# 1D wave equation (Runge-Kutta implementation) with OpenCL

• 02-10-2013, 01:36 AM
1D wave equation (Runge-Kutta implementation) with OpenCL
Dear all,

I have spent some time trying to figure out my problem, but haven't succeeded so I am posting here.

Since I thought about OpenCL for the first time, I thought it would be great to implement method of lines for solving PDE equation. So I started from the very basic example - 1D hyperbolic equation (simple string oscillations).

Starting from initialization:
Code :

```int fixed=1; for (i = 0; i < loops; i++) { u[0][i] = fixed; u[1][i] = fixed; u[2][i] = fixed;   u[n-1][i] = fixed; u[n-2][i] = fixed; u[n-3][i] = fixed;   y[0] = 0.0; y[n-1] = 0.0; }   for (i = 0; i < n; i++) { u[i][0] = fosc (i2x (i)); u[i][1] = fosc (i2x (i)); u[i][2] = fosc (i2x (i)); input[i] = u[i][2]; y[i] = (u[i][2] - u[i][0])/2.0/dt; }```

Where function fosc gives me simple Sine function profile from -50 to 50.
Code :

```float fosc (float x) { float osc; osc=1+sin(x*3.1415926/100+3.1415926/2.0); //simple string return osc; }```

I have created following buffers for input, output and derivatives:

Code :

```cl_mem inputBuffer = clCreateBuffer(context, CL_MEM_READ_WRITE|CL_MEM_COPY_HOST_PTR, n * sizeof(float),(void *) input, NULL); cl_mem outputBuffer = clCreateBuffer(context, CL_MEM_READ_WRITE , n*loops * sizeof(float), NULL, NULL); cl_mem devs = clCreateBuffer(context, CL_MEM_READ_WRITE|CL_MEM_COPY_HOST_PTR, n * sizeof(float),(void *)y, NULL);```

Since it is not valid to pass 2D arrays in kernel, I slice the output function with indexing
[x+SizeX*y]

Code :

``` for (j=0; j<loops; j++){ for (i=0; i<n; i++){ u[i][j+2]=output[i+n*j]; if (i%(n/8) == 0) { cout << u[i][j] << " "; } } cout<<endl; }```

Then I came up with the following kernel:

Code :

```float an (float fn2, float fn1, float fn, float fn11, float fn22, float dh) { return (-fn2 + 16.0 * fn1 - 30.0 * fn + 16.0 * fn11 - fn22) / 12.0 / dh / dh - func (fn); //4-th space order second derivative }     __kernel void helloworld(__global float* in, __global float* out, int n, int loops, __global float* devs) { int t; float dh=100.0/n; float dt=100.0/loops;   int i = get_global_id(0); float y[1000]; float u[1000];   float k1[1000];float k2[1000];float k3[1000];float k4[1000]; float m1[1000]; float m2[1000]; float m3[1000]; float m4[1000];   if ( (i>-1) && (i<n) ) { u[i]=in[i]; //receiving initial field values y[i]=devs[i]; //receiving initial derivatives }   for (t=0; t < loops; t++) {   if ( (i>1) && (i<n-2) ) {   k1[i] = an (u[i - 2], u[i - 1], u[i], u[i + 1], u[i + 2], dh) * dt; m1[i] = y[i] * dt;   k2[i] = an (u[i - 2] + m1[i - 2] / 2.0, u[i - 1] + m1[i - 1] / 2.0, u[i] + m1[i] / 2.0, u[i + 1] + m1[i + 1] / 2.0, u[i + 2] + m1[i + 2] / 2.0, dh) * dt; m2[i] = (y[i] + k1[i] / 2.0) * dt;   k3[i] = an (u[i - 2] + m2[i - 2] / 2.0, u[i - 1] + m2[i - 1] / 2.0, u[i] + m2[i] / 2.0, u[i + 1] + m2[i + 1] / 2.0, u[i + 2] + m2[i + 2] / 2.0, dh) * dt; m3[i] = (y[i] + k2[i] / 2.0) * dt;   k4[i] = an (u[i - 2] + m3[i - 2], u[i - 1] + m3[i - 1], u[i] + m3[i], u[i + 1] + m3[i + 1], u[i + 2] + m3[i + 2], dh) * dt; m4[i] = (y[i] + k3[i]) * dt;   y[i] = y[i] + (k1[i] + 2.0 * k2[i] + 2.0 * k3[i] + k4[i]) / 6.0; u[i] = u[i] + (m1[i] + 2.0 * m2[i] + 2.0 * m3[i] + m4[i]) / 6.0;   out[i+n*t] = u[i];   } else { out[i+n*t] = 1; } }   }```

Now the problem is that the code is working in usual C++ program but when I moved to OpenCL it doesn't. Instead of harmonic oscillations, I can see random numbers popping up here and there.

The algorithm looks fine to me, I can not figure out the problem.
I would appreciate any help.
• 03-05-2013, 05:18 AM
clint3112
Re: 1D wave equation (Runge-Kutta implementation) with OpenC
Hi,

one problem could be
Code :

```float k1[1000];float k2[1000];float k3[1000];float k4[1000]; float m1[1000]; float m2[1000]; float m3[1000]; float m4[1000];```

this means, every workitem would need a memory of 8 * 8000 * 4 bytes of memory. normally, the local memory is about 48k. Look for local memory.
Because you need that memory for your computations, there might be a problem. Try to lower that value to 16 or so, to see if there ist a problem.

Greetings,
clin3112
• 03-20-2013, 10:09 AM
`barrier(CLK_LOCAL_MEM_FENCE);`