Papers by Fernando Reitich
Computational Electromagnetics
New approach to the solution of problems of scattering by bounded obstacles
Proceedings of SPIE, May 1, 1994
New approach to the solution of problems of scattering by bounded obstacles. [Proceedings of SPIE... more New approach to the solution of problems of scattering by bounded obstacles. [Proceedings of SPIE 2192, 20 (1994)]. Oscar P. Bruno, Fernando L. Reitich. Abstract. We introduce a new numerical method, based on rigorous perturbative ...
Una mirada al acero: desafíos y oportunidades
Mathematical and Computer Modelling, 2001
Magnetorheological (MR) uids represent a class of smart materials whose rheological properties ch... more Magnetorheological (MR) uids represent a class of smart materials whose rheological properties change in response to the application of a magnetic eld. These uids typically consist of small (m) magnetizable particles dispersed in a non-magnetic carrier uid that generally contains additives such as surfactants and anti-wear agents 1]. Due to such additives, there is an outer non-magnetic layer on the particles that keeps them from touching. The goal of this paper is to study the e ective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the e ective magnetic properties of MR uids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the e ective permeability of MR uids as an extension of the work of Keller 3] and Doyle 4].
Journal of the Optical Society of America, Nov 1, 1993
We recently introduced a method of variation of boundaries for the solution of diffraction proble... more We recently introduced a method of variation of boundaries for the solution of diffraction problems [J. Opt. Soc. Am. A 10, 1168 (1993)]. This method, which is based on a theorem of analyticity of the electromagnetic field with respect to variations of the interfaces, has been successfully applied in problems of diffraction of light by perfectly conducting gratings. We continue our investigation of diffraction problems. Using our previous results on analytic dependence with respect to the grating groove depth, we present a new numerical algorithm that applies to dielectric and metallic gratings. We also incorporate Padg approximation in our numerics. This addition enlarges the domain of applicability of our methods, and it results in computer codes that can predict more accurately the response of diffraction gratings in the resonance region. In many cases results are obtained that are several orders of magnitude more accurate than those given by other methods available at present, such as the integral or differential formalisms. We present a variety of numerical applications, including examples for several types of grating profile and for wavelengths of light ranging from microwaves to ultraviolet, and we compare our results with experimental data. We also use Pad6 approximants to gain insight into the analytic structure and the spectrum of singularities of the fields as functions of the groove depth. Finally, we discuss some connections between Pad6 approximation and another summation mechanism, enhanced convergence, which we introduced in the earlier paper. It is argued that, provided that certain numerical difficulties can be overcome, the performance of our algorithms could be further improved by a combination of these summation methods.
Journal of the Optical Society of America, Jun 1, 1993
International Journal of Modern Physics B, Mar 20, 2001
Numerische Mathematik, Sep 25, 2009
In this paper we continue our analysis of the treatment of multiple scattering effects within a r... more In this paper we continue our analysis of the treatment of multiple scattering effects within a recently proposed methodology, based on integral-equations, for the rigorous numerical solution of scattering problems at high frequencies. In more detail, here we extend the two-dimensional results in part I of this work to fully three-dimensional geometries. As in the former case, our concern here is the determination of the rate of convergence of the multiple-scattering iterations that are inherent in the aforementioned highfrequency schemes. To this end, we follow a similar strategy to that we devised in part I: first, we recast the (iterated, Neumann) multiple-scattering series in the form of a sum of periodic orbits (of increasing period) corresponding to multiple reflections that periodically bounce off a series of scattering sub-structures; then, we proceed to derive a high-frequency recurrence that relates the "currents" (i.e. the normal derivative of the fields) induced on these structures as the waves reflect periodically; and, finally, we analyze this recurrence to provide an explicit rate of convergence associated with each orbit. While the procedure is analogous to its two-dimensional counterpart, the actual analysis is significantly more involved and, perhaps more interestingly, it uncovers new phenomena that cannot be distinguished in two-dimensional configurations (e.g. the further dependence of the convergence rate on the relative orientation of interacting structures). As in the two-dimensional case, and beyond their intrinsic interest, we also explain here how the results of our analysis can be used to accelerate the convergence of the multiple-scattering series and, thus, to provide significant savings in computational times.
High-order domain variations in boundary value and free boundary problems
Contemporary mathematics, 2004
An efficient high-order algorithm for scattering from penetrable thin structures
In this thesis, we present a new high-order accelerated algorithm for the solution of the integra... more In this thesis, we present a new high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of "thin" structures as they arise in certain applications (e.g. material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and "partitions of unity" (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented in the context of Helmholtz model of acoustic scattering, both in two and three dimensions. A review of the corresponding error analysis establishes the high-order convergence of the numerical method. An analysis of computational cost reveals that the optimal complexity of this algorithm lie between O (N log N) and O (N11/8 log N) in three dimensions, whereas in two dimensions, its optimal complexity is found to be between O (N log N) and O (N5/3 log N), where N is the number of degree for freedom. The accuracy and efficiency of the method are further exemplified with a variety of numerical results; obtained through implementations of the algorithm for the treatment of both two and three dimensional geometries.
Mathematical modeling in industry - IMA Summer program for graduate students, May 26-June 3, 2002
See individual papers: 1866-1, Modeling planarization in chemical-mechanical polishing by Dilek A... more See individual papers: 1866-1, Modeling planarization in chemical-mechanical polishing by Dilek Alagoz, Stephanie Hoogendoorn, Satyanarayana Kakollu, Maria Reznikoff, Richard Schugart, and Michael Sostarecz (Leonard Borucki, mentor); 1866-2, Vehicle networks: achieving regular formation by Madalena Chaves, Robert Day, Lucia Gomez Ramos, Parthasarathi Nag, Anca Williams, and Wei Zhang (Sonja Glavaski, mentor); 1866-3, Designing airplane struts using minimal surfaces by Sara Del Valle, Todd Moeller, Siva Kumar Natarajan, Gergina V. Pencheva, Jason C. Sherman, and Steven M. Wise (Thomas Grandine, mentor); 1866-4, Mobility management in cellular telephony by Benjamin P. Cooke, Darongsae Kwon, Dmitry Glotov, Simon Schurr, Daniel Taylor, and Todd Wittman (David F. Shallcross, mentor); 1866-5, Optimal design for a varying environment by Serguei Lapin, Xuan Hien Nguyen, Jiyeon Oh, Daniel Vasiliu, Pei Yin, and Ningyi Zhang (David Misemer, mentor); 1866-6, Modeling the economics of differentiated durable-goods markets by Miyuki Breen, George Chikhladze, Jose Figueroa-Lopez, Yaniv Gershon, Yanto Muliadi, and Ivy Prendergast (Suzhou Huang, mentor).
Mathematical modeling in industry - IMA Summer program for graduate students, July 19--28, 2000
See individual papers: 1866-1, Modeling planarization in chemical-mechanical polishing by Dilek A... more See individual papers: 1866-1, Modeling planarization in chemical-mechanical polishing by Dilek Alagoz, Stephanie Hoogendoorn, Satyanarayana Kakollu, Maria Reznikoff, Richard Schugart, and Michael Sostarecz (Leonard Borucki, mentor); 1866-2, Vehicle networks: achieving regular formation by Madalena Chaves, Robert Day, Lucia Gomez Ramos, Parthasarathi Nag, Anca Williams, and Wei Zhang (Sonja Glavaski, mentor); 1866-3, Designing airplane struts using minimal surfaces by Sara Del Valle, Todd Moeller, Siva Kumar Natarajan, Gergina V. Pencheva, Jason C. Sherman, and Steven M. Wise (Thomas Grandine, mentor); 1866-4, Mobility management in cellular telephony by Benjamin P. Cooke, Darongsae Kwon, Dmitry Glotov, Simon Schurr, Daniel Taylor, and Todd Wittman (David F. Shallcross, mentor); 1866-5, Optimal design for a varying environment by Serguei Lapin, Xuan Hien Nguyen, Jiyeon Oh, Daniel Vasiliu, Pei Yin, and Ningyi Zhang (David Misemer, mentor); 1866-6, Modeling the economics of differentiated durable-goods markets by Miyuki Breen, George Chikhladze, Jose Figueroa-Lopez, Yaniv Gershon, Yanto Muliadi, and Ivy Prendergast (Suzhou Huang, mentor).
On the slow motion of the interface of layered solutions to the scalar Ginzburg-Landau equation
... Moreover, V(z,x)= [F^2(a + ß Г FW-- f [F-"'2 f V/2))] Jo e Jo Jo = V(ZiV)\v... more ... Moreover, V(z,x)= [F^2(a + ß Г FW-- f [F-"'2 f V/2))] Jo e Jo Jo = V(ZiV)\v=U°((xz}/e) ' £Í£) = _fl(i + ф/е)) |Р1(г/£) + ffie-"2'/« (1 + d3(z/e)) (l + dA((l - z)/e)) } + 0(1 + ф/е)) L2(z/e) + tLp-e-^1-*"' (l + dz{z/e)) (l + d^z/e)) } (3.12) where 01 = -ае"2Ф^~е + 0(1)) + be-M-'V<(^£^ 0(1)) , (3.13) v ...
Mathematical modeling in industry X - IMA Workshop for graduate students (August 9-18, 2006)
See individual papers: # 2133-1, Birefringence data analysis by Christopher Bailey, Ginmo Chung, ... more See individual papers: # 2133-1, Birefringence data analysis by Christopher Bailey, Ginmo Chung, Alvaro Guevara, Sean Hardesty, Joseph Kenney, Sarthok Sircar, and Douglas Allan (mentor); # 2133-2, Web-spline finite elements by Yanping Cao, Olga Terlyga, Jon Van Laarhoven, Jianbao Wu, Guangri Xue, Ping Zhang, and Thomas Grandine (mentor); # 2133-3, Cell-foreign particle interaction by Benjamin Cook, Tanya Kazakova, Pedro Madrid, Jeremy Neal, Miguel Pauletti, Ruijun Zhao, and SuPing Lyu (mentor); # 2133-4, Reservoir model optimization under uncertainty by Sasanka Are, Paul Dostert, Bree Ettinger, Juan Liu, Vadim Sokolov, Ang Wei, and Klaus Wiegand (mentor); # 2133-5, Blind image deconvolution: Motion blur estimation by Felix Krahmer, Youzuo Lin, Bonnie McAdoo, Katharine Ott, Jiakou Wang, David Widemann, and Brendt Wohlberg (mentor); # 2133-6 Algorithms for the carpool problem by Joao Pedro Boavida, Vikram Kamat, Darshana Nakum, Ryan Nong, Xinyi Zhang, and Chai Wah Wu (mentor)
Journal of Intelligent Material Systems and Structures, 1999
Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, wh... more Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior ...
IEEE Transactions on Magnetics, 2001
In this paper we deal with the dynamics of material interfaces such as solid-liquid, grain or ant... more In this paper we deal with the dynamics of material interfaces such as solid-liquid, 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 two-dimensional model proposes that the motion of an interface F,j between regions i and j (z,j = 1,2,3, i ^ j) is governed by the equation Here Vij, K tJ , /i tJ and / tJ denote, respectively, the normal velocity, the curvature, the mobility and the surface tension of the interface and the numbers F^ 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 fa are small, fa = efa and e <C 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 fa = 0. It turns out that this problem, (0.1) with fij = 0, admits infinitely many solutions. Here, we show that a unique solution, "the vanishing surface tension (VST) solution", is selected by letting e-> 0. Furthermore, we introduce the concept of weak viscosity solution for the problem with 6 = 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.
CEM'13 Computational Electromagnetics International Workshop, 2013
Nanoplasmonics forms a major part of the field of nanophotonics, which explores how electromagnet... more Nanoplasmonics forms a major part of the field of nanophotonics, which explores how electromagnetic fields can be confined over dimensions on the order of or smaller than the wavelength. Here, we present an integral-equation formulation of the mathematical model that delivers accurate solutions in small computational times for surface plasmons coupled by periodic corrugations of flat surfaces.
A difficulty that arises in the context of two-dimensional in finite,d−periodic rough-surface sca... more A difficulty that arises in the context of two-dimensional in finite,d−periodic rough-surface scattering relates to the effective numerical evaluation of the corresponding “quasi-periodic Green function” Gqp(x, y). Recently, we introduced a novel scheme, based on the integr al representation of Gqp(x, y), that can be shown to outperform every alternative numerica l evaluation procedure, and is especially effective for high-frequency calculations. In this paper, we extend our algorithm to the evaluation of the partial derivatives of the Gqp(x, y) (as necessary, for instance, in the solution of integral equations that involve double layer potential rep resentations). Moreover, we further introduce a stabilizing mechanism based on multi-precision eval uations which, unlike those applicable to more classical algorithms for the calculation of Gqp, entails higher precision computation of only a few selected quantities.
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Papers by Fernando Reitich