Gauss-Seidel Research Articles

Iterative algorithms and architectures in massive MIMO detection

Massive multiple-input multiple-output (MIMO) wireless systems play an important role in the 5G networks. The complexity of signal detection in massive MIMO is increasing rapidly due to the growth of the number of transmitting antennas. In this paper, we introduced different iterative algorithms to decrease the computational cost of the approximate minimum mean-square error (MMSE) algorithm, including the Neumann Series algorithm, Jacobi method, Gauss-Seidel method, Successive Over Relaxation method and the Conjugate Gradient method. In addition, the VLSI architecture implementations of algorithms mentioned above are also discussed in the article.

Power Flow Analysis of Electrical Network Systems Using Gauss-Seidel Method and Python

This study aims to analyze the power flow in a 150kV radial power system on the island of Bali, the reason the author uses the Bali island system is because the number of busbars in the system is not too many and the data on the system is known. The problem of this research is limited by determining the voltage, power flow, and power losses in the system. The method used in this study is the Gauss-Seidel method through simulation with the help of Visual Studio Code software and the Python 3.9.2 program. The simulation is carried out by producing a total of 8 iterations. The simulation is carried out to find the parameters of the load voltage, apparent power on the slack bus, current, power flow and power losses on the line. The simulation results show that, under a load condition of 70% of the load transformer capacity, the voltage at the load bus node experiences a voltage drop, reaching 4.48% at bus 10. So when the system operates for generation conditions, the power that can be generated is 1,275.6 MegaWatt of the total generator installed, and the power delivered to each bus node is 2,090 MVa and the power losses in the system are 3.69% of the total power distributed to the bus nodes

Effectiveness of Preconditioned m-Order Gauss-Seidel Method for Linear System

Focusing on the current and the proposed preconditioner, this work examines the efficacy of the preconditioned m-order Gauss-Seidel method. Type I + S and I+N preconditioning are used for the current and proposed preconditioner respectively. Preconditioning algorithms for a linear system are constructed using iterative approaches. MATLAB are used to get the findings. The effectiveness of iterative method is compared concerning convergence, condition number, determinant, spectral radius, and the number of iterations for the current and proposed preconditioner. The numerical results show that for a linear system, the preconditioned m-order Gauss-Seidel method converges at a faster rate and the proposed preconditioner succeeds where the current preconditioner fails.

Integrated Nanogrid for the Impressed Current Cathodic Protection System in Desalination Plant

The impressed current cathodic protection (ICCP) scheme is a more reliable and efficient method of corrosion prevention mechanism than the sacrificial method. Currently, the grid connected transformer rectifier units supported with a battery banks are used for the ICCP-based corrosion protection system in the desalination plant. This conventional method is entirely grid-dependent, more expensive, and suffers during prolonged grid failure. The present trend of industrialization is the application of multi-renewable energy sources based on a nanogrid to power the station’s auxiliary power supply. This paper introduces a concept of distributed energy resources (DERs) operated integrated nanogrid (ING) system to provide a stable power supply solution to the ICCP scheme. A 100-million-litter per day capacity-based seawater desalination plant (SWDP) in India has been chosen as the test station. The conceptual hardware design and operational logic details for smooth integration of the integrated nanogrid module into the ICCP scheme of the Desalination plant is proposed. This research aims to investigate the behaviour of DERs during on-grid, off-grid and switching over from one mode of operation to another and vice-versa by using the accelerated Gauss–Seidel method in ETAP software (version 16.0.0). The simulation results confirm that the ING suffers from a high-frequency change rate during islanded operation, and in some cases, a complete blackout occurs. A PLC-based Smart Versatile ING Controller has been suggested to overcome the blackout issue. Finally, it has been proven that the stability of an industrial power system can be improved further by introducing the ING module into it.

A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method

This paper presents a novel flow update policy, namely the successive over relaxation (SOR) iteration method, which can be implemented in traffic assignment algorithms. Most existing solution algorithms for the user equilibrium traffic assignment problem (UE-TAP) mainly use two flow update policies: Jacobi and Gauss-Seidel iteration methods. The proposed flow update policy SOR can be a more efficient replacement. Following the path-based gradient projection (GP) algorithm, we developed a new method GP-SOR for the UE-TAP. This study first provides the complete procedure of applying the GP-SOR algorithm to solve the UE-TAP. Subsequently, a few properties of the proposed method are rigorously proven. However, empirical tests of the GP-SOR algorithm demonstrate serious oscillations and poor convergence. To cope with this problem, the Armijo Rule is employed to determine the relaxation factor, which substantially improves the convergence of GP-SOR algorithm. The preliminary numerical examples show that the GP-SOR algorithm has speedier convergence compared with the known alternatives, which is reflected by the evident reduction of the computing time and the number of iterations.

Numerical simulation of the natural double-diffusive convection in an elliptical cylinder -Impact of the buoyancy force-

The natural laminar and stable heat and mass convection in an enclosure defined by two horizontal confocal elliptical cylinders with normal and opposite buoyancy forces under uniform concentration and temperature has been numerically explored in this study. The physical Cartesian domain is transformed into an elliptical domain. For the numerical simulation, the equations of conservation of mass, momentum and energy as well as the boundary conditions are discretized by the numerical approach of finite volumes. The algebraic equations obtained were solved by the iterative Gauss-Seidel method. As a function of the effective variables, which are the Rayleigh number, the buoyancy force number N, the Prandtl number, and the Lewis number, the findings are shown as fields of velocities, temperatures, and concentrations as well as the average Nusselt and Sherwood numbers. The results showed that there is a critical buoyancy ratio Ncr = −1, where the mean Sherwood and Nusselt number values are minimal. Their values are decreased by rising values of N when N < Ncr and raised by rising values of N when N > Ncr, and raising the buoyancy ratio N's absolute value results in higher heat and mass transfer characteristics (averages Nusselt and Sherwood numbers).

Practical methods for GPU-based whole-core Monte Carlo depletion calculation

Several practical methods for accelerating the depletion calculation in a GPU-based Monte Carlo (MC) code PRAGMA are presented including the multilevel spectral collapse method and the vectorized Chebyshev rational approximation method (CRAM). Since the generation of microscopic reaction rates for each nuclide needed for the construction of the depletion matrix of the Bateman equation requires either enormous memory access or tremendous physical memory, both of which are quite burdensome on GPUs, a new method called multilevel spectral collapse is proposed which combines two types of spectra to generate microscopic reaction rates: an ultrafine spectrum for an entire fuel pin and coarser spectra for each depletion region. Errors in reaction rates introduced by this method are mitigated by a hybrid usage of direct online reaction rate tallies for several important fissile nuclides. The linear system to appear in the solution process adopting the CRAM is solved by the Gauss-Seidel method which can be easily vectorized on GPUs. With the accelerated depletion methods, only about 10% of MC calculation time is consumed for depletion, so an accurate full core cycle depletion calculation for a commercial power reactor (BEAVRS) can be done in 16 h with 24 consumer-grade GPUs.

Investigation and Simulation of Technical Power Losses on 33/11kv Distribution Feeders Based on Gauss-Seidel Iterative Approach

Loss of technical performance is one of the main causes of energy shortages and inefficient operation of electrical machines in energy systems. In this study, an analysis of power losses for six selected 33/11 kV distribution feeders was presented. (Kakoba, Ntare, Karamurani, Ishaka MbararaNorth1 and Mbarara North 2) at Mbarara Central Substation Network of UMEME Electricity Distribution Company in Uganda. Data such as cable type, conductor resistance, conductor reactance, and route length were obtained from energy suppliers. From this data, the Gauss-Seidel method was used to determine the total active power and associated reactive power of the entire substation system. The findings showed that the substation is profitable due to the small calculated total power losses. Although it is possible to reduce the total loss to at least 9-12%. Losses were due to old substations, overloaded transformers, and copper losses core losses in lengthy feeder routes. To improve the performance of power distribution networks, it was recommended to replace old conductors to reduce losses.

Accurate and efficient constrained molecular dynamics of polymers using Newton's method and special purpose code

In molecular dynamics simulations we can often increase the time step by imposing constraints on bond lengths and bond angles. This allows us to extend the length of the time interval and therefore the range of physical phenomena that we can afford to simulate. We examine the existing algorithms and software for solving nonlinear constraint equations in parallel and we explain why it is necessary to advance the state-of-the-art. We present ILVES-PC, a new algorithm for imposing bond constraints on proteins accurately and efficiently. It solves the same system of differential algebraic equations as the celebrated SHAKE algorithm, but ILVES-PC solves the nonlinear constraint equations using Newton's method rather than the nonlinear Gauss-Seidel method. Moreover, ILVES-PC solves the necessary linear systems using a specialized linear solver that exploits the structure of the protein. ILVES-PC can rapidly solve constraint equations as accurately as the hardware will allow. The run-time of ILVES-PC is proportional to the number of constraints. We have integrated ILVES-PC into GROMACS and simulated proteins of different sizes. Compared with SHAKE, we have achieved speedups of up to 4.9× in single-threaded executions and up to 76× in shared-memory multi-threaded executions. Moreover, ILVES-PC is more accurate than P-LINCS algorithm. Our work is a proof-of-concept of the utility of software designed specifically for the simulation of polymers.

A new preconditioner for Gauss–Seidel method for solving multi-linear systems

A new preconditioner for Gauss–Seidel method for solving multi-linear systems

Performance analysis of a queueing system based on working vacation with repairable fault in the P2P network

In recent years, peer-to-peer (P2P) as a means of content distribution and sharing service are receiving extensive attention. In this paper, the hybrid P2P network structure model is combined with the knowledge of queueing theory. In order to address the problem generated by unnecessary online behavior of nodes, the working sleep mechanism for the serving nodes is introduced, and the synchronous multiple working vacation strategy is also adopted to decrease the system energy consumption. Then a queueing model with working vacation and repairable fault is built, which used to simulate the resource transmission process of P2P network and to study the performance of P2P sharing system. The steady-state probability vector is derived by employing quasi-birth-and-death process and matrix-geometric solution method. And the expressions for system performance indicators, such as the average delay, are obtained by employing Gauss–Seidel iteration method. Through numerical experiments, the performance indicators of the P2P resource sharing system are studied, which provides a theoretical basis to decrease online energy consumption of nodes in the hybrid P2P network. And through employing Nash equilibrium and social optimal strategy, the value of the social maximum benefit under the social optimization is obtained.

ANALYSIS OF CHANGES IN THE INPUT OUTPUT STRUCTURE OF DKI JAKARTA PROVINCE IN 2016 AND 2024: USING THE DYNAMIC INPUT OUTPUT (DIO) MODEL

This study aims to look at the estimated structural changes in the input output table for DKI Jakarta Province in 2024. Estimates for changes in the structure are obtained by making projections of the input-output table for DKI Jakarta Province in 2024 using the Dynamic Input Output (DIO) model, namely by embedding the econometric model into the input output model, using the 2016 based year, 52 economic sectors, and 22 data series from 2000 to 2021.DIO is a hybrid model that places more emphasis on non-survey aspects that combines macro-econometric equations with identity equations in input-output analysis. This model has many dynamic equations consisting of 425 equation model. The parameters value of the equation are estimated using a combination of three estimation methods: (1) Ordinary Least Square, (2) First Order of Autoregressive, and (3) Second Order of Autoregressive. The general balance value in the DIO model is formulated using the Gauss-Seidel iteration "RAS" method.The results of the study show that in 2024 the corporate services sector, the chemical, pharmaceutical and traditional medicine industry sector, and the transportation equipment industry sector are the dominant sectors in shaping changes in the structure of intermediate demand. The Construction Sector, the Corporate Services sector, and the transportation equipment industry sector are the dominant sectors shaping changes in the structure of intermediate input. The construction sector, the real estate sector, and the wholesale and retail trade sector, not cars and motorcycles, are the dominant sectors in shaping changes in the structure of final demand. For the gross value added component, the Wholesale and Retail Trade sector, Not Cars and Motorcycles, the Private Information and Communication sector, and the Financial Intermediary Services sector other than the Central Bank are the largest sectors in the formation of structural changes.

An internal coupling method between neutronics and thermal-hydraulics with RMC and CTF

To tackle the high-fidelity multi-physics coupling challenge in nuclear reactors, an internal coupling method was proposed and implemented to closely couple the neutron transport Monte Carlo code RMC and the sub-channel thermal-hydraulics solver COBRA-TF (CTF) using direct memory data transfers. In this coupling system, fixed-point Picard iteration scheme and Gauss-Seidel iteration method were implemented and evaluated. Two acceleration algorithms were proposed and both proved effective, including the hybrid MPI/OpenMP parallelism scheme and the asymptotic batch coupling method. The coupling system was validated against the VERA benchmarks and compared with literatures. The k eigenvalue differed by 7 pcm and the relative differences in the radial power profiles were less than 0.30%. Moreover, the simulation time was reduced by 48.1% due to quicker convergence with the two acceleration methods. Further analyses also proved the superior precision of this method, especially for asymmetric problems.

Influence of Thickness of the Porous Layer on Thin Film Condensation in Forced Convection in a Canal Whose Walls are Covered with a Porous Material: Determination of Lengths of Entry

We have examined film condensation in a channel whose walls are covered with porous media numerically. The transfers in the porous medium and the liquid film are respectively described by the Darcy-Brinkman-Forchheimer model and the equations of the hydrodynamic and thermal boundary layers and are solved by the decentered implicit finite difference method and the iterative Gauss-Seidel method.&#x0D; After validating, the influence of the thickness of the porous layer on the longitudinal velocity and the temperature profiles in both media (pure liquid and porous medium), the thickness of the liquid film, the local Nusselt number and the lengths of entry have been studied.&#x0D; We note that an increase in the thickness of the porous layer increases the friction and decreases the contact of the fluid with the cold plate and allows a decrease in the longitudinal velocity and an increase in the temperatures in the porous medium and the pure liquid, a decrease liquid film thickness (disadvantaged condensation) and increases the local Nusselt number and also an increase in the length of entry. The increase in length of entry is quasi-linear. The sensitivity of condensation to a change in thickness of the porous layer is constant.

A new, fast method for solving finite-element equations iteratively based on Gauss–Seidel

Solving large equation systems is the most time-consuming part of finite-element modelling – iterative techniques are favoured for models with numerous degrees of freedom where direct techniques have high storage requirements. Classical iterative techniques such as Gauss–Seidel (GS) are robust due to guaranteed convergence and algorithmic simplicity. Performance of iterative techniques chiefly depends on system scale and stiffness matrix properties – which are influenced by structural configuration. However, it is possible to adjust an iterative algorithm such that its speed is greatly enhanced for a certain class of structural configurations. This paper presents an adjusted GS solver, ‘constrained Gauss–Seidel’ (CGS), which has been formulated to solve typical multi-storey structures with an enhanced speed. The innovation in CGS originates from the adoption of a diaphragmatic relaxation mechanism that results in dividing equations into two groups to optimally deal with the different unknown types. In this paper, the concept and algorithm of the newly developed CGS method are elucidated. Then, 16 practical examples are solved to assess the solving speed of CGS against other iterative methods – GS and modified Gauss–Seidel (MGS, MGS*). The convergence speed of CGS attained 33 times, 3.7 times and 2 times those of GS, MGS and MGS*, respectively.

Joint Compensation of TX/RX IQ Imbalance and Channel Parameters for OTSM Systems

Orthogonal time sequency multiplexing (OTSM), robust to doubly-selective fading channel, performs similar to orthogonal time frequency space (OTFS) system with less modulation/demodulation complexity. Direct conversion OTSM system suffers from hardware impairments such as in-phase and quadrature phase (IQ) imbalance at the transmitter (TX) and receiver (RX). At high frequencies, hardware imperfections are inevitable and should be compensated for better performance. In this Letter, we propose joint estimation of TX and RX IQ imbalance and estimate channel parameters in the delay time domain using pseudo noise based training sequence approach. The mean square error of the estimated channel parameters reduce with increase in training sequence length and power. With matched filtered Gauss-Seidel iterative method of detection of low complexity, it is shown that the compensated system performs close to ideal system under fractional delay and fractional Doppler.

Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system

This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New Symmetric Gauss-Seidel (NSGS), and Parametric Symmetric Gauss-Seidel (PSGS) methods for solving the linear system Ax = b are considered. This system is preconditioned with precondition type I + S. Convergence properties are analyzed with standard procedures and a numerical experiment is undertaken to compare the efficiency of the matrix. Algorithms are prepared. MATLAB software is used for checking computational efficiency of preconditioned iterative methods. Results indicate the effectiveness of preconditioning.

On the convergence of iterative schemes for solving a piecewise linear system of equations

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first provide a negative answer via a counterexample to a conjecture on the global and finite convergence of the Newton iteration for symmetric and positive definite matrices. Additionally, we discuss some surprising features of the semi-smooth Newton iteration in low dimensions and its behavior in higher dimensions. Secondly, we present two iterative schemes inspired by the classical Jacobi and Gauss-Seidel methods for linear systems of equations for finding a solution to the problem. We study sufficient conditions for the convergence of both proposed procedures, which are also sufficient for the existence and uniqueness of solutions to the problem. Lastly, we perform some computational experiments designed to illustrate the behavior (in terms of CPU time) of the proposed iterations versus the semi-smooth Newton method for dense and sparse large-scale problems. Moreover, we included the numerical solution of a discretization of the Boussinesq PDE modeling a two-dimensional flow in a homogeneous phreatic aquifer.

Splitting-based randomized iterative methods for solving indefinite least squares problem

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose a simple and effective splitting (SP) method according to its own structure, and prove that it converges for any initial value. Further, to avoid implementing some matrix multiplications and calculating the inverse of large matrix, and considering the acceleration and efficiency of the randomized strategy, we develop two randomized iterative methods on the basis of the SP method as well as the randomized Kaczmarz, Gauss-Seidel and coordinate descent methods, and describe their convergence properties. Numerical results show that our three methods all have quite decent performance in both computing time and iteration numbers compared with the latest iterative method of the ILS problem, and also demonstrate that the two randomized methods indeed yield significant acceleration in terms of computing time.

Understanding the Convergence of the Preconditioned PDHG Method: A View of Indefinite Proximal ADMM

The primal-dual hybrid gradient (PDHG) algorithm is popular in solving min-max problems which are being widely used in a variety of areas. To improve the applicability and efficiency of PDHG for different application scenarios, we focus on the preconditioned PDHG (PrePDHG) algorithm, which is a framework covering PDHG, alternating direction method of multipliers (ADMM), and other methods. We give the optimal convergence condition of PrePDHG in the sense that the key parameters in the condition can not be further improved, which fills the theoretical gap in the-state-of-art convergence results of PrePDHG, and obtain the ergodic and non-ergodic sublinear convergence rates of PrePDHG. The theoretical analysis is achieved by establishing the equivalence between PrePDHG and indefinite proximal ADMM. Besides, we discuss various choices of the proximal matrices in PrePDHG and derive some interesting results. For example, the convergence condition of diagonal PrePDHG is improved to be tight, the dual stepsize of the balanced augmented Lagrangian method can be enlarged to 4/3 from 1, and a balanced augmented Lagrangian method with symmetric Gauss-Seidel iterations is also explored. Numerical results on the matrix game, projection onto the Birkhoff polytope, earth mover’s distance, and CT reconstruction verify the effectiveness and superiority of PrePDHG.