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M Hussein - One of the best experts on this subject based on the ideXlab platform.
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bloch mode synthesis ultrafast methodology for elastic Band Structure Calculations
Physical Review E, 2014Co-Authors: Dimitri Krattiger, M HusseinAbstract:We present a methodology for fast Band-Structure Calculations that is generally applicable to problems of elastic wave propagation in periodic media. The methodology, called Bloch mode synthesis, represents an extension of component mode synthesis, a set of substructuring techniques originally developed for structural dynamics analysis. In Bloch mode synthesis, the unit cell is divided into interior and boundary degrees-of-freedom, which are described, respectively, by a set of normal modes and a set of constraint modes. A combination of these mode sets then forms a reduced basis for the Band Structure eigenvalue problem. The reduction is demonstrated on a phononic-crystal model and a locally resonant elastic-metamaterial model and is shown to accurately predict the frequencies and Bloch mode shapes with a dramatic decrease in computation time in excess of two orders of magnitude.
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reduced bloch mode expansion for periodic media Band Structure Calculations
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2009Co-Authors: M HusseinAbstract:Reduced Bloch mode expansion (RBME) is presented for fast periodic media Band Structure Calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the irreducible Brillouin zone at high symmetry points determined by the medium’s crystal Structure and group theory (and possibly at additional related points). At each of the reciprocal lattice selection points, a number of Bloch eigenfunctions are selected up to the frequency/energy range of interest for the Band Structure Calculations. As it is common to initially discretize the periodic unit cell and solution field using some choice of basis, RBME is practically a secondary expansion that uses a selected set of Bloch eigenvectors. Such expansion therefore keeps, and builds on, any favourable attributes a primary expansion approach might exhibit. Being in line with the well-known concept of modal analysis, the proposed approach maintains accuracy while reducing the computation time by up to two orders of magnitudes or more depending on the size and extent of the Calculations. Results are presented for phononic, photonic and electronic Band Structures.
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reduced bloch mode expansion for periodic media Band Structure Calculations
arXiv: Computational Physics, 2008Co-Authors: M HusseinAbstract:Reduced Bloch mode expansion is presented for fast periodic media Band Structure Calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the irreducible Brillouin zone at high symmetry points determined by the medium's crystal Structure and group theory (and possibly at additional related points). At each of the reciprocal lattice selection points, a number of Bloch eigenfunctions are selected up to the frequency range of interest for the Band Structure Calculations. Since it is common to initially discretize the periodic unit cell and solution field using some choice of basis, reduced Bloch mode expansion is practically a secondary expansion that uses a selected set of Bloch eigenvectors. Such expansion therefore keeps, and builds on, any favorable attributes a primary expansion approach might exhibit. Being in line with the well known concept of modal analysis, the proposed approach maintains accuracy while reducing the computation time by up to two orders of magnitudes or more depending on the size and extent of the Calculations. Results are presented for phononic, photonic and electronic Band Structures.
Raymond Fresard - One of the best experts on this subject based on the ideXlab platform.
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magnetic ordering in the striped nickelate la5 3sr1 3nio4 a Band Structure point of view
EPL, 2008Co-Authors: U Schwingenschlogl, C Schuster, Raymond FresardAbstract:We report on a comprehensive study of the electronic and magnetic Structure of the striped nickelate La5/3Sr1/3NiO4. The investigation is carried out using Band Structure Calculations based on the density functional theory. A magnetic Structure compatible with experiment is obtained from spin-polarized Calculations within the generalized gradient approximation (GGA), whereas inclusion of a local Coulomb interaction in the LDA+U framework results in a different ground state. The influence of the various interaction parameters is discussed in detail.
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magnetic ordering in the striped nickelate la5 3sr1 3nio4 a Band Structure point of view
arXiv: Strongly Correlated Electrons, 2007Co-Authors: U Schwingenschlogl, C Schuster, Raymond FresardAbstract:We report on a comprehensive study of the electronic and magnetic Structure of the striped nickelate La5/3Sr1/3NiO4. The investigation is carried out using Band Structure Calculations based on density functional theory. A magnetic Structure compatible with experiment is obtained from spin-polarized Calculations within the generalized gradient approximation (GGA), whereas inclusion of a local Coulomb interaction in the LDA+U framework results in a different ground state. The influence of the various interaction parameters is discussed in detail.
Tomomi Shimazaki - One of the best experts on this subject based on the ideXlab platform.
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dielectric dependent screened hartree fock exchange potential and slater formula with coulomb hole interaction for energy Band Structure Calculations
Journal of Chemical Physics, 2014Co-Authors: Tomomi Shimazaki, Takahito NakajimaAbstract:We previously reported a screened Hartree–Fock (HF) exchange potential for energy Band Structure Calculations [T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009); T. Shimazaki and Y. Asai, J. Chem. Phys. 132, 224105 (2010)]. In this paper, we discuss the Coulomb-hole (COH) interaction and screened Slater-formula and determine the energy Band diagrams of several semiconductors, such as diamond, silicon, AlAs, AlP, GaAs, GaP, and InP, based on the screened HF exchange potential and Slater-formula with COH interaction, to demonstrate the adequacy of those theoretical concepts. The screened HF exchange potential and Slater-formula are derived from a simplified dielectric function and, therefore, include the dielectric constant in their expressions. We also present a self-consistent calculation technique to automatically determine the dielectric constant, which is incorporated into each self-consistent field step.
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first principles Band Structure Calculations based on self consistent screened hartree fock exchange potential
Journal of Chemical Physics, 2009Co-Authors: Tomomi Shimazaki, Yoshihiro AsaiAbstract:A screened Hartree–Fock (HF) exchange potential with the dielectric constant was previously reported by Shimazaki and Asai [Chem. Phys. Lett. 466, 91 (2008)], in which the inverse of the dielectric constant was used to represent a fraction of the HF exchange term. In that report, the experimentally obtained value for the dielectric constant was employed. Herein, we discuss a self-consistent technique, in which the value of the dielectric constant can be automatically determined. This technique enables the energy Band Structure to be determined without using the experimental value. The Band energy Structure of diamond is calculated, a self-consistent procedure is determined to give closer Bandgaps compared with the local density approximation and the generalized gradient approximation.
N Sukumar - One of the best experts on this subject based on the ideXlab platform.
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spectral extended finite element method for Band Structure Calculations in phononic crystals
Journal of Computational Physics, 2021Co-Authors: Eric B Chin, Amir Ashkan Mokhtari, Ankit Srivastava, N SukumarAbstract:Abstract In this paper, we compute the Band Structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on Structured higher-order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of Structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bezier representation of curved (circular) geometries, and construct suitable material enrichment functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band Structure Calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on Structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O ( 10 − 8 ) accuracy in frequency Calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements.
Yoshihiro Asai - One of the best experts on this subject based on the ideXlab platform.
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first principles Band Structure Calculations based on self consistent screened hartree fock exchange potential
Journal of Chemical Physics, 2009Co-Authors: Tomomi Shimazaki, Yoshihiro AsaiAbstract:A screened Hartree–Fock (HF) exchange potential with the dielectric constant was previously reported by Shimazaki and Asai [Chem. Phys. Lett. 466, 91 (2008)], in which the inverse of the dielectric constant was used to represent a fraction of the HF exchange term. In that report, the experimentally obtained value for the dielectric constant was employed. Herein, we discuss a self-consistent technique, in which the value of the dielectric constant can be automatically determined. This technique enables the energy Band Structure to be determined without using the experimental value. The Band energy Structure of diamond is calculated, a self-consistent procedure is determined to give closer Bandgaps compared with the local density approximation and the generalized gradient approximation.
