Parallel Iterative Solution of the Hermite Collocation Equations on GPUs

We consider the computationally intense problem of solving the large, sparse and non-symmetric system of equations arising from the discretization of elliptic Boundary Value Problems (BVPs) by the Collocation finite element method using Hermite bi-cubic elements. As the size of the problem directly suggests the usage of parallel iterative methods, we consider the implementation on multiprocessor shared memory parallel architectures with Graphics Processing Units of the non-stationary preconditioned Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative method. To induce scalability to our computation, we structure the Collocation matrix to a particular line red-black ordered form, leading to the development of a well-structured parallel algorithm for the iterative method. The realization of the said algorithm took place on a HP SL390 multiprocessor machine with Tesla M2070 GPUs. Execution time measurements are used to reveal the efficiency of our parallel implementation.