Search results for "Partial solution"
showing 2 items of 2 documents
A parallel radix-4 block cyclic reduction algorithm
2013
SUMMARY A conventional block cyclic reduction algorithm operates by halving the size of the linear system at each reduction step, that is, the algorithm is a radix-2 method. An algorithm analogous to the block cyclic reduction known as the radix-q partial solution variant of the cyclic reduction (PSCR) method allows the use of higher radix numbers and is thus more suitable for parallel architectures as it requires fever reduction steps. This paper presents an alternative and more intuitive way of deriving a radix-4 block cyclic reduction method for systems with a coefficient matrix of the form tridiag{ − I,D, − I}. This is performed by modifying an existing radix-2 block cyclic reduction me…
On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
2018
Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…