Your edited question is confusing because you say you are sending your kernel an array of size 1000 x 1000 but you want to know how to do this using a global array. The only way I know of to send this much data to a kernel is to use a global array, so you are probably already doing this with an array in global memory.
Nevertheless, there are 2 methods, at least, to create and initialize an array in global memory:
1.statically, using __device__ and cudaMemcpyToSymbol, for example:
#define SIZE 100
__device__ int A[SIZE];
...
int main(){
int myA[SIZE];
for (int i=0; i< SIZE; i++) myA[i] = 5;
cudaMemcpyToSymbol(A, myA, SIZE*sizeof(int));
...
(kernel calls, etc.)
}
(device variable reference, cudaMemcpyToSymbol reference)
2.dynamically, using cudaMalloc and cudaMemcpy:
#define SIZE 100
...
int main(){
int myA[SIZE];
int *A;
for (int i=0; i< SIZE; i++) myA[i] = 5;
cudaMalloc((void **)&A, SIZE*sizeof(int));
cudaMemcpy(A, myA, SIZE*sizeof(int), cudaMemcpyHostToDevice);
...
(kernel calls, etc.)
}
(cudaMalloc reference, cudaMemcpy reference)
For clarity I'm omitting error checking which you should do on all cuda calls and kernel calls.