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In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

The purpose of this paper is to propose novel factored approximate sparse inverse schemes and multi-level methods for the solution of large sparse linear systems.

The main motive for the derivation of the various generic preconditioning schemes lies to the efficiency and effectiveness of factored preconditioning schemes in conjunction with Krylov subspace iterative methods as well as multi-level techniques for solving various model problems. Factored approximate inverses, namely, Generic Factored Approximate Sparse Inverse, require less fill-in and are computed faster due to the reduced number of nonzero elements. A modified column wise approach, namely, Modified Generic Factored Approximate Sparse Inverse, is also proposed to further enhance performance. The multi-level approximate inverse scheme, namely, Multi-level Algebraic Recursive Generic Approximate Inverse Solver, utilizes a multi-level hierarchy formed using Block Independent Set reordering scheme and an approximation of the Schur complement that results in the solution of reduced order linear systems thus enhancing performance and convergence behavior. Moreover, a theoretical estimate for the quality of the multi-level approximate inverse is also provided.

Application of the proposed schemes to various model problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than results by other researchers for some of the model problems.

Further enhancements are investigated for the proposed factored approximate inverse schemes as well as the multi-level techniques to improve quality of the schemes. Furthermore, the proposed schemes rely on the definition of multiple parameters that for some problems require thorough testing, thus adaptive techniques to define the values of the various parameters are currently under research. Moreover, parallel schemes will be investigated.

The proposed approximate inverse preconditioning schemes as well as multi-level schemes are efficient computational methods that are valuable for computer scientists and for scientists and engineers in engineering computations.

A new class of explicit preconditioning methods based on the concept of sparse approximate factorization procedures and inverse matrix techniques is introduced for solving biharmonic equations. Isomorphic methods in conunction with explicit preconditioned schemes based on approximate inverse matrix techniques are presented for the efficient solution of biharmonic equations. Application of the proposed method on linear systems is discussed and numerical results are given.

Multiple-input multiple-output (MIMO) combined with multi-user massive MIMO has been a well-known approach for high spectral efficiency in wideband systems, and it was targeted to detect the MIMO signals. The increasing data rates with multiple antennas and multiple users that share the communication channel simultaneously lead to higher capacity requirements and increased complexity. Thus, different detection algorithms were developed for the Massive MIMO.

This paper focuses on the various literature analyzes on various detection algorithms and techniques for MIMO detectors. Here, it reviews several research papers and exhibits the significance of each detection method.

This paper provides the details of the performance analysis of the MIMO detectors and reveals the best value in the case of each performance measure. Finally, it widens the research issues that can be useful for future researchers to be accomplished in MIMO massive detectors

This paper has presented a detailed review of the detection of massive MIMO on different algorithms and techniques. The survey mainly focuses on different types of channels used in MIMO detections, the number of antennas used in transmitting signals from the source to destination, and vice-versa. The performance measures and the best performance of each of the detectors are described.

The purpose of this paper is to demonstrate improvement of the accuracy of electrical tomography reconstruction by incorporation of a priori knowledge into the inverse problem solution.

The fusion of two different inversion algorithms capable of real‐time operation is discussed, namely a non‐iterative monotonicity‐based approach, determining the a priori knowledge and an iterative Gauss‐Newton (GN)‐based reconstruction algorithm. Furthermore, the method is compared with the unmodified algorithms themselves by means of reconstructions from simulated inclusions at different noise levels.

The accuracy of the inverse problem reconstructions, especially at the boundary regions of the unknown inclusions, benefit from the investigations of incorporating a priori knowledge about material values and can be considerable improved. The monotonicity method itself, which has low complexity, provides remarkable reconstruction results in electrical tomography.

The paper is applied to simulated discrete two‐phase scenarios, e.g. gas/oil mixtures. In a further step the method would be tested with measured data. Moreover, investigations have to be carried out in order to make the monotonicity‐based reconstruction principle more robust against disturbing artifacts.

The fusion of the non‐iterative monotonicity‐based method with the GN‐based algorithm demonstrates a novel approach of improving the reconstruction accuracy in electrical tomography.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

First of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.

The properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.

All the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.

The problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.

All the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.

The purpose of this paper is to solve the second-order nonlinear boundary value problem with nonlinear boundary conditions by an iterative numerical method.

The authors introduce eigenfunctions as test functions, such that a weak-form integral equation is derived. By expanding the numerical solution in terms of the weighted eigenfunctions and using the orthogonality of eigenfunctions with respect to a weight function, and together with the non-separated/mixed boundary conditions, one can obtain the closed-form expansion coefficients with the aid of Drazin inversion formula.

When the authors develop the iterative algorithm, removing the time-varying terms as well as the nonlinear terms to the right-hand sides, to solve the nonlinear boundary value problem, it is convergent very fast and also provides very accurate numerical solutions.

Basically, the authors’ strategy for the iterative numerical algorithm is putting the time-varying terms as well as the nonlinear terms on the right-hand sides.

Starting from an initial guess with zero value, the authors used the closed-form formula to quickly generate the new solution, until the convergence is satisfied.

Through the tests by six numerical experiments, the authors have demonstrated that the proposed iterative algorithm is applicable to the highly complex nonlinear boundary value problems with nonlinear boundary conditions. Because the coefficient matrix is set up outside the iterative loop, and due to the property of closed-form expansion coefficients, the presented iterative algorithm is very time saving and converges very fast.

The purpose of this paper is to describe two‐ and three‐dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm.

A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic‐based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs.

For the first time, a stable fully explicit algorithm has been applied to detailed multi‐dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature.

For the first time, thanks to a stabilization analysis conducted, the AC‐CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid‐electrode interface.