Parallelization of Recurrent Loops Due to the Preliminary Computation of Superpositions

Steinberg, Oleg

doi:10.14529/mmp200305

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…This work continues the series of publications of the authors [26,28,30]. The solvers presented in this article are embedded in the ACELAN COMPOS application software package for modeling the properties of new materials [18,20].…”

Section: Introductionmentioning

confidence: 66%

“…Decomposition of the matrix C into a product of two-diagonal (block-two-diagonal) matrices can take a long time. It is important that the calculation of C −1 * y should be performed quickly, if possible, with parallelization [30]. If the matrix C is symmetric, then its decomposition L • D • L T allows you to store only the matrices L and D, which should give acceleration.…”

Section: Iterative Algorithms For Linear Systemsmentioning

confidence: 99%

“…Solving system of linear algebraic equations with a bi-diagonal matrix reduces to computing a loop with linear recurrent dependence. Parallel algorithms for computing such loops were described in the articles [29,30]. In this work, the matrix of the system of linear algebraic equations has a special block structure (periodically zero blocks appear), which significantly improves the efficiency of parallelized.…”

Section: Exploring the Parallelization Options Of Acelan-compos Solversmentioning

confidence: 99%

“…These intermediate values are stored in the fast register memory. The remaining values of the array X are then calculated in parallel in (N /8−1) step [30].…”

Section: For (mentioning

confidence: 99%

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Fast Solvers for Systems of Linear Equations with Block-Band Matrices

Steinberg¹,

Steinberg²,

Oganesyan³

et al. 2023

EAJAM

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This article deals with parallel iterative algorithms for linear systems with block-band matrices. The algorithms can be used in mathematical modeling of the problems involving finite difference and finite element methods. The solvers are adjusted to the problem and to the computing systems, which use special precompilers. Applications of the algorithms to the ACELAN-COMPOS software package focused on the new material modeling, is described. To achieve a high performance, both parallel programming techniques and the optimization of the processor memory hierarchy are used. The results of numerical experiments confirm the efficiency of the methods and algorithms.

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Section: Introductionmentioning

confidence: 66%

Section: Iterative Algorithms For Linear Systemsmentioning

confidence: 99%

Section: Exploring the Parallelization Options Of Acelan-compos Solversmentioning

confidence: 99%

“…These intermediate values are stored in the fast register memory. The remaining values of the array X are then calculated in parallel in (N /8−1) step [30].…”

Section: For (mentioning

confidence: 99%

See 2 more Smart Citations