Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

Akhunov, R. R.; Gazizov, Talgat R.; Kuksenko, S. P.

doi:10.1134/s0965542516080030

Cited by 4 publications

(4 citation statements)

References 3 publications

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“…We use the second approach. For this purpose we developed methods of adaptive recomputing preconditioner based on the threshold of the number of iterations [33], the average arithmetic complexity [34], and the average solution time [35]. Recomputation of the preconditioner is not necessary if the seed matrix for calculating the preconditioner has been selected properly.…”

Section: Structures and Approach For Investigationmentioning

confidence: 99%

Solving the Complexity Problem in the Electronics Production Process by Reducing the Sensitivity of Transmission Line Characteristics to Their Parameter Variations

2019

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In this paper we consider the complexity problem in electronics production process. Particularly, we investigate the ways to reduce sensitivity of transmission line characteristics to their parameter variations. The reduction is shown for the per-unit-length delay and characteristic impedance of several modifications of microstrip transmission lines. It can be obtained by means of making an optimal choice of parameter values, enabling proper electric field redistribution in the air and the substrate. To achieve this aim we used an effective simulation technique and software tools. Taken together, for the first time, they have allowed formulating general approach which is relevant to solve a wide range of similar tasks.

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Section: Structures and Approach For Investigationmentioning

confidence: 99%

Solving the Complexity Problem in the Electronics Production Process by Reducing the Sensitivity of Transmission Line Characteristics to Their Parameter Variations

2019

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“…For long 2D-structures a quasi-static approach is often relevant as it allows to obtain fast and accurate results. However, even for this approach the decrease of simulation time is important and can be achieved by various methods, for example by implementation of new algorithms [11]. The calculation of matrices of per unit length parameters of the structure is the essential stage of the analysis.…”

Section: Introductionmentioning

confidence: 99%

Simulation of asymmetrical modal filter with different segmentation

Gazizov

Zabolotsky

Gazizov

2016

2016 International Siberian Conference on Control and Communications (SIBCON)

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The problem of protection of communication and control systems against intentional electromagnetic interference is considered. The importance of effective simulation of new protective devices is highlighted. The asymmetrical modal filter has been described and quasi-static simulation of its time-domain response to ultrashort pulse has been carried out with different segmentation of boundaries. The paper shows that we can use a rough segmentation to obtain accurate values of main characteristics of a modal filter, which requires very short simulation time. Quasi-static simulation has been compared with electrodynamic one as well as with the experiment. Results of this paper are applicable for the class of protective devices based on coupled microstrip lines.

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“…However, it is a priori impossible to determine when to recompute matrix M. Thus, the search for an a priori condition of the recomputation is relevant. Paper [13] is devoted to one of the conditions. Other conditions proposed by the authors have been investigated in paper [14], so they are omitted in this paper.…”

Section: Approaches To Solving the Sequence Of Linear Systemsmentioning

confidence: 99%

“…However, the effectiveness of the preconditioner decreases, as the difference between the first and the current matrix increases. To solve this problem, it was suggested to recompute matrix M when the convergence rate of solving the current linear system is too slow [13]. Existence of optimal threshold value was shown.…”

Section: Approaches To Solving the Sequence Of Linear Systemsmentioning

confidence: 99%

Choosing order of operations to accelerate strip structure analysis in parameter range

Kuksenko

Akhunov

Gazizov

2018

J. Phys.: Conf. Ser.

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Abstract. The paper considers the issue of using iteration methods in solving the sequence of linear algebraic systems obtained in quasistatic analysis of strip structures with the method of moments. Using the analysis of 4 strip structures, the authors have proved that additional acceleration (up to 2.21 times) of the iterative process can be obtained during the process of solving linear systems repeatedly by means of choosing a proper order of operations and a preconditioner. The obtained results can be used to accelerate the process of computer-aided design of various strip structures. The choice of the order of operations to accelerate the process is quite simple, universal and could be used not only for strip structure analysis but also for a wide range of computational problems. IntroductionDistributed circuits based on various strip structures are widely used in radioelectronic equipment, both as transmission lines that maintain proper characteristics for desired signals for a long time and as a basis for new protective devices. A strip structure consists of signal and ground conductors and a dielectric substrate. The separation between conductors, their thickness, other geometrical parameters and dielectric permittivity of a substrate can be repeatedly changed during simulation and optimization of elements and devices. These processes significantly increase computational costs. Generally, hardware accelerators (multicore workstations, clusters, graphical processing units) are used to decrease computational costs, while algorithmic methods are often ignored. A quasistatic approach, which is based on calculating electric capacitance with the method of moments [1], is widely used to decrease computational costs of strip structure analysis in contrast to the electrodynamic approach. The method of moments implies solving linear systems with dense matrix. This paper presents the research into application of iterative methods for solving dense linear systems repeatedly during multivariant analysis of strip structures using the method of moments with the optimal choice of order of operations.

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Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

Cited by 4 publications

References 3 publications

Solving the Complexity Problem in the Electronics Production Process by Reducing the Sensitivity of Transmission Line Characteristics to Their Parameter Variations

Solving the Complexity Problem in the Electronics Production Process by Reducing the Sensitivity of Transmission Line Characteristics to Their Parameter Variations

Simulation of asymmetrical modal filter with different segmentation

Choosing order of operations to accelerate strip structure analysis in parameter range

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