++){

u[i][j] =
=u[i][j]+dt*(D_u*lap[i][j]+(a-(b+1)*u[i][j]+v[i][j]*u[i][j]*u[i][j]));

}

lap[0][0]=(v[0][1]-4*v[0][0]+v[0][M-1]+v[1][0]+v[N-1][0]);

for(j=1;j<=M-2;j++)
{
lap[0][j]=(v[0][j+1]-4*v[0][j]+v[0][j-1]+v[1][j]+v[N-1][j]);
}

lap[0][M-1]=(v[0][0]-4*v[0][M-1]+v[0][M-2]+v[1][M-1]+v[N-1][M-1]);

for(i=1;i<=N-2;i++)
{
lap[i][0]=(v[i][1]-4*v[i][0]+v[i][M-1]+v[i+1][0]+v[i-1][0]);
}

for(i=1;i<=N-2;i++)
{

lap[i][M-1]=(v[i][0]-4*v[i][M-1]+v[i][M-2]+v[i+1][M-1]+v[i-1][M-1]);
}

lap[N-1][0]=(v[N-1][1]-4*v[N-1][0]+v[N-1][M-1]+v[0][0]+v[N-2][0]);

lap[N-1][M-1]=(v[N-1][0]-4*v[N-1][M-1]+v[N-1][M-2]+v[0][M-1]+v[N-2][M-1]);

for(j=1;j<=M-2;j++)
{

lap[N-1][j]=(v[N-1][j+1]-4*v[N-1][j]+v[N-1][j-1]+v[0][j]+v[N-2][j]);
}

for(i=2;i<=N-2;i++)
for(j=2;j<=M-2;j++)
{
lap[i][j]=(v[i][j+1]-4*v[i][j]+v[i][j-1]+v[i+1][j]+v[i-1][j]);
}

for(i=0;i<M;i++)
for(j=0;j<N;j++){
v[i][j] =
=v[i][j]+dt*(D_v*lap[i][j]+(b*u[i][j]-v[i][j]*u[i][j]*u[i][j]));
}

endt=clock();

fprintf(stderr,"%d\n",endt-startt);

```

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