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Andry Finit

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16

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15

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Kansas State University

Università di Bologna

Yannis Hamilakis

Brown University

Dr.Yousery Sherif

Mansoura University

Moscow State University

Hungarian Academy of Sciences

Universitas Pendidikan Indonesia (UPI) Bandung

Derek H Alderman

University of Tennessee Knoxville

University of Wisconsin-Madison

Dimitris P. Drakoulis

Aristotle University of Thessaloniki

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Papers by Andry Finit

Global simulation of heat transport, including melt convection in a Czochralski crystal growth process—combined finite element/finite volume approach

Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1993

... convection in the melt 11 Governing equations Momentum conservation equations Mass conservati... more

An object-oriented framework for the integration of interactive animation techniques

ACM Siggraph Computer Graphics, 1991

We present an interactive modeling and animation system that facilitates the integration of a var... more We present an interactive modeling and animation system that facilitates the integration of a variety of simulation and animation paradigms. This system permits the modeling of diverse objects that change in shape, appearance, and behavior over time. Our system thus extends modeling tools to include animation controls. Changes can be effected by various methods of control, including scripted, gestural, and behavioral specification. The system is an extensible testbed that supports research in the interaction of disparate control methods embodied in controller objects. This paper discusses some of the issues involved in modeling such interactions and the mechanisms implemented to provide solutions to some of these issues,

On the class of languages recognizable by 1-way quantum finite automata

It is an open problem to characterize the class of languages recognized by quantum finite automat... more It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.

1Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counte... more We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFA can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata.

hp-Version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFE... more We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp-DGFEM on shape-regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non-symmetric versions of DGFEM. Subject classifications: AMS(MOS): 65N12, 65N15, 65N30

Superstructure and finite-size effects in a Si photonic woodpile crystal

Physical Review B, 2003

The reflectivity of finite-thickness silicon photonic woodpile structures was measured in the wav... more The reflectivity of finite-thickness silicon photonic woodpile structures was measured in the wavelength range from 0.9 to 1.7 μm. Polarization and surface orientation dependent measurements were performed as function of angle of incidence and the data were compared with rigorous calculations for the finite structure. Due to the finite size, the reflectivity near the stop gap edge is strongly orientation and polarization dependent. Clear stop gaps can be identified and good agreement with calculations is found. Outside the stop gap region, Fabry-Perot type resonances are observed that are related to the finite thickness of the photonic crystal. In the stop gap region clear dips are found that are not reproduced in the calculation for perfect, finite-size crystals. These are due an irregularity in the pitch of the woodpile structure as observed in electron microscopy images. This irregularity can be described in terms of a superstructure that introduces additional bands due to zone folding of the bandstructure. Calculations based on the superstructure successfully reproduce the major features in the experimental data.

hp-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems

Siam Journal on Numerical Analysis, 2007

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFE... more We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp-DGFEM on shape-regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non-symmetric versions of DGFEM. Subject classifications: AMS(MOS): 65N12, 65N15, 65N30

A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems

Ima Journal of Numerical Analysis, 2005

We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element me... more We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors of arbitrary form are covered in the theory presented. A new, refined recipe for the choice of the discontinuity-penalisation parameter (that is present in the formulation of the IP-DGFEM) is given. Making use of the recently introduced augmented Sobolev space framework, we prove an hp-optimal error bound in the energy norm and an h-optimal and slightly p-suboptimal (by only half an order of p) bound in the L 2 norm, provided that the solution belongs to an augmented Sobolev space.

Method of Lines and Finite Difference Schemes with the Exact Spectrum for Solution the Hyperbolic Heat Conduction Equation

Mathematical Modelling and Analysis, 2011

This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat cond... more This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third kind is solved by the spectral method. Method of lines and the Fourier method are considered for the time discretization.Finite difference schemes with central difference and exact spectrum are analyzed. A novel method for solving the discrete spectral problem is used. Special matrix with orthonormal eigenvectors is formed. Numerical results are obtained for steel quenching problem in the plate and in the sphere with holes. The hyperbolic heat conduction problem in the sphere with holes is reduced to the problem in the plate. Some examples and numerical results for two typical problems related to hyperbolic heat conduction equation are presented.

Flow and temperature calculations of electrolyte for a finite cylinder in the alternating field of finite number circular wires

The distribution of electromagnetic fields, forces and temperatures induced by a three-phase axia... more The distribution of electromagnetic fields, forces and temperatures induced by a three-phase axially-symmetric system of electric current in a conducting cylinder of finite length has been calculated. An original method is used to calculate the mean values of electromagnetic forces. The magnetohydrodynamics (MHD) flow of a viscous incompressible liquid (electrolyte) and the distribution of temperature are obtained by the finite-difference method, using the monotonous finite difference schemes. Figs 14, Refs 6.

Global simulation of heat transport, including melt convection in a Czochralski crystal growth process—combined finite element/finite volume approach

Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1993

... convection in the melt 11 Governing equations Momentum conservation equations Mass conservati... more

An object-oriented framework for the integration of interactive animation techniques

ACM Siggraph Computer Graphics, 1991

We present an interactive modeling and animation system that facilitates the integration of a var... more We present an interactive modeling and animation system that facilitates the integration of a variety of simulation and animation paradigms. This system permits the modeling of diverse objects that change in shape, appearance, and behavior over time. Our system thus extends modeling tools to include animation controls. Changes can be effected by various methods of control, including scripted, gestural, and behavioral specification. The system is an extensible testbed that supports research in the interaction of disparate control methods embodied in controller objects. This paper discusses some of the issues involved in modeling such interactions and the mechanisms implemented to provide solutions to some of these issues,

On the class of languages recognizable by 1-way quantum finite automata

It is an open problem to characterize the class of languages recognized by quantum finite automat... more It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.

1Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counte... more We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFA can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata.

hp-Version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFE... more We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp-DGFEM on shape-regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non-symmetric versions of DGFEM. Subject classifications: AMS(MOS): 65N12, 65N15, 65N30

Superstructure and finite-size effects in a Si photonic woodpile crystal

Physical Review B, 2003

The reflectivity of finite-thickness silicon photonic woodpile structures was measured in the wav... more The reflectivity of finite-thickness silicon photonic woodpile structures was measured in the wavelength range from 0.9 to 1.7 μm. Polarization and surface orientation dependent measurements were performed as function of angle of incidence and the data were compared with rigorous calculations for the finite structure. Due to the finite size, the reflectivity near the stop gap edge is strongly orientation and polarization dependent. Clear stop gaps can be identified and good agreement with calculations is found. Outside the stop gap region, Fabry-Perot type resonances are observed that are related to the finite thickness of the photonic crystal. In the stop gap region clear dips are found that are not reproduced in the calculation for perfect, finite-size crystals. These are due an irregularity in the pitch of the woodpile structure as observed in electron microscopy images. This irregularity can be described in terms of a superstructure that introduces additional bands due to zone folding of the bandstructure. Calculations based on the superstructure successfully reproduce the major features in the experimental data.

hp-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems

Siam Journal on Numerical Analysis, 2007

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFE... more We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp-DGFEM on shape-regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non-symmetric versions of DGFEM. Subject classifications: AMS(MOS): 65N12, 65N15, 65N30

A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems

Ima Journal of Numerical Analysis, 2005

We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element me... more We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors of arbitrary form are covered in the theory presented. A new, refined recipe for the choice of the discontinuity-penalisation parameter (that is present in the formulation of the IP-DGFEM) is given. Making use of the recently introduced augmented Sobolev space framework, we prove an hp-optimal error bound in the energy norm and an h-optimal and slightly p-suboptimal (by only half an order of p) bound in the L 2 norm, provided that the solution belongs to an augmented Sobolev space.

Method of Lines and Finite Difference Schemes with the Exact Spectrum for Solution the Hyperbolic Heat Conduction Equation

Mathematical Modelling and Analysis, 2011

This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat cond... more This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third kind is solved by the spectral method. Method of lines and the Fourier method are considered for the time discretization.Finite difference schemes with central difference and exact spectrum are analyzed. A novel method for solving the discrete spectral problem is used. Special matrix with orthonormal eigenvectors is formed. Numerical results are obtained for steel quenching problem in the plate and in the sphere with holes. The hyperbolic heat conduction problem in the sphere with holes is reduced to the problem in the plate. Some examples and numerical results for two typical problems related to hyperbolic heat conduction equation are presented.

Flow and temperature calculations of electrolyte for a finite cylinder in the alternating field of finite number circular wires

The distribution of electromagnetic fields, forces and temperatures induced by a three-phase axia... more The distribution of electromagnetic fields, forces and temperatures induced by a three-phase axially-symmetric system of electric current in a conducting cylinder of finite length has been calculated. An original method is used to calculate the mean values of electromagnetic forces. The magnetohydrodynamics (MHD) flow of a viscous incompressible liquid (electrolyte) and the distribution of temperature are obtained by the finite-difference method, using the monotonous finite difference schemes. Figs 14, Refs 6.