Scientific computing on vector computers
Scientific computing on vector computers
Utilizing virtual shared memory in a topology independent, multicomputer environment
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Iterative solution methods
Experience in implementing the algebraic multilevel iteration method on a SIMD-type computer
Applied Numerical Mathematics - Special issue on massively parallel computing and applications
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
The SGI Origin: a ccNUMA highly scalable server
Proceedings of the 24th annual international symposium on Computer architecture
MPI: The Complete Reference
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
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We consider the algebraic multilevel iteration (AMLI) for the solution of systems of linear equations as they arise form a finite-difference discretization on a rectangular grid. Key operation is the matrix-vector product, which can efficiently be executed on vector and parallel-vector computer architectures if the nonzero entries of the matrix are concentrated in a few diagonals. In order to maintain this structure for all matrices on all levels coarsening in alternating directions is used. In some cases it is necessary to introduce additional dummy grid hyperplanes. The data movements in the restriction and prolongation are crucial, as they produce massive memory conflicts on vector architectures. By using a simple performance model the best of the possible vectorization strategies is automatically selected at runtime. Examples show that on a Fujitsu VPP300 the presented implementation of AMLI reaches about 85% of the useful performance, and scalability with respect to computing time can be achieved.