A GPU parallelized spectral method for elliptic equations in rectangular domains

We design and implement a polynomial-based spectral method on graphic processing units (GPUs). The key to success lies in the seamless integration of the matrix diagonalization technique and the new generation CUDA tools. The method is applicable to elliptic equations in rectangular domains with general boundary condition. We show remarkable speedups of up to 15 times in the 2-D case and more than 35 times in the 3-D case.