Multigrid Algorithms on the Hypercube Multiprocessor
IEEE Transactions on Computers
The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Multicolor ICCG methods for vector computers
SIAM Journal on Numerical Analysis
Constructive interference in parallel algorithms
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Krylov subspace methods on supercomputers
SIAM Journal on Scientific and Statistical Computing
Multigrid methods on parallel computers—a survey of recent developments
IMPACT of Computing in Science and Engineering
How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
Multicolor reordering of sparse matrices resulting from irregular grids
ACM Transactions on Mathematical Software (TOMS)
Advanced Computer Architecture: Parallelism,Scalability,Programmability
Advanced Computer Architecture: Parallelism,Scalability,Programmability
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In order to execute a parallel PDE (partial differential equation) solver on a shared-memory multiprocessor, we have to avoid memory conflicts in accessing multidimensional data grids. A new multicoloring technique is proposed for speeding sparse matrix operations. The new technique enables parallel access of grid-structured data elements in the shared memory without causing conflicts. The coloring scheme is formulated as an algebraic mapping which can be easily implemented with low overhead on commercial multiprocessors. The proposed multicoloring scheme has been tested on an Alliant FX/80 multiprocessor for solving 2D and 3D problems using the CGNR method. Compared to the results reported by Saad (1989) on an identical Alliant system, our results show a factor of 30 times higher performance in Mflops. Multicoloring transforms sparse matrices into ones with a diagonal diagonal block (DDB) structure, enabling parallel LU decomposition in solving PDE problems. The multicoloring technique can also be extended to solve other scientific problems characterized by sparse matrices.