An iterative algorithm for solving a series of linear algebraic systems with partially varying coefficient matrix is suggested. Simple formulas for evaluating the speed up obtained are derived and used in choosing the related parameters. As examples, the choice of the drop tolerance and initial guesses are considered. Multiple solutions of linear systems of orders 708, 1416, 3540, 4425 arising in computing (by the method of moments) the electric capacity of two strips on a dielectric layer above a perfect conductive plane in the range of dielectric permeability is analyzed. As compared with Gaussian elimination, a 49 times speed up in solving 1000 linear systems of order 4425 is achieved. Bibliography 8 titles.

The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures-microstrip when its thickness varies and a modal filter as the gap between the conductors varies-is carried out. The speedups turned out to be close to the optimal ones.

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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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