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In this paper, we consider the study of the extreme problem of the fictitious domain method based on the use of the Lagrange functional, with a multiplier defined on the actual boundary and associated with genuine boundary conditions. The theorem of the existence of a generalized solution of the auxiliary FDM problem is proved. The convergence of the solution of the auxiliary FDM problem is shown. For mathematical research, the theory of functional spaces and the technique of obtaining a priori estimates in functional spaces are used. To verify the effectiveness of the developed method, numerical analysis and comparison with other methods of solving the problem were carried out. [ABSTRACT FROM AUTHOR]

The paper presents two-dimensional model of gas filtration flow in a porous medium as well as efficient computational algorithm. The analysis of performed numerical calculations showed that when the gas filtration parameters and properties are viewed as functions of pressure, then the studying process can be adequately described as a whole and the numerical results correctly reflect its essence. The results of computer calculations were used to substantiate a decision support system for selecting the operating modes of wells in order to obtain optimal and more economical production routine. Computer calculations demonstrated that the longitudinal-transverse directions scheme in some cases may be more preferable than the locally-one-dimensional method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value problems is investigated. Our investigation will be carried out by adapting the theory of Nystrom-series and using the sets of second order rooted trees for solving second-order ODEs which leads to a general set of order conditions. In this paper the method of order three using constant step-size algorithm is derived. The stability region of method is also proposed. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the third order partial differential equation with time delay is studied. The first and second order of accuracy difference schemes for the numerical solution of the third order partial differential equation with time delay are presented. The illustrative numerical results are provided. [ABSTRACT FROM AUTHOR]

In this paper we will investigate a family of five-stages high algebraic order embedded explicit six-step finite difference pairs, for the numerical solution of second order initial and/or boundary-value problems with periodical and/or oscillating solutions. Requiring the elimination of the phase-lag of the methods of the family of five-stages embedded explicit six-step algorithms and requiring also the elimination of the phase-lag's derivatives of the methods of the family of five-stages embedded explicit six-step schemes, we obtain a system of of equations. The solution of the previously obtained system of equations, leads to the determination of the free parameters of the new proposed finite difference pairs. Following the building of the new proposed finite difference pairs, we analyze theoretically the resulting schemes as follows: • We will study the local truncation error (LTE) of the resulting schems. • We will study the asymptotic form of the LTE which are produced using as model problem the radial Schrödinger equation. • We will study the comparison of the asymptotic forms of LTEs for several finite difference schemes of the same family. The comparison leads to the conclusions on the effectiveness of each member of the family of five-stages high algebraic order embedded explicit six-step finite difference pairs. • We will study the stability and the interval of periodicity of the resulting algorithms of the family of five-stages high algebraic order embedded explicit six-step finite difference pairs. • We will study the applications of the new builded family of five-stages high algebraic order embedded explicit six-step finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The previously described applications lead to the conclusions on the effectiveness of the members of the new proposed family of five-stages high algebraic order embedded explicit six-step finite difference pairs. [ABSTRACT FROM AUTHOR]

Any large functioning system consists of equipment that needs to be repaired during its lifetime. The methods of mathematical programming are used to formalize the optimization problem of preventive equipment repair planning in this paper. The method is used to find the annual optimal plan of preventive equipment repair. The goal of such plan is the uniform distribution of repair works by the months. It is supposed, that the deviation from the standard plan of repair works can not be more than one month. An algorithm to find the optimal plan of repair works is provided. A numerical example is given. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm for constructing of synthesizing control function. This algorithm is sufficiently convenient for numerical implementation and a wide class of nonlinear nonstationary systems of ordinary differential equations, provide the passage from initial state into to origin coordinates. We obtain a constructive condition for the choice of initial state for which the passage is possible with regard of the constraints imposed on the control. We consider an problem of control of single manipulator, for which we carry numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a modified Thiele-Werner algorithm to construct a kind of reliable vector-valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector-valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given. [ABSTRACT FROM AUTHOR]

This paper poses a magnetic field problem in cylindrical coordinate for two regions with different permeability for each one. The linear partial differential equation governing this problem is in the form of Laplace and Poisson equation. This problem is then solved using classical Gauss-Seidel Algorithm for the Finite difference (FD) solution of linear partial differential equation. In order to obtain adequate solution for a reasonable number of grid points for the regions under consideration a considerable amount of time will take for the program to converge. The paper presents a different technique known as Weighted Multi-Grid which will speed up the convergence process. In this method, the solution to the differential equation between two grid points for obtaining the initial condition is considered to be linear in nature with different weight for the value of each grid point. This problem is then solved for the minimum number of grid points let’s say one point in each region plus the boundary points. The initial guess for each new point for every level of computation is found as the weighted average of the two adjacent points. It then continues with finding the optimum weighting values for Laplace’s or Poisson’s equation. The main contribution is made by regarding the effect of the optimum initial weighted values of the variable vector in the convergence time for the Gauss-Seidel algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we describe a variant of a solution for a common problem in applied statistics—we offer a variant method for estimating the parameters of a dynamic system, and observe its magnitudes, which statistically depend on the sequence of states of the system that are not observed. The method is realized by means of the multipolynomial approximations algorithm (the MPA algorithm). The method is validated by applying it to a problem of correction of finite sets of nominal experimental data on which nominal functions are constructed equationsby means of interpolation from the current states of the system. Nominal experimental data are presented on a finite set of points covering the domains of definition of the nominal functions. The nominal equations of motion of the dynamical system are defined by the nominal functions. In this paper, the concrete example of the nominal equations of motion correspond to the longitudinal motion of the aircraft similar of the F-l6 aircraft. The nominal functions are the calculated aerodynamic characteristics. The nominal experimental data are recorded by means of experiments in a wind-tunnel. The outcomes of measurements of the parameters of motion of the aircraft act on inputs for the MPA algorithm on a segment of real flight. The MPA algorithm defines a 32×1-vector of estimates of parameters, which are additive corrections to the nominal experimental data. [ABSTRACT FROM AUTHOR]

Matching pursuit is an iterative method whereby a signal is decomposed into a linear combination of functions that are selected from a redundant dictionary. In the original paper by Mallat and Zhang, a dictionary of Gabor functions is proposed. Each Gabor function is the product of a Gaussian function with a complex sinusoid, and is specified by time, frequency and scale. Since these functions are qualitatively and quantitatively very similar to ultrasonic echoes, it is appropriate to use the matching pursuit method to decompose ultrasonic signals to locate and identify discrete echoes embedded in complex signals. In this paper, a modified implementation of the matching pursuit algorithm is described, where the algorithm is specifically designed for an efficient decomposition of ultrasonic signals. The size of the wavelet dictionary is adaptively determined by the spectrum of the ultrasonic signal and is further controlled by additional physically meaningful restrictions. In each iterative step, the pursuit of the matching function begins with a coarse grid in the parameter space of the dictionary, and the highest energy matching function is found by interpolation of this coarse grid over the parameters. The algorithm is applied to a variety of measured ultrasonic signals. Signals consisting of multiple echoes are successfully decomposed, and the individual wavelets are well-matched to the original echoes. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit®[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms. [ABSTRACT FROM AUTHOR]

Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit®[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms. [ABSTRACT FROM AUTHOR]

Log-Aesthetic (LA) curves have been implemented in a CAD/CAM system for various design feats. LA curves possess linear Logarithmic Curvature Graph (LCG) with gradient (shape parameter) denoted as α. In 2009, a generalized form of LA curves called Generalized Log-Aesthetic Curves (GLAC) has been proposed which has an extra shape parameter as V compared to LA curves. Recently, G¹ continuous GLAC algorithm has been proposed which utilizes the extra shape parameter using four control points. This paper discusses on the existence of inflection points in a GLAC segment satisfying G¹ Hermite data and the effect of inflection point on convex hull property. It is found that the existence of inflection point can be avoided by manipulating the value of α. Numerical experiments show that the increase of α may remove the inflection point (if any) in a GLAC segment. [ABSTRACT FROM AUTHOR]

In the paper the semi-Lagrangian method is considered in the context of its implementation with the CUDA technology. We have scrutinized the bottleneck of our sequential algorithm; its parallel versions are studied in detail; and the main reason of poor CUDA performance is clarified. As the result, we revise the computation of partial integrals in order to improve the efficiency of the algorithm. Numerical experiments demonstrate good CUDA performance of the revised version of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent. [ABSTRACT FROM AUTHOR]

Consider the following problem related to an ordinary differential equation: 'For given constans ua,ub,M,N, function f(x) in [a,b], find ∂u/∂n at x = a,b which satisfies u"+Mu′+Nu = f in (a,b),u(a) = ua,u(b) = ub'. This kind of problem is called the "Dirichlet-Neumann map problem". This problem is usually solved in two steps. The solution is obtained in the first steps. In the second step, u′(a), u′(b) is computed by differentiating the solution. However, this two-step procedure is inefficient because the solution in (a,b) obtained in the first step is not essentially required. In this paper, the author presents a new strategy for obtaining Neumann data directly via a boundary integral equation formulation. Using this strategy, an explicit analytical expression of the Dirichlet-Neumann map of this problem can be directly obtained by solving 2 × 2 matrices. Furthermore, an extension of the strategy to partial differential equations in two-dimensional space and numerical algorithms is also presented. [ABSTRACT FROM AUTHOR]

The digital piracy involving images, music, movies, books, and so on, is a legal problem that has not found a solution. Therefore it becomes crucial to create and to develop methods and numerical algorithms in order to solve the copyright problems. In this paper we focus the attention on a new approach of watermarking technique applied to digital color images. Our aim is to describe the realized watermarking algorithm based on multichannel wavelet functions with multiplicity r = 3, called MCWM 1.0. We report a large experimentation and some important numerical results in order to show the robustness of the proposed algorithm to geometrical attacks. [ABSTRACT FROM AUTHOR]

This paper is concerned with an accurate computing for matrix multiplication. We show that matrix multiplication can be transformed into a summation of floating-point matrices by mainly using level 3 operations in BLAS. We call it 'errorfree transformation of matrix multiplication'. By combining this error-free transformation and accurate summation algorithms for floating-point numbers, we can obtain an accurate result of matrix multiplication. Numerical examples are presented to illustrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical computation of the determinant of a matrix. An algorithm for accurately computing the determinant is proposed using accurate matrix factorizations, especially extremely ill-conditioned cases are treated. For the purpose, an accurate algorithm for the inverse LU factorization is used. Then accurate results of the determinant can efficiently be obtained for much wider range of the problems. Numerical results are also presented showing the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a potential flow numerical solution for the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible fluid in a stratified shear flow. As a problem: the two-fluid model becomes illposed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the potential equation method for the time derivatives in conjunction with the two-fluid model is analyzed. The normal stress balance (with the normal viscous stress) at the interface for the two-fluid model is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis shows that: stability condition for two-fluid with equal kinematic viscosity ratio and inviscid flow, supply numerical stability. Excellent agreement has obtained according to analytical result that existing of imaginary part in solution which specialized this method. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density and viscosity ratios in rectangular channel. Simulation of this model has implemented by writing a code in FORTRAN programming. [ABSTRACT FROM AUTHOR]

Computational aerodynamics is a key technology in aircraft design which is ahead of physical experiment and complements it. Of course all three components of computational modeling are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of computer architecture. Numerical algorithms are developed more conservative. More precisely, they are offered and theoretically justified for more simple mathematical problems. Nevertheless, computational mathematics now has amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. A significant step in this direction was the European Project ADIGMA whose positive experience will be used in International Project TRISTAM for further movement in the field of computational technologies for aerodynamics. This paper gives a general overview of objectives and approaches intended to use and a description of the recommended four-stage computer technology. [ABSTRACT FROM AUTHOR]

In this paper we give a unified presentation of efficient algorithms for meshless interpolation on a general domain K. In particular, here we focus on two specific cases: the former considers as interpolation domain the unit square, i.e. K = [0,1]2[contained_within]R2, whereas the latter is given by the unit two-sphere, namely K = S2[contained_within]R3. Such algorithms are based on a partition of unity method, which is characterized by the use of radial or zonal basis functions as local interpolants. These procedures are implemented by using efficient searching techniques, exploiting suitable and optimal partitions of the domain in strips or spherical zones. Some numerical tests show accuracy and efficiency of the considered algorithms. [ABSTRACT FROM AUTHOR]

In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence. This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described which is efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. The main idea of the algorithm is to use a 'dual' change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval. The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion, together with elements of Markov chain theory. [ABSTRACT FROM AUTHOR]

This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic. [ABSTRACT FROM AUTHOR]

This paper presents a new calibration procedure to identify the geometric parameters which improve the kinematic model accuracy of a mechanism. This procedure has been applied to a 2-DOF spatial parallel mechanism, obtaining the identified parameters by means of the direct kinematic model and reducing the position error of the moving platform. Data acquisition is performed by measuring three standard spheres, fixed to the moving platform, by means of a coordinate measuring machine. The method implemented defines an objective function which is optimized though a numerical method based on the Levenberg-Marquardt algorithm. This function compares the measured and calculated moving platform coordinates and minimizes this difference. Results show that in both cases, identification and test position, the position error is reduced considerably. The method developed can be easily generalized to other parallel mechanism. [ABSTRACT FROM AUTHOR]

The paper deals with comparison of two 2D formulations of Navier-Stokes equations: stream function-vorticity and its derivation the velocity-vorticity formulation. The boundary condition for vorticity transport equation is the crucial part. Both sets of governing equations are solved using the same numerical algorithm based on multidomain boundary element method (BEM). Driven cavity flow is the numerical example showing considerable efficiency advantage for stream-vorticity, while accuracy is practically the same. [ABSTRACT FROM AUTHOR]

Lens-based imaging is able to directly provide an image of objects. The high quality lenses required, however, are not readily available for x-rays. Coherent diffraction imaging (CDI) bypasses this difficulty by numerically inverting the diffraction process undertaken by an object wave. The current CDI methods still face difficulties such as demanding experimental requirements in data collection and sample-dependent, unreliable convergence in their iterative reconstruction. Recently, we have proposed a new method to resolve these problems. The method employs a modulator and a novel phasing algorithm. Unlike imaging lenses or mirrors, the modulator can take various forms; therefore, it has less demanding requirements on its fabrication. In this paper, we describe more details about the technique. [ABSTRACT FROM AUTHOR]

This paper discusses the possibility of using evolutionary algorithms for the reconstruction of chaotic systems. The main aim of this work is to show that evolutionary algorithms are capable of the reconstruction of chaotic systems without any partial knowledge of internal structure, i.e. based only on measured data. Algorithm SOMA was used in reported experiments here. Systems selected for numerical experiments here is the well-known Lorenz system. For each algorithm and its version, repeated simulations were done, totaling 20 simulations. According to obtained results it can be stated that evolutionary reconstruction is an alternative and promising way as to how to identify chaotic systems. [ABSTRACT FROM AUTHOR]

In the last years a great interest in optimization algorithms aimed to design forming processes was demonstrated by many researches. Proper design methodologies to reduce times and costs have to be developed mostly based on computer aided procedures. Response surface methods (RSM) proved their effectiveness in the recent years also for the application in sheet metal forming aiming to reduce the number of numerical simulations. Actually, the main drawback of such method is the number of direct problem to be solved in order to reach good function approximations. A very interesting aspect in RSM application regards the possibility to build response surfaces basing on moving least squares approximations (MLS) by utilizing a moving and zooming region of interest. In this paper, MLS is utilized to solve an optimization problem for a complex sheet metal forming process. The influence on the optimization results was analyzed basing on MLS peculiarities. In particular, the analysis was carried out studying the effect of weighting functions shape and of the points belonging to the design of experiments. [ABSTRACT FROM AUTHOR]

This paper presents a well-balanced numerical scheme for solving free surface flows involving wetting and drying. The proposed algorithm combines a component-wise approach with hydrostatic reconstruction strategy to compute flows over wet or dry surfaces and to satisfy the steady state condition of still water. The robustness of the proposed scheme is verified under several benchmark hydraulic tests. [ABSTRACT FROM AUTHOR]

This paper deals with numerical solution of nonlinear evolution systems modelling reaction-diffusion-convection processes in the natural and engineering sciences. Using Rothe method, we concentrate on construction of effective solution of the corresponding nonlinear stationary problems on each time level. First we discuss the solution by Newton-Bellman & Kalaba quasilinearization. Then, on this base high order and cheaper (with respect to computational cost) algorithms are proposed. Numerical results for a parabolic-hyperbolic system of two equations from the filtration are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a new immersed boundary algorithm is developed by combining the ghost cell method with adaptive tree Cartesian grid method. Furthermore, the presented method has been successfully used to evaluate an inviscid compressible flow with immersed boundary. Numerical example shows the present method be effective. [ABSTRACT FROM AUTHOR]

We study the inclined oil-water two-phase flow using complex networks and construct flow pattern complex network with the conductance fluctuating signals measured from oil-water two-phase flow experiments. A new method, based on Time-Delay Embedding and modularity, is proposed to construct network from nonlinear time series. Through detecting the community structure of the resulting network using the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used to identify three inclined oil-water flow patterns. In this paper, from a new perspective, we not only introduce complex network theory to the study of oil-water two-phase flow, but also demonstrate that complex network may be a powerful tool for exploring nonlinear time series in practice. [ABSTRACT FROM AUTHOR]

A comparison study of algorithm on a rectangular collocated mesh is conducted for variable density Navier-Stokes equations with continuous surface forces. The algorithms include the original projection method (AI-TI) with the surface force calculated only in the predictor steps, the named balanced-force projection method (AII-TIV) with the surface force and the pressure gradient calculated together, and a consistent projection method (AIII-TVII) developed in this paper. Detailed comparisons are also conducted among the techniques for calculation of the pressure gradient and surface force at a cell center. A consistent projection method updates the velocity at a cell center in a very difference way with the balanced-force projection formula. A conservative interpolation is used to update the velocity a cell center, which is further used to obtain the sum of the pressure gradient and the surface force. [ABSTRACT FROM AUTHOR]

In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed. [ABSTRACT FROM AUTHOR]

The paper shows the a-priori error estimates for the Fedorenko finite superelement method in application to physical problems with small-scale singularities. [ABSTRACT FROM AUTHOR]

In this paper we solve by exponentially-fitted difference scheme a singularly perturbed nonlinear two-dimensional convection-diffusion equation. To find the solution of the nonlinear algebraic system we use both Newton and Picard methods. We propose a new version of the two-grid method with an exponential interpolation. In the first step the nonlinear differential problem is solved on a “coarse” grid of size H. In the second step, the problem is linearized around an appropriate interpolant of the computed solution on the first step and the linear problem then is solved on a fine grid of size h<