Reitich, F.
Overview
Works:  34 works in 46 publications in 1 language and 46 library holdings 

Roles:  Author 
Publication Timeline
.
Most widely held works by
F Reitich
Asymptotic behavior for a coalescence problem by
University of Minnesota(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain by
University of Minnesota(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Numerical solution of diffraction problems: a method of variation of boundaries by
University of Minnesota(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Parameter identification in reactiondiffusion models by
Avner Friedman(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling by
University of Minnesota(
Book
)
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
A hyperbolic inverse problem arising in the evolution of combustion aerosol by
University of Minnesota(
Book
)
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
On the slow motion of the interface of layered solutions to the scalar GinzburgLandau equation by
University of Minnesota(
Book
)
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
The Stefan problem with small surface tension by
University of Minnesota(
Book
)
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
The overall elastic energy of polycrystalline martensitic solids by
University of Minnesota(
Book
)
2 editions published in 1996 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1996 in English and held by 2 WorldCat member libraries worldwide
Electromagnetic Scattering(
Book
)
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
The problems and techniques addressed under the present contract deal with issues of analysis and computation in electromagnetics. The primary goal consists of the development of efficient numerical tools for the prediction of scattered fields in a number of practical configurations. For this, substantial effort will be devoted to the extension and enhancement 0 the Method of Variation of Boundaries (MVB). Specific objectives in connection with MVB include: (1) advancement and implementation of algorithmic improvements for very highorder calculations; (2) application to the solution of eigenvalue problems (related to cavities, resonators and waveguides); to the calculation of electromagnetic scattering from damaged objects and rough terrain; and to inverse scattering problems. (3) Concurrent with these endeavors the program will pursue the incorporation of the boundaryvariation approach in more classical computational techniques, such as the finiteelement methods (FEM). A first instance of such interactions will be sought through the implementation of highorder boundary perturbation approximations to computational radiation conditions (typically imposed on separable geometries). To enable and enhance such applications, the plan includes the development of new (highorder) discontinuous Galerkin (DG) finite element approach to electromagnetic scattering calculations which is expected to provide an advantageous setting for adaptivity and parallelization. Alternative highorder methods (e.g., based on integral equation formulations) will also be considered
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
The problems and techniques addressed under the present contract deal with issues of analysis and computation in electromagnetics. The primary goal consists of the development of efficient numerical tools for the prediction of scattered fields in a number of practical configurations. For this, substantial effort will be devoted to the extension and enhancement 0 the Method of Variation of Boundaries (MVB). Specific objectives in connection with MVB include: (1) advancement and implementation of algorithmic improvements for very highorder calculations; (2) application to the solution of eigenvalue problems (related to cavities, resonators and waveguides); to the calculation of electromagnetic scattering from damaged objects and rough terrain; and to inverse scattering problems. (3) Concurrent with these endeavors the program will pursue the incorporation of the boundaryvariation approach in more classical computational techniques, such as the finiteelement methods (FEM). A first instance of such interactions will be sought through the implementation of highorder boundary perturbation approximations to computational radiation conditions (typically imposed on separable geometries). To enable and enhance such applications, the plan includes the development of new (highorder) discontinuous Galerkin (DG) finite element approach to electromagnetic scattering calculations which is expected to provide an advantageous setting for adaptivity and parallelization. Alternative highorder methods (e.g., based on integral equation formulations) will also be considered
Threephase boundary motions under constant velocities by
F Reitich(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Abstract: "In this paper we deal with the dynamics of material interfaces such as solidliquid, grain or antiphase boundaries. We concentrate on the situation in which these internal surfaces separate three regions in the material with different physical attributes (e.g. grain boundaries in a polycrystal). The basic twodimensional model proposes that the motion of an interface [gamma][subscript ij] between regions i and j (i, j = 1,2,3, i [not =] j) is governed by the equation V[subscript ij] = [mu subscript ij] (f[subscript ij]k[subscript ij] + F[subscript ij]). (0.1) Here V[subscript ij], k[subscript ij], [mu subscript ij] and F[subscript ij] denote, respectively, the normal velocity, the curvature, the mobility and the surface tension of the interface and the numbers F[subscript ij] stand for the (constant) difference in bulk energies. At the point where the three phases coexist, local equilibrium requires that the curves meet at prescribed angles. (0.2) In case the material constants f[subscript ij] are small, f[subscript ij] = [bracket over epsilon f subscript ij] and [epsilon] <<1, previous analyses based on the parabolic nature of the equations (0.1) do not provide good qualitative information on the behavior of solutions. In this case it is more appropriate to consider the singular case with f[subscript ij] = 0. It turns out that this problem, (0.1) with f[subscript ij] = 0, admits infinitely many solutions. Here, we show that a unique solution, 'the vanishing surface tension (VST) solution', is selected by letting [epsilon] > 0. Furthermore, we introduce the concept of weak viscosity solution for the problem with [epsilon] = 0 and show that the VST solution coincides with the unique weak solution. Finally, we give examples showing that, in several cases of physical relevance, the VST solution differs from results proposed previously."
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Abstract: "In this paper we deal with the dynamics of material interfaces such as solidliquid, grain or antiphase boundaries. We concentrate on the situation in which these internal surfaces separate three regions in the material with different physical attributes (e.g. grain boundaries in a polycrystal). The basic twodimensional model proposes that the motion of an interface [gamma][subscript ij] between regions i and j (i, j = 1,2,3, i [not =] j) is governed by the equation V[subscript ij] = [mu subscript ij] (f[subscript ij]k[subscript ij] + F[subscript ij]). (0.1) Here V[subscript ij], k[subscript ij], [mu subscript ij] and F[subscript ij] denote, respectively, the normal velocity, the curvature, the mobility and the surface tension of the interface and the numbers F[subscript ij] stand for the (constant) difference in bulk energies. At the point where the three phases coexist, local equilibrium requires that the curves meet at prescribed angles. (0.2) In case the material constants f[subscript ij] are small, f[subscript ij] = [bracket over epsilon f subscript ij] and [epsilon] <<1, previous analyses based on the parabolic nature of the equations (0.1) do not provide good qualitative information on the behavior of solutions. In this case it is more appropriate to consider the singular case with f[subscript ij] = 0. It turns out that this problem, (0.1) with f[subscript ij] = 0, admits infinitely many solutions. Here, we show that a unique solution, 'the vanishing surface tension (VST) solution', is selected by letting [epsilon] > 0. Furthermore, we introduce the concept of weak viscosity solution for the problem with [epsilon] = 0 and show that the VST solution coincides with the unique weak solution. Finally, we give examples showing that, in several cases of physical relevance, the VST solution differs from results proposed previously."
A new approach to the solution of problems of scattering by bounded obstacles by Oscar P Bruno(
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Partial Differential Equations from the Materials Sciences: Analysis and Computation(
Book
)
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F496209510113. With regards to problems of wave propagation, advances in the development of highorder perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two and threedimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasinormal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shapememory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F496209510113. With regards to problems of wave propagation, advances in the development of highorder perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two and threedimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasinormal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shapememory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF
A highorder perturbation approach to profile reconstruction. I: perfectly conducting gratings by
University of Minnesota(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
Symmetrybreaking bifurcation of analytic solutions to free boundary problems : an application to a model of tumor growth by
Avner Friedman(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Numerical solution of diffraction problems : a method of variation of boundaries by Oscar P Bruno(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Abstract: "We present a new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface. This method is based on a high order rigorous perturbative technique, whose application to singly periodic gratings was treated in the first two papers of this series. We briefly discuss the theoretical basis of our algorithm, namely, the property of analyticity of the diffracted fields with respect to variations of the interfaces. While the algebraic derivation of some basic recursive formulae is somewhat involved, it results in expressions which are easy to implement numerically. We present a variety of numerical examples (for bisinusoidal gratings), in order to demonstrate the accuracy exhibited by our method as well as its limited requirements in terms of computing power. Generalization of our computer code to crossed gratings other than bisinusoidal is in principle immediate, but the full domain of applicability of our algorithm remains to be explored. Comparison with results presented previously for actual experimental configurations shows a substantial improvement in the resolution of our numerics over that given by other methods introduced in the past."
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Abstract: "We present a new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface. This method is based on a high order rigorous perturbative technique, whose application to singly periodic gratings was treated in the first two papers of this series. We briefly discuss the theoretical basis of our algorithm, namely, the property of analyticity of the diffracted fields with respect to variations of the interfaces. While the algebraic derivation of some basic recursive formulae is somewhat involved, it results in expressions which are easy to implement numerically. We present a variety of numerical examples (for bisinusoidal gratings), in order to demonstrate the accuracy exhibited by our method as well as its limited requirements in terms of computing power. Generalization of our computer code to crossed gratings other than bisinusoidal is in principle immediate, but the full domain of applicability of our algorithm remains to be explored. Comparison with results presented previously for actual experimental configurations shows a substantial improvement in the resolution of our numerics over that given by other methods introduced in the past."
Analysis of a mathematical model for the growth of tumors by
University of Minnesota(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Evaluation of HighFrequency Electromagnetic Scattering via HighOrder MultipleScattering Integral Asymptotics(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
Report developed under STTR contract for topic AFOlTOO9. We introduced a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering in the highfrequency regime. This algorithm combines the use of an ansatz for the unknown density in a boundary integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. In particular, we obtained numerical results illustrating the high order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
Report developed under STTR contract for topic AFOlTOO9. We introduced a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering in the highfrequency regime. This algorithm combines the use of an ansatz for the unknown density in a boundary integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. In particular, we obtained numerical results illustrating the high order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases
Computational Electromagnetics(
)
2 editions published between 2004 and 2007 in English and held by 0 WorldCat member libraries worldwide
Progress in the development of fast, errorcontrollable algorithms for the simulation of electromagnetic scattering throughout the frequency spectrum is reported. Advances are described in the development of (1) accelerated, highorder methods for the solution of general, penetrable scattering problems in the lowtomoderate frequency regime; (2) spectral methods for the solution of approximate highfrequency models (geometrical optics GO ); and (3) general errorcontrollable highfrequency scattering solvers. Major accomplishments include the completion of work on (1) in relation with scalar scattering models and the extension of the algorithms to vector models and composite backgrounds; the design, implementation and refinement of a spectral/discontinuous Galerkin method to resolve the GO model in phase space; the advancement of a spectral inverse raytracing approach; the development of methods for the evaluation of highfrequency scattering off composite rough surfaces; the derivation of general highfrequency scattering solvers applicable to both single and multiplescattering configurations consisting of bounded obstacles in two and three dimensions; and the analysis and implementation of strategies to account for and accelerate the evaluation of multiplescattering effects
2 editions published between 2004 and 2007 in English and held by 0 WorldCat member libraries worldwide
Progress in the development of fast, errorcontrollable algorithms for the simulation of electromagnetic scattering throughout the frequency spectrum is reported. Advances are described in the development of (1) accelerated, highorder methods for the solution of general, penetrable scattering problems in the lowtomoderate frequency regime; (2) spectral methods for the solution of approximate highfrequency models (geometrical optics GO ); and (3) general errorcontrollable highfrequency scattering solvers. Major accomplishments include the completion of work on (1) in relation with scalar scattering models and the extension of the algorithms to vector models and composite backgrounds; the design, implementation and refinement of a spectral/discontinuous Galerkin method to resolve the GO model in phase space; the advancement of a spectral inverse raytracing approach; the development of methods for the evaluation of highfrequency scattering off composite rough surfaces; the derivation of general highfrequency scattering solvers applicable to both single and multiplescattering configurations consisting of bounded obstacles in two and three dimensions; and the analysis and implementation of strategies to account for and accelerate the evaluation of multiplescattering effects
Dynamic Simulation of the Temporal Response of Microstructure Formation in Magnetorheological Fluids(
)
1 edition published in 1999 in English and held by 0 WorldCat member libraries worldwide
Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as twodimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development (Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997). As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes
1 edition published in 1999 in English and held by 0 WorldCat member libraries worldwide
Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as twodimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development (Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997). As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes
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