Using CUDA Thrust to evaluate recurrence relations for nonlinear partial differential equations

Question

I need to compute double precision recurrence relations of the form

1. X[n] = A[n]*X[n-1] + B[n]
2. X[n] = A[n]*X[n-1] + B[n]*X[n-2] + C[n]

I'm using these in conjunction with nonlinear PDE's. Is Thrust's inclusive scan operator flexible enough to compute these?

Answer 1

As mentioned by talonmies, recurrence relations involved in the solution of nonlinear partial differential equations are something different from prefix sums.

The above relations are typically in the form of update relations like

see also the book "Partial Difference Equations" by Sui Sun Cheng.

To evaluate this update equation in parallel, a possibility is using zip iterators in conjunction with transforms, as in the below example

#include <thrust\device_vector.h>

struct Recurrence{
template <typename Tuple>
    __host__ __device__ double operator()(Tuple a) {

        // --- X[n] = A[n]*X[n-1] + B[n]*X[n-2] + C[n]
        return (thrust::get<0>(a) * thrust::get<3>(a) + thrust::get<1>(a) * thrust::get<4>(a) + thrust::get<2>(a));

    }
};


int main() {

    const int N = 10;

    thrust::device_vector<double> d_x(N, 1.f);
    thrust::device_vector<double> d_a(N, 2.f);
    thrust::device_vector<double> d_b(N, 3.f);
    thrust::device_vector<double> d_c(N, 4.f);

    thrust::transform(thrust::make_zip_iterator(thrust::make_tuple(d_a.begin() + 2, d_b.begin() + 2, d_c.begin() + 2, d_x.begin() + 1,     d_x.begin())), 
                      thrust::make_zip_iterator(thrust::make_tuple(d_a.begin() + N, d_b.begin() + N, d_c.begin() + N, d_x.begin() + N - 1, d_x.begin() + N - 2)), 
                      d_x.begin() + 2, Recurrence());

    for (int i=2; i<N; i++) {
        double temp = d_x[i];
        printf("%i %f\n", i, temp);
    }

    return 0;
}