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**Memory aspects and performance of iterative solvers.**
*(English)*
Zbl 0798.65045

The article presents an analysis on the relationship between memory aspects and performance in real applications in the domain of very large scale integration device simulation and demonstrates performance variations due to memory-related architectural features on a number of computers ranging from workstations to supercomputers for typical and ill-conditioned linear systems, using different iterative methods and preconditioners.

The experiments are done using PILS, a package of iterative linear solvers. PILS implements a large number of iterative methods and preconditioners and allows them to combine in a flexible way. The described experiments are preceded by an overview of the methods. Section 4.1 analyses the effect that problem size and grid dimension have on the storage requirements of direct and iterative linear solvers. In section 4.2 the iterative solver is fixed. The Mflops (millions of floating-point operations per second) rates of one particular preconditioned iterative method on a set of machines and on a representative set of linear systems are given in a list.

In section 4.3 one typical linear system is selected and the speed and performance of several iterative methods applied to the problem using the same preconditioner are analyzed. In section 4.4 the iterative method is fixed and applied to the same typical linear system with different preconditioners. In section 4.5 the convergence speed and storage requirements of different preconditioners on an ill-conditioned linear system, are examined.

The experiments are done using PILS, a package of iterative linear solvers. PILS implements a large number of iterative methods and preconditioners and allows them to combine in a flexible way. The described experiments are preceded by an overview of the methods. Section 4.1 analyses the effect that problem size and grid dimension have on the storage requirements of direct and iterative linear solvers. In section 4.2 the iterative solver is fixed. The Mflops (millions of floating-point operations per second) rates of one particular preconditioned iterative method on a set of machines and on a representative set of linear systems are given in a list.

In section 4.3 one typical linear system is selected and the speed and performance of several iterative methods applied to the problem using the same preconditioner are analyzed. In section 4.4 the iterative method is fixed and applied to the same typical linear system with different preconditioners. In section 4.5 the convergence speed and storage requirements of different preconditioners on an ill-conditioned linear system, are examined.

Reviewer: D.Petcu (Timişoara)

### MSC:

65F10 | Iterative numerical methods for linear systems |

65Y20 | Complexity and performance of numerical algorithms |