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M. W. Buksas

Bio: M. W. Buksas is an academic researcher from Los Alamos National Laboratory. The author has contributed to research in topics: Finite difference coefficient & Dielectric. The author has an hindex of 3, co-authored 6 publications receiving 92 citations.

Papers
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Book
01 Jan 1987
TL;DR: Theoretical methods for dielectrics with supraconductive boundary and physical modeling for general polarization models are described, as well as methods for acoustically backed dielectric models.
Abstract: Preface 1. Introduction 2. Introduction and physical modeling 3. Wellposedness 4. Computational methods for dielectrics with supraconductive boundary 5. Computational methods for general polarization models 6. Computational methods for acoustically backed dielectrics 7. Concluding summary and remarks of potential applications Bibliography Index.

71 citations

01 Jan 2007
TL;DR: In this article, a mixed finite element method for the discretization of the perfectly matched layer (UPML) model for Maxwell's equations in the time domain is presented and an anisotropic uniaxial formulation of the UPML model is considered.
Abstract: We consider the anisotropic uniaxial formulation of the perfectly matched layer (UPML) model for Maxwell's equations in the time domain. We present and an- alyze a mixed finite element method for the discretization of the UPML in the time domain to simulate wave propagation on unbounded domains in two dimensions. On rectangles the spatial discretization uses bilinear finite elements for the electric field and the lowest order Raviart-Thomas divergence conforming elements for the mag- netic field. We use a centered finite difference method for the time discretization. We compare the finite element technique presented to the finite difference time domain method (FDTD) via a numerical reflection coefficient analysis. We derive the numeri- cal reflection coefficient for the case of a semi-infinite PML layer to show consistency between the numerical and continuous models, and in the case of a finite PML to study the effects of terminating the absorbing layer. Finally, we demonstrate the effectiveness of the mixed finite element scheme for the UPML by a numerical example and provide comparisons with the split field PML discretized by the FDTD method. In conclusion, we observe that the mixed finite element scheme for the UPML model has absorbing properties that are comparable to the FDTD method. AMS subject classfications: 65M60, 78M10

7 citations

01 Jan 1996
TL;DR: In this paper, a time domain approach for the investigation of dispersion mechanisms of a medium in electromagnetic field problems is presented, where the polarization is given in terms of a convolu-tion of the electric field with an impulse response function.
Abstract: We present a time domain approach for the investigation of dispersion mechanisms of a medium in electromagnetic eld problems. Maxwell's equations coupled with a generalized electric polarization model are considered. The polarization is given in terms of a convolu-tion of the electric eld with an impulse response function. Existence, uniqueness and continuous dependence of solutions on data are presented for a one-dimensional dispersive medium case. Estimation of electromagnetic properties of media is demonstrated via numerical examples. Parameters representing the electromagnetic property of a medium may include the static permittivity, relaxation time, natural frequency, static conductivity, etc. depending on the polarization model chosen. 1 Model Formulation Microwave images of tissue structures and soils play very important roles in many areas, including clinical and environmental medicine. These microwave images are useful in detection=enhanced treatment of abnormality of human organs and tissue, and detection= remediation of underground toxic wastes. The electromagnetic properties of a medium are generally characterized by its electric and magnetic polarization mechanisms and its static conductivity. Here we focus on the development of partial diier-ential equation (Maxwell's equations) based identiication techniques for

6 citations

Book ChapterDOI
TL;DR: In this article, the authors consider a class of dielectric media with instantaneous conductivity and nonlocal in time (hysteretic) polarization laws and formulate such systems in an operator-theoretic framework and show that, under certain conditions on the response function, the resulting systems generate Co semigroups.
Abstract: : We consider Maxwell systems with instantaneous conductivity and nonlocal in time (hysteretic) polarization laws which are characteristic of dispersive dielectric media. We formulate such systems in an operator theoretic framework and show that, under certain conditions on the dielectric response function, the resulting systems generate Co semigroups. It is shown that multiple Debye polarization models are included in those for which a semigroup formulation is possible.

3 citations

14 Apr 2006
TL;DR: In this article, a mixed finite element method for the time domain discretization of the perfectly matched layer model (UPML) is presented and compared with the finite difference time domain method.
Abstract: : We consider the anisotropic uniaxial formulation of the perfectly matched layer model (UPML). We prove the decay of different energies for the UPML, under certain assumptions, to demonstrate the well-posedness of this formulation. We present and analyze a mixed finite element method for the time domain discretization of UPML to simulate wave propagation in unbounded domains in two dimensions. On rectangles the spatial discretization uses bilinear finite elements for the electric field and the lowest order Raviart-Thomas divergence conforming elements for the magnetic field. We use a centered finite difference method for the time discretization. We compare the finite element technique presented to the finite difference time domain method (FDTD) via a stability, dispersion, phase error and numerical reflection coefficient analysis. We derive the reflection coefficient for the case of a semi-infinite layer to show consistency between the numerical and continuous models, and in the case of a finite PML to study the effects of terminating the absorbing layer. Finally, we demonstrate the effectiveness of the mixed finite element scheme by numerical examples and provide comparisons with the split field PML discretized by FDTD method. In conclusion, we observe that the mixed finite element scheme for the PML model has absorbing properties that are comparable to the FDTD method.

3 citations


Cited by
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Journal ArticleDOI
TL;DR: Banks, V A Bokil and N L Gibson as discussed by the authors analyzed stability and dispersion in a Finite Element Method for Debye and Lorentz Media, 25(4), pp 885-917, July 2009.
Abstract: This is the pre-peer reviewed version of the following article: H T Banks, V A Bokil and N L Gibson, Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Media, Numerical Methods for Partial Differential Equations, 25(4), pp 885-917, July 2009, which has been published in final form at http://www3intersciencewileycom/journal/122341241/issue

61 citations

01 Jan 2003
TL;DR: A survey of several recent and emerging ideas and ideas on modeling and system interrogation in the presence of uncertainty that the authors feel have potential for applications related to bioterrorism.
Abstract: In this paper we present a survey of several recent and emerging ideas and e orts on modeling and system interrogation in the presence of uncertainty that we feel have signi cant potential for applications related to bioterrorism. The rst focuses on physiologically based pharmacokinetic (PBPK) type models and the e ects of drugs, toxins and viruses on tissue, organs, individuals and populations wherein both intraand inter-individual variability are present when one attempts to determine kinetic rates, susceptibility, eÆcacy of toxins, antitoxins, etc., in aggregate populations. Methods combining deterministic and stochastic concepts are necessary to formulate and computationally solve the associated estimation problems. Similar issues arise in the HIV infectious models we also present below. A second e ort concerns the use of remote electromagnetic interrogation pulses linked to dielectric properties of materials to carry out macroscopic structural imaging of bulk packages (drugs, explosives, etc.) as well as test for presence and levels of toxic chemical compounds in tissue. These techniques also may be useful in functional imaging (e.g., of brain and CNS activity levels) to determine levels of threat in potential adversaries via changes in dielectric properties and conductivity. The PBPK and cellular level virus infectious models we discuss are special examples of a much wider class of population models that one might utilize to investigate potential agents for use in attacks, such as viruses, bacteria, fungi and other chemical, biochemical or radiological agents. These include general epidemiological models such as SIR infectious

54 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms, and give theoretical and computational results for specific problems with multiple Debye mechanisms.
Abstract: : We consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms. a theoretical and computational framework for such problems is given. Computational results for specific problems with multiple Debye mechanisms are given in the case of discrete, uniform, log-normal, and log-Bi-Gaussian distributions.

46 citations