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1

Sensitivity and stability analysis for groundwater numerical modeling: a field study of finite element application in the arid region

Jafarzadeh Ahmad, Pourreza-Bilondi Mohsen, Akbarpour Abolfazl, Khashei-Siuki Abbas, Azizi Mohsen

Acta Geophysica

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2023

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Vol. 71, no. 2

1045--1062

EN

This study intends to investigate the impacts of scheme type, time step, and error threshold on the stability of numerical simulation in the groundwater modeling. Hence, a two-dimensional finite element (FE) was implemented to simulate groundwater flow in a synthetic test case and a real-world study (Birjand aquifer). To verify the proposed model in both cases, the obtained results were compared with analytical solutions and observed values. The stability of numerical results was analyzed through different schemes and time-step sizes. Besides, the effect of the error threshold was examined by considering different threshold values. The results confirmed that the FE model has a good capacity to simulate groundwater fluctuations even for the real problem with more complexities. Examination of implicit outputs indicated that groundwater simulations based on this scheme have good accuracy, stability, and proper convergence in all time intervals. However, in the explicit and Crank–Nicolson schemes the time interval should be less than or equal to 0.001 and 0.1 day, respectively. Also, results reveal that for making stability in all schemes the value of the error threshold should not be more than 0.0001 m. Moreover, it derived that the boundary conditions of the aquifer influence the stability of numerical outputs. Finally, it was comprehended that as time interval and error threshold increases, the oscillation rate propagated.

2

Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian

Shilpa, Dwivedi Gaurav

Journal of Applied Analysis

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2022

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Vol. 28, nr 2

211--218

EN

In this article, we prove the existence of a solution to a nonlocal biharmonic equation with nonlinearity depending on the gradient and the Laplacian.We employ an iterative technique based on the mountain pass theorem to prove our result.

3

On Finding the Optimal Tree of a Complete Weighted Graph

Hosseini Seyed Soheil, Wormald Nick, Tian Tianhai

Annals of Computer Science and Information Systems

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2020

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Vol. 21

271--275

EN

We want to find a tree where the path length between any two vertices on this tree is as close as possible to their corresponding distance in the complete weighted graph of vertices upon which the tree is built. We use the residual sum of squares as the optimality criterion to formulate this problem, and use the Cholesky decomposition to solve the system of linear equations to optimise weights of a given tree. We also use two metaheuristics, namely Simulated Annealing (SA) and Iterated Local Search (ILS) to optimise the tree structure. Our results suggest that SA and ILS both perform well at finding the optimal tree structure when the dispersion of distances in the complete graph is large. However, when the dispersion of distances is small, only ILS has a solid performance.

4

Iterating Transducers

Sutner K.

Fundamenta Informaticae

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2015

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Vol. 138, nr 1/2

259--272

EN

We discuss simple functional transductions defined by invertible Mealy automata under iteration and in particular the question when the orbit relation defined by iteration is rational. We identify a class of these automata that has relatively complicated orbits, yet some of them are still orbit rational and discuss a number of decision problems associated with these devices.

5

A Note on the Singh Six-order Variant of Newton’s Method

Marciniak A., Wolf M.

Computational Methods in Science and Technology

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2015

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Vol. 21, No. 4

261--261

EN

In 2009 in this journal it was published the paper of M. K. Singh [1], in which the author presented a six-order variant of Newton’s method. Unfortunately, in this paper there were a number of printer errors and a serious error in the proof of theorem on the order of the method proposed. Therefore, we have opted for presenting the correct proof of this theorem.

6

A Comparison of Iterative Methods of the Cubic Rate Convergence in the Problem of Transformation between Cartesian and Geodetic Coordinates

Bajorek M., Kulczycki M., Ligas M.

Geomatics and Environmental Engineering

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2014

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Vol. 8, no. 2

15--25

EN

The problem of transformation between Cartesian and geodetic (ellipsoidal) coordinates occurs often in day-to-day geodetic practice. Thus, from years it attracts interest of many scientists and practitioners. Despite the fact that many algorithms of the conversion exist to this day one may still observe new methods and approaches to the problem. In this work a comparison as to the efficiency of iterative methods of the cubic rate convergence to the solution of "latitude equation" in three representations has been presented. Two of them are polynomial representations (quartic equations) and one is in the form of an irrational equation. A comparison has been performed on two ellipsoidal height intervals: from -10 km to 10 km, from 10 km to 36 000 km and from 0° to 90° for the latitude.

PL

Problem transformacji między współrzędnymi kartezjańskim i współrzędnymi geodezyjnymi (elipsoidalnymi) pojawia się często w praktyce geodezyjnej, dlatego od lat stanowi przedmiot zainteresowania wielu naukowców oraz praktyków. Mimo że znanych jest wiele algorytmów przeliczania współrzędnych, ciągle pojawiają się nowe metody i sposoby. W artykule przedstawiono porównanie efektywności metod iteracyjnych o zbieżności sześciennej oraz „równania szerokości" w trzech reprezentacjach. Dwie z nich to reprezentacje wielomianowe (równania czwartego stopnia), a jedna to reprezentacja w formie równania niewymiernego. Porównanie przeprowadzono dla dwóch przedziałów wysokości elipsoidalnej: od -10 km do 10 km oraz od 10 km do 36 000 km, a także dla przedziału szerokości geodezyjnej od 0° do 90°.

7

Properties of Languages with Catenation and Shuffle

Kudlek M., Flick N. E.

Fundamenta Informaticae

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2014

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Vol. 129, nr 1/2

117--132

EN

We present structural properties of languages constructed with catenation and shuffle, comprising iteration lemmata and closure properties of the language classes, as well as decidability results that follow.

8

Performance evaluation of iterative methods to unconstrained single variable minimization problems

Horla D.

Studia z Automatyki i Informatyki

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2013

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T. 38

7--33

EN

The paper considers performance issues of a class of iterative minimization methods of unconstrained single variable problems. Problem structures that assure superior performance of a specific method have been stipulated with appropriate conclusions drawn.

PL

W artykule poruszono zagadnienie szybkości działania metod minimalizacji funkcji jednej zmiennej dla zadań programowania nieliniowego bez ograniczeń. Wskazano przypadki, dla których konkretna metoda działa szybciej niż pozostałe oraz wyciągnięto wnioski odnośnie takiego stanu rzeczy.

9

Some efficient seventh-order derivative-free families in root-finding

Soleymani F.

Opuscula Mathematica

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2013

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Vol. 33, no. 1

163-173

EN

The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.

10

Interactive mapping using range sensor data under localization uncertainty

Vieira P., Ventura R.

Journal of Automation Mobile Robotics and Intelligent Systems

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2013

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Vol. 7, No. 1

47--53

EN

Several methods have been proposed in the literature to address the problem of automatic mapping by a robot using range scan data, under localization uncertainty. Most scan matching methods rely on the minimization of the matching error among individual range scans. However, uncertainty in sensor data often leads to erroneous matching, hard to cope with in a purely automatic approach. This paper proposes a semi-automatic approach, denoted interactive mapping, involving a human operator in the process of detecting and correcting erroneous matches. Instead of allowing the operator complete freedom in correcting the matching in a frame by frame basis, the proposed method facilitates the adjustment along the directions with more ambiguity, while constraining the others. Experimental results using LIDAR data are presented to validate empirically the approach, together with a preliminary user study to evaluate the benefits of the approach.

11

A Hierarchy of Languages with Catenation and Shuffle

Kudlek M., Flick N. E.

Fundamenta Informaticae

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2013

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Vol. 128, nr 1-2

113--128

EN

We present basic structures, definitions, normal forms, and a hierarchy of languages based on catenation, shuffle and their iterations, defined by algebraic closures or least fixed point solutions to systems of equations.

12

Solving RFIC Simulation Tasks Using GPU Computations

Andrei M. I., Kula S.

Computational Methods in Science and Technology

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2013

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Vol. 19, No. 2

89--97

EN

New generation of General Purpose Graphic Processing Unit (GPGPU) cards with their large computation power allow to approach difficult tasks from Radio Frequency Integrated Circuits (RFICs) modeling area. Using different electromagnetic modeling methods, the Finite Element Method (FEM) and the Finite Integration Technique (FIT), to model Radio Frequency Integrated Circuit (RFIC) devices, large linear equations systems have to be solved. This paper presents the benefits of using Graphic Processing Unit (GPU) computations for solving such systems which are characterized by sparse complex matrices. CUSP is a GPU generic parallel algorithms library for sparse linear algebra and graph computations based on Compute Unified Device Architecture (CUDA). The code is calling iterative methods available in CUSP in order to solve those complex linear equation systems. The tests were performed on various Central Processing Units (CPU) and GPU hardware configurations. The results of these tests show that using GPU computations for solving the linear equations systems, the electromagnetic modeling process of RFIC devices can be accelerated and at the same time a high level of computation accuracy is maintained. Tests were carried out on matrices obtained for an integrated inductor designed for RFICs, and for Micro Stripe (MS) designed for Photonics Integrated Circuit (PIC).

13

Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids

Collignon T. P., Van Gijzen M. B.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 1

109-121

EN

Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.

14

Remarks on the convergence of an iterative method of solution of generalized least squares problem

Bartoszewski Z.

Demonstratio Mathematica

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2010

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Vol. 43, nr 4

931-938

EN

In this paper we consider an iterative method of finding a regularized solution of a general linear system Ax = b. For a given scalar α and an initial vector g it produces a sequence that converges to the least squares solution of this system. The limiting point minimizes the distance between g and the set of all least squares solutions of the problem. An estimate of the rate of convergence is also provided.

15

Approximation methods for a class of discrete Wiener-Hopf equations

Nowak M. A.

Opuscula Mathematica

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2009

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Vol. 29, no. 3

271-288

EN

In this paper, we consider approximation methods for operator equations of the form Au + Bu = ƒ, where A is a discrete Wiener-Hopf operator on lp (1≤ p < ∞) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation B and ƒ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.

16

Iteracyjne strojenie nastaw regulatora PID

Królikowski A., Tarczewski T.

Studia z Automatyki i Informatyki

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2005

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T. 30

85--94

PL

W artykule przedstawiono metodę iteracyjnego strojenia nastaw regulatora PID o strukturze równoległej. Symulacje przeprowadzono dla modelu drugiego rzędu z opóźnieniem. Przedstawioną metodę porównano z metodą projektowania odpornego regulatora PID zaproponowaną w [4].

EN

Iterative feedback tuning (IFT) method for a parallel structure of PID controller is derived and simulated. The performance of PID controller tuned with IFT is compared with robust PID controller proposed in [4]. To this end a plant model of second-order with time delay is considered.

17

Numerical stability of the Richardson second order method

Smoktunowicz A., Wróbel I.

Demonstratio Mathematica

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2005

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Vol. 38, nr 1

255--263

EN

In this paper we study numerical properties of the Richardson second order method (RS) for solving a linear system Ax = b, where A € Rnxn is infinitysymmetric and positive definite. We consider the standard model of floating point arithmetic (cf. [6], [7], [11]). We prove that the RS-algorithm is numerically stable. This means that the algorithm computes approximations xk to the exact solution x* = A-1b such that the error limfk||xk - x*ll2 ls of order eMcond(A), where eM is the machine precision and cond(A) = ||A || 2 ||A-1|| denotes the condition number of the matrix A.

18

P-type iterative learning control of nonlinear systems with uncertainties

Chen P., Qin H., Ye X.

Systems Science

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2004

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Vol. 30, no 3

77-84

EN

This paper deals with the problem of robustness of P-type iterative learning control for uncertain nonlinear system. Besides the vector field, the control matrix and output matrix of the control system considered in this paper all have uncertainties. Iterative learning laws for initial states and for inputs are presented. A new technique has been developed to estimate the tracking errors of iterative control systems, which have an initial state error. Based on the estimation, upper bounds of the norms of the uncertainties of the control matrix and the output matrix are obtained, which guarantee that the iterative learning laws for initial states and for inputs are convergent. The results in this paper show that the P-type iterative learning control has robustness with respect to the uncertainties of the control matrix and the output matrix.

19

Scheduling of tasks on moving executors using advanced evolutionary algorithms

Józefczyk J.

Systems Science

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2003

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Vol. 29, nr 3

95-106

EN

The paper concerns the application of advanced evolutionary algorithms for solving a complex scheduling problem of manufacturing tasks. The case of scheduling of independent, non-preemptive tasks on unrelated moving executors, to minimize the makespan is considered. New heuristic solution algorithms based on an evolutionary computation are proposed. They use three different ways of multiple crossovers. The computer simulation experiments have been performed to investigate the dependence of results of the tasks scheduling on parameters of evolutionary algorithms as well as the quality of the solution algorithms in terms of the makespan and the time of computation. The evolutionary algorithms have been compared with a traditional solution algorithm that has been determined using the functional decomposition of the problem. A numerical example together with conclusions completes the paper.

20

Parallel computing applied to solving large Markov chains. A feasibility study.

Szczerbiński Z.

Studia Informatica

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2003

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Vol. 24, nr 4

7-28

EN

The article is concerned with parallel computation issues arising in numerical solution of systems of linear eąuations which describe stationary pro-babilitifis of stat.es in largc Markov chairis. Upon introduction to the .subject of Markov chains and their solution, several adeąuate solution methods arę surreyed, froni the cla.ssical through projection to decompositional ones. Each algoriUiin is accoinpaniocl by a study of its suitability to parallel computing (rnulti- and vector procfissing). Additional opinions on aspects of the potential for parallelization in the discussed methods arę contained in the conclusion.

PL

Artykuł jest poświęcony zagadnieniom obliczeń równoległych, występującym w trakcie numerycznego rozwiązywania układów równań liniowych, opisujących stacjonarne prawdopodobieństwa stanów w dużych łańcuchach Markowa. Po wprowadzeniu do tematyki łańcuchów Markowa, dokonano przeglądu wybranych metod rozwiązywania, począwszy od klasycznych, poprzez projekcyjne, do metod dekompozycyjnych. Dla każdego algorytmu została dokonana analiza, na ile nadaje się on do wykonania w trybie równoległym (wieloprocesorowyrn lub wektorowym). Dodatkowe uwagi dotyczące możliwości zrównoleglania dla omawianych metod zawarto w części końcowej.