I. Gavrilyuk - Academia.edu (original) (raw)

Papers by I. Gavrilyuk

Research paper thumbnail of Раздел 3. Современные Проблемы Метрологического Обеспечения Производства Обслуживание Заказчиков Через Личный Кабинет При Проведении Поверки Средств Измерений В Фбу «Уралтест» Service of Customers Through a Private Office When Carrying Out Checking of Measuring Instruments in Fbu «Uraltest»

ФБУ «УРАЛТЕСТ», Екатеринбург ФГАОУ ВО «Российский государственный профессионально-педагогический ... more ФБУ «УРАЛТЕСТ», Екатеринбург ФГАОУ ВО «Российский государственный профессионально-педагогический университет», Екатеринбург FBU «Uraltest», Ekaterinburg Аннотация. Рассматриваются вопросы создания системы по обслуживанию за-казчиков, предоставляющих средства измерения на поверку и калибровку. Доказывается эффективность внедрения личного кабинета заказчиков и совершенствования локальной сети по взаимодействию подразделений предприятия. Abstract. Questions of creation of system on service of the customers providing gages in actual fact and calibration are considered. Efficiency of introduction of a private office of customers and improvement of a local network on interaction of divisions of the enterprise is proved. Ключевые слова: поверка; калибровка; средство измерения; заказчик. Принципиальные перемены в развитии мира и страны требуют значи-тельного повышения конкурентоспособности выпускаемой продукции. Ре-шение этой глобальной задачи определяется реализацией широкого комплек-са ме...

Research paper thumbnail of Protein Markers for Increasing Efficiency of Triticeae Dum. Genetic Resources Utilisation in Breeding

To serve by effective basis for improvement of cultivated plants, genetic diversity stored in the... more To serve by effective basis for improvement of cultivated plants, genetic diversity stored in the gene banks, should be carefully and comprehensively evaluated and characterised (investigated). Collections should be rationally organised. Each accession should be identified and registered. The preservation of genetic constitution of accessions is included also into the category of basic problems. The objective of gene bank is to maintain the accession without change as regards its genetic constitution. It means preservation not only sample as such, but with its valuable properties, in particular adaptive etc. Understanding of genetic structure of biodiversity (relationships inside genepool or between structural elements of genetic diversity) is the important goal of gene bank activity. All above mentioned directions of activity should be developed to facilitate the use of germplasm for improvement of cultivars. Protein markers (PM) are successfully used in VIR since 1969 for increasi...

Research paper thumbnail of Preliminary results ∗

oscillations of a stretched hyperelastic

Research paper thumbnail of Non-classical asymptotic expansions for eigenvalue problems with a parameter in the boundary conditions

The aim of this work is to obtain exponentially convergent asymptotic expansions for eigenvalues ... more The aim of this work is to obtain exponentially convergent asymptotic expansions for eigenvalues and eigenfunctions of an eigenvalue problem containing the eigenvalue parameter in the boundary condition. Such eigenvalue problems are used when solving sloshing problems by analytical-numerical methods. Key words and phrases: asymptotic expansion, boundary eigenvalue parameter, sloshing analysis. AMS subject classification: 65L15, 665N25. 1.

Research paper thumbnail of Computer-based multimodal modeling of liquid sloshing in a circular cylindrical tank

By employing the nonlinear multimodal technique, the paper proposes an algorithm and computer cod... more By employing the nonlinear multimodal technique, the paper proposes an algorithm and computer code (SLOSHER) for derivation of asymptotic [third-order] nonlinear modal systems describing the nonlinear liquid sloshing in a vertical circular cylindrical tank. Applicability of the code is demonstrated for the benchmark modal system by Lukovsky (1990). A novel nonlinear modal system which takes into account most principal third-order modes is derived.

Research paper thumbnail of Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions

Research paper thumbnail of Estimates of the convergence rate of difference solutions to solutions of the second boundary value problem for fourth order equation at minimal requirements to smoothness

Research paper thumbnail of Eigenoscillations of a thin-walled non-closed shell of revolution

In this paper a numerical method is proposed to compute the eigenoscillations of a thin-walled no... more In this paper a numerical method is proposed to compute the eigenoscillations of a thin-walled non-closed shell of revolution. The method is based on the well-known Ritz method. The use of special coordinate functions which are adapted to the boundary layer behaviour at the clamped ends guarantees a uniform convergence to the natural modes and their (up to fourth order) derivatives. It is shown that the convergence of the new method does not significantly depend on the thickness of the shell. c © Gavrilyuk, Hermann, V.Trotsenko, Yu.Trotsenko, Timokha

Research paper thumbnail of Coupled dynamics of a tower with an elevated wave tank . Part 1 : Equations of motion and eigenoscillations

Based on the linear modal sloshing theory and a variational statement, a nonclassical “hybrid” bo... more Based on the linear modal sloshing theory and a variational statement, a nonclassical “hybrid” boundary problem is derived to describe coupled dynamics of a tower with an elevated tank on the tower top. Mathematically, the problem couples the generalized Euler-Bernoulli beam equation and an infinite-dimensional system of linear ordinary differential equations. The coupled eigenoscillations of the whole composite structure are analyzed. c © Gavrilyuk, Hermann, V.Trotsenko, Yu.Trotsenko, Timokha

Research paper thumbnail of Modal modeling of the fluid-structure interaction associated with sloshing in a tapered conical tank

Employing a variational solution of basic boundary problems of the linear modal sloshing theory i... more Employing a variational solution of basic boundary problems of the linear modal sloshing theory in a tapered conical tank, we derive a multimodal model describing the forced liquid motions and associated hydrodynamic loads. The multimodal model can be used in problems on the fluid-structure interaction. This fact is exemplified for Sretenski’s problem on the dynamic damper as well as for coupled eigenoscillations of a water tower with a conical elevated tank. c © Gavrilyuk, Hermann, Lukovsky, Solodun, Timokha

Research paper thumbnail of Analytical velocity potentials for a liquid contacting with a rigid spherical wall

By using Kelvin’s inversion, we construct analytical harmonic functions satisfying the zero-Neuma... more By using Kelvin’s inversion, we construct analytical harmonic functions satisfying the zero-Neumann condition on the inner spherical wall everywhere except a single point where the velocity is infinite. This set of functions can be used to construct approximate velocity potentials associated with liquid sloshing in a spherical tank, and in other related hydrodynamic problems. c © Barnyak, Gavrilyuk, Hermann, Timokha

Research paper thumbnail of Exponentially Convergent Duhamel-Like Algorithms for Differential Equations with an Operator Coefficient Possessing a Variable Domain in a Banach Space

SIAM Journal on Numerical Analysis, 2008

A suitable abstract setting of the initial value problem for the first order differential equatio... more A suitable abstract setting of the initial value problem for the first order differential equation with an unbounded operator coefficient in a Banach space where the domain of the operator depends on the dependent variable t is introduced. A new exponentially convergent algorithm for such problems is proposed. This algorithm is based on a generalization of the Duhamel's integral for vector-valued functions which allows to translate the initial problem into a boundary integral equation and then approximate it with exponential accuracy. Examples of boundary value problems for the heat equation with time-dependent boundary conditions are given which confirm and illustrate the theoretical results obtained.

Research paper thumbnail of Exponentially Convergent Method for them-Point Nonlocal Problem for a First Order Differential Equation in Banach Space

Numerical Functional Analysis and Optimization, 2010

The m-point nonlocal problem for the first order differential equation with an operator coefficie... more The m-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space X is considered. An exponentially convergent algorithm is proposed and justified provided that the operator coefficient A is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm is based on representations of operator functions by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of A and on the proper quadratures involving short sums of resolvents. The efficiency of the proposed algorithms is demonstrated by numerical examples.

Research paper thumbnail of ℋ-Matrix Approximation for Elliptic Solution Operators in Cylinder Domains

Journal of Numerical Mathematics, 2001

We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine fa... more We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine family generated by a strongly P-positive elliptic operator defined in [4, 7]. In the preceding papers [14]-[18], a class of H-matrices has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. An H-matrix approximation to the operator exponent with a strongly P-positive operator was proposed in [5]. In the present paper, we apply the H-matrix techniques to approximate the elliptic solution operator on cylindric domains Ω × [a, b] associated with the elliptic operator d 2 dx 2 − L, x ∈ [a, b]. It is explicitly presented by the operator-valued normalised hyperbolic sine function sinh −1 (√ L) sinh(x √ L) of an elliptic operator L defined in Ω. Starting with the Dunford-Cauchy representation for the hyperbolic sine operator, we then discretise the integral by the exponentially convergent quadrature rule involving a short sum of resolvents. The latter are approximated by the H-matrix techniques. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [a, b]. The approach is applied to elliptic partial differential equations in domains composed of rectangles or cylinders. In particular, we consider the H-matrix approximation to the interface Poincaré-Steklov operators with application in the Schur-complement domain decomposition method.

Research paper thumbnail of Natural Sloshing Frequencies in Truncated Conical Tanks

Conical-shaped or conical-bottom reservoirs are widely used as water containment for elevated tan... more Conical-shaped or conical-bottom reservoirs are widely used as water containment for elevated tanks. After earthquakes water tanks play an important role, by making the water available needed for extinguishing fires which arise with such catastrophic events frequently. Therefore special care must be practiced with the construction of the tanks in order to assure their safety and functionality during a seismic event. The occurrence of resonant vibrations caused by the closeness of the lowest natural sloshing frequency of the contained water to the effective frequency domain of seismic excitations is very dangerously. Robust and CPU-efficient numerical methods are therefore required for quantifying the natural sloshing frequencies and modes. The present paper employs the Treftz variational scheme and two distinct harmonic basic systems of functions to develop two numerical-analytical methods. Extensive numerical experiments establish the limits of their applicability in terms of semi-...

Research paper thumbnail of Linear oscillations of a stretched hyperelastic circular membrane encapsulating a sloshing liquid . Preliminary results ∗

The eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circula... more The eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circular cylindrical cavity filled by a liquid, is examined. The preprint presents basic mathematical formulations, preliminary mathematical results and proposes a numerical approach.

Research paper thumbnail of Resonant Equations with Classical Orthogonal Polynomials. II

Ukrainian Mathematical Journal

Research paper thumbnail of Resonant Equations with Classical Orthogonal Polynomials. I

Ukrainian Mathematical Journal

Research paper thumbnail of Difference schemes for nonlinear BVPs on the semiaxes

The paper is concerned with the numerical solution of scalar nonlinear boundary value problems (B... more The paper is concerned with the numerical solution of scalar nonlinear boundary value problems (BVPs) of the form d 2 u dx 2 -m 2 u=-f(x,u),x∈(0,∞),u(0)=μ 1 ,lim x→∞ u(x)=0, where m is a positive constant and f is sufficiently smooth with respect to the first variable between a finite number of discontinuity points. First, the authors give sufficient conditions for the existence and uniqueness of solutions of the BVPs. Then, the authors show that there exist an exact difference scheme constructed on a nonuniform finite grid whose solution coincides with the exact solution of the BVP at gridpoints. This exact difference scheme is implemented by the so-called truncated difference schemes of arbitrary order. The details of the algorithms together with the issues of adaptive mesh generation and error analysis are given. The theoretical results and the efficiency of the algorithms are confirmed by illustrative numerical examples. The paper is well organized and written. However, nearly a...

Research paper thumbnail of Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption

Journal of Soviet Mathematics, 1993

A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation... more A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation of the second kind which arises in the study of the mathematical model of internal-diffusion kinetics of adsorption of a substance from an aqueous solution of constant and bounded volume. The efficiency of the method is demonstrated using prototype examples and in application to inverse problems of adsorption kinetics.

Research paper thumbnail of Раздел 3. Современные Проблемы Метрологического Обеспечения Производства Обслуживание Заказчиков Через Личный Кабинет При Проведении Поверки Средств Измерений В Фбу «Уралтест» Service of Customers Through a Private Office When Carrying Out Checking of Measuring Instruments in Fbu «Uraltest»

ФБУ «УРАЛТЕСТ», Екатеринбург ФГАОУ ВО «Российский государственный профессионально-педагогический ... more ФБУ «УРАЛТЕСТ», Екатеринбург ФГАОУ ВО «Российский государственный профессионально-педагогический университет», Екатеринбург FBU «Uraltest», Ekaterinburg Аннотация. Рассматриваются вопросы создания системы по обслуживанию за-казчиков, предоставляющих средства измерения на поверку и калибровку. Доказывается эффективность внедрения личного кабинета заказчиков и совершенствования локальной сети по взаимодействию подразделений предприятия. Abstract. Questions of creation of system on service of the customers providing gages in actual fact and calibration are considered. Efficiency of introduction of a private office of customers and improvement of a local network on interaction of divisions of the enterprise is proved. Ключевые слова: поверка; калибровка; средство измерения; заказчик. Принципиальные перемены в развитии мира и страны требуют значи-тельного повышения конкурентоспособности выпускаемой продукции. Ре-шение этой глобальной задачи определяется реализацией широкого комплек-са ме...

Research paper thumbnail of Protein Markers for Increasing Efficiency of Triticeae Dum. Genetic Resources Utilisation in Breeding

To serve by effective basis for improvement of cultivated plants, genetic diversity stored in the... more To serve by effective basis for improvement of cultivated plants, genetic diversity stored in the gene banks, should be carefully and comprehensively evaluated and characterised (investigated). Collections should be rationally organised. Each accession should be identified and registered. The preservation of genetic constitution of accessions is included also into the category of basic problems. The objective of gene bank is to maintain the accession without change as regards its genetic constitution. It means preservation not only sample as such, but with its valuable properties, in particular adaptive etc. Understanding of genetic structure of biodiversity (relationships inside genepool or between structural elements of genetic diversity) is the important goal of gene bank activity. All above mentioned directions of activity should be developed to facilitate the use of germplasm for improvement of cultivars. Protein markers (PM) are successfully used in VIR since 1969 for increasi...

Research paper thumbnail of Preliminary results ∗

oscillations of a stretched hyperelastic

Research paper thumbnail of Non-classical asymptotic expansions for eigenvalue problems with a parameter in the boundary conditions

The aim of this work is to obtain exponentially convergent asymptotic expansions for eigenvalues ... more The aim of this work is to obtain exponentially convergent asymptotic expansions for eigenvalues and eigenfunctions of an eigenvalue problem containing the eigenvalue parameter in the boundary condition. Such eigenvalue problems are used when solving sloshing problems by analytical-numerical methods. Key words and phrases: asymptotic expansion, boundary eigenvalue parameter, sloshing analysis. AMS subject classification: 65L15, 665N25. 1.

Research paper thumbnail of Computer-based multimodal modeling of liquid sloshing in a circular cylindrical tank

By employing the nonlinear multimodal technique, the paper proposes an algorithm and computer cod... more By employing the nonlinear multimodal technique, the paper proposes an algorithm and computer code (SLOSHER) for derivation of asymptotic [third-order] nonlinear modal systems describing the nonlinear liquid sloshing in a vertical circular cylindrical tank. Applicability of the code is demonstrated for the benchmark modal system by Lukovsky (1990). A novel nonlinear modal system which takes into account most principal third-order modes is derived.

Research paper thumbnail of Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions

Research paper thumbnail of Estimates of the convergence rate of difference solutions to solutions of the second boundary value problem for fourth order equation at minimal requirements to smoothness

Research paper thumbnail of Eigenoscillations of a thin-walled non-closed shell of revolution

In this paper a numerical method is proposed to compute the eigenoscillations of a thin-walled no... more In this paper a numerical method is proposed to compute the eigenoscillations of a thin-walled non-closed shell of revolution. The method is based on the well-known Ritz method. The use of special coordinate functions which are adapted to the boundary layer behaviour at the clamped ends guarantees a uniform convergence to the natural modes and their (up to fourth order) derivatives. It is shown that the convergence of the new method does not significantly depend on the thickness of the shell. c © Gavrilyuk, Hermann, V.Trotsenko, Yu.Trotsenko, Timokha

Research paper thumbnail of Coupled dynamics of a tower with an elevated wave tank . Part 1 : Equations of motion and eigenoscillations

Based on the linear modal sloshing theory and a variational statement, a nonclassical “hybrid” bo... more Based on the linear modal sloshing theory and a variational statement, a nonclassical “hybrid” boundary problem is derived to describe coupled dynamics of a tower with an elevated tank on the tower top. Mathematically, the problem couples the generalized Euler-Bernoulli beam equation and an infinite-dimensional system of linear ordinary differential equations. The coupled eigenoscillations of the whole composite structure are analyzed. c © Gavrilyuk, Hermann, V.Trotsenko, Yu.Trotsenko, Timokha

Research paper thumbnail of Modal modeling of the fluid-structure interaction associated with sloshing in a tapered conical tank

Employing a variational solution of basic boundary problems of the linear modal sloshing theory i... more Employing a variational solution of basic boundary problems of the linear modal sloshing theory in a tapered conical tank, we derive a multimodal model describing the forced liquid motions and associated hydrodynamic loads. The multimodal model can be used in problems on the fluid-structure interaction. This fact is exemplified for Sretenski’s problem on the dynamic damper as well as for coupled eigenoscillations of a water tower with a conical elevated tank. c © Gavrilyuk, Hermann, Lukovsky, Solodun, Timokha

Research paper thumbnail of Analytical velocity potentials for a liquid contacting with a rigid spherical wall

By using Kelvin’s inversion, we construct analytical harmonic functions satisfying the zero-Neuma... more By using Kelvin’s inversion, we construct analytical harmonic functions satisfying the zero-Neumann condition on the inner spherical wall everywhere except a single point where the velocity is infinite. This set of functions can be used to construct approximate velocity potentials associated with liquid sloshing in a spherical tank, and in other related hydrodynamic problems. c © Barnyak, Gavrilyuk, Hermann, Timokha

Research paper thumbnail of Exponentially Convergent Duhamel-Like Algorithms for Differential Equations with an Operator Coefficient Possessing a Variable Domain in a Banach Space

SIAM Journal on Numerical Analysis, 2008

A suitable abstract setting of the initial value problem for the first order differential equatio... more A suitable abstract setting of the initial value problem for the first order differential equation with an unbounded operator coefficient in a Banach space where the domain of the operator depends on the dependent variable t is introduced. A new exponentially convergent algorithm for such problems is proposed. This algorithm is based on a generalization of the Duhamel's integral for vector-valued functions which allows to translate the initial problem into a boundary integral equation and then approximate it with exponential accuracy. Examples of boundary value problems for the heat equation with time-dependent boundary conditions are given which confirm and illustrate the theoretical results obtained.

Research paper thumbnail of Exponentially Convergent Method for them-Point Nonlocal Problem for a First Order Differential Equation in Banach Space

Numerical Functional Analysis and Optimization, 2010

The m-point nonlocal problem for the first order differential equation with an operator coefficie... more The m-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space X is considered. An exponentially convergent algorithm is proposed and justified provided that the operator coefficient A is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm is based on representations of operator functions by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of A and on the proper quadratures involving short sums of resolvents. The efficiency of the proposed algorithms is demonstrated by numerical examples.

Research paper thumbnail of ℋ-Matrix Approximation for Elliptic Solution Operators in Cylinder Domains

Journal of Numerical Mathematics, 2001

We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine fa... more We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine family generated by a strongly P-positive elliptic operator defined in [4, 7]. In the preceding papers [14]-[18], a class of H-matrices has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. An H-matrix approximation to the operator exponent with a strongly P-positive operator was proposed in [5]. In the present paper, we apply the H-matrix techniques to approximate the elliptic solution operator on cylindric domains Ω × [a, b] associated with the elliptic operator d 2 dx 2 − L, x ∈ [a, b]. It is explicitly presented by the operator-valued normalised hyperbolic sine function sinh −1 (√ L) sinh(x √ L) of an elliptic operator L defined in Ω. Starting with the Dunford-Cauchy representation for the hyperbolic sine operator, we then discretise the integral by the exponentially convergent quadrature rule involving a short sum of resolvents. The latter are approximated by the H-matrix techniques. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [a, b]. The approach is applied to elliptic partial differential equations in domains composed of rectangles or cylinders. In particular, we consider the H-matrix approximation to the interface Poincaré-Steklov operators with application in the Schur-complement domain decomposition method.

Research paper thumbnail of Natural Sloshing Frequencies in Truncated Conical Tanks

Conical-shaped or conical-bottom reservoirs are widely used as water containment for elevated tan... more Conical-shaped or conical-bottom reservoirs are widely used as water containment for elevated tanks. After earthquakes water tanks play an important role, by making the water available needed for extinguishing fires which arise with such catastrophic events frequently. Therefore special care must be practiced with the construction of the tanks in order to assure their safety and functionality during a seismic event. The occurrence of resonant vibrations caused by the closeness of the lowest natural sloshing frequency of the contained water to the effective frequency domain of seismic excitations is very dangerously. Robust and CPU-efficient numerical methods are therefore required for quantifying the natural sloshing frequencies and modes. The present paper employs the Treftz variational scheme and two distinct harmonic basic systems of functions to develop two numerical-analytical methods. Extensive numerical experiments establish the limits of their applicability in terms of semi-...

Research paper thumbnail of Linear oscillations of a stretched hyperelastic circular membrane encapsulating a sloshing liquid . Preliminary results ∗

The eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circula... more The eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circular cylindrical cavity filled by a liquid, is examined. The preprint presents basic mathematical formulations, preliminary mathematical results and proposes a numerical approach.

Research paper thumbnail of Resonant Equations with Classical Orthogonal Polynomials. II

Ukrainian Mathematical Journal

Research paper thumbnail of Resonant Equations with Classical Orthogonal Polynomials. I

Ukrainian Mathematical Journal

Research paper thumbnail of Difference schemes for nonlinear BVPs on the semiaxes

The paper is concerned with the numerical solution of scalar nonlinear boundary value problems (B... more The paper is concerned with the numerical solution of scalar nonlinear boundary value problems (BVPs) of the form d 2 u dx 2 -m 2 u=-f(x,u),x∈(0,∞),u(0)=μ 1 ,lim x→∞ u(x)=0, where m is a positive constant and f is sufficiently smooth with respect to the first variable between a finite number of discontinuity points. First, the authors give sufficient conditions for the existence and uniqueness of solutions of the BVPs. Then, the authors show that there exist an exact difference scheme constructed on a nonuniform finite grid whose solution coincides with the exact solution of the BVP at gridpoints. This exact difference scheme is implemented by the so-called truncated difference schemes of arbitrary order. The details of the algorithms together with the issues of adaptive mesh generation and error analysis are given. The theoretical results and the efficiency of the algorithms are confirmed by illustrative numerical examples. The paper is well organized and written. However, nearly a...

Research paper thumbnail of Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption

Journal of Soviet Mathematics, 1993

A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation... more A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation of the second kind which arises in the study of the mathematical model of internal-diffusion kinetics of adsorption of a substance from an aqueous solution of constant and bounded volume. The efficiency of the method is demonstrated using prototype examples and in application to inverse problems of adsorption kinetics.