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  • 1
    Online Resource
    Online Resource
    Sharjah :Bentham Science Publishers,
    Keywords: Mathematical physics. ; Wave mechanics. ; Electronic books.
    Description / Table of Contents: Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories.In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume.Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems.Periodic structure problems arise quite often in many modern application areas like semiconductor nanostructures (e.g. quantum dots and nanocrystals), semiconductor superlattices, photonic crystals structures, meta materials or Bragg gratings of surface plasmon polariton waveguides.This first volume treats both mathematical analysis of periodic structure problems and state-of-the art numerical techniques, such as frequency domain methods, beam propagation methods and eigenmode expansion methods. Several chapters are devoted to concrete applications of periodic media simulation. The book is a useful resource for individuals interested in complex wave mechanics of unique physical structures.
    Type of Medium: Online Resource
    Pages: 1 online resource (240 pages)
    Edition: 1st ed.
    ISBN: 9781608051502
    Series Statement: Progress in Computational Physics (PiCP), 1 ; v.1
    DDC: 530.4/1/0113;530.410113
    Language: English
    Note: 00 Title Page Cover.pdf -- 01 Title Page -- 02 Contents -- 04 preface -- 05 Contributors -- 06 Part I -- 07 Chapter 1 06 -- 08 Chapter 2 43 -- 09 Chapter 3 23 -- 10 Part II -- 11 Chapter 4 35 -- 12 Chapter 5 27 -- 13 Chapter 6 32 -- 14 Part III -- 15 Chapter 7 30 -- 16 Chapter 8 30 -- 17 Index 04.
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  • 2
    Online Resource
    Online Resource
    Sharjah :Bentham Science Publishers,
    Keywords: Transport theory -- Mathematical models. ; Mathematical physics. ; Electronic books.
    Description / Table of Contents: The third volume - Novel Trends in Lattice Boltzmann Methods contains 10 chapters devoted to mathematical analysis of different issues related to the lattice Boltzmann methods, advanced numerical techniques for physico-chemical flows, fluid structure interaction and practical applications of these phenomena to real world problems.
    Type of Medium: Online Resource
    Pages: 1 online resource (284 pages)
    Edition: 1st ed.
    ISBN: 9781608057160
    Series Statement: Progress in Comuptational Physics ; v.3
    DDC: 530.4/1/0113
    Language: English
    Note: Title -- Cover -- EUL -- Contents -- Foreward -- Preface -- Part 01 -- Chapter 01 -- Part 02 -- Chapter 02 -- Chapter 03 -- Chapter 04 -- Chapter 05 -- Part 03 -- Chapter 06 -- Chapter 07 -- Part 04 -- Chapter 08 -- Part 05 -- Chapter 09 -- Index -- Back.
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  • 3
    Keywords: Mathematical physics. ; Porous materials. ; Fluid dynamics. ; Electronic books.
    Description / Table of Contents: This second volume contains both, the mathematical analysis of the coupling between fluid flow and porous media flow and state-of-the art numerical techniques, like tailor-made finite element and finite volume methods. Readers will come across articles devoted to concrete applications of these models in the field of energy, biology and environmental research.
    Type of Medium: Online Resource
    Pages: 1 online resource (140 pages)
    Edition: 1st ed.
    ISBN: 9781608052547
    Series Statement: Progress in Computational Physics (PiCP) ; v.2
    DDC: 530.0285
    Language: English
    Note: 01 Title.pdf -- 03 REVISED eBooks End User License Agreement-Website -- 04 contents -- 05 Foreword -- 06 preface -- 07 Contributors -- 08 1 ChapterEhrhardt -- 09 2 ChapterChandesris -- 10 3 ChapterSochala -- 11 4 ChapterBernardi -- 12 5 ChapterCai -- 13 6 ChapterMaury -- 14 7 ChapterHoppe -- 15 index.
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  • 4
    Online Resource
    Online Resource
    Bremen : Zentrum für Technomathematik, Univ. Bremen
    Keywords: Forschungsbericht
    Type of Medium: Online Resource
    Pages: Online-Ressource (22 S., 1,22 MB)
    Series Statement: Berichte aus der Technomathematik 11-03
    Language: English
    Note: Systemvoraussetzungen: Acrobat reader.
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  • 5
    Keywords: Forschungsbericht
    Description / Table of Contents: For the simulation of the propagation of optical waves in open wave guiding structures of integrated optics the parabolic approximation of the scalar wave equation is commonly used. This approach is commonly termed the beam propagation method (BPM). It is of paramount importance to have well-performing transparent boundary conditions applied on the boundaries of the finite computational window, to enable the superfluous portion of the propagating wave to radiate away from the wave guiding structure. Three different formulations (continuous, semi-discrete and fully-discrete) of the non-local transparent boundary conditions are described and compared here.
    Type of Medium: Online Resource
    Pages: Online-Ressource (16 S., 395 KB)
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1440
    DDC: 510
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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  • 6
    Keywords: Forschungsbericht
    Description / Table of Contents: Periodic media problems widely exist in many modern application areas like semiconductor nanostructures (e.g. quantum dots and nanocrystals), semi-conductor superlattices, photonic crystals (PC) structures, meta materials or Bragg gratings of surface plasmon polariton (SPP) waveguides, etc. Often these application problems are modeled by partial differential equations with periodic coefficients and/or periodic geometries. In order to numerically solve these periodic structure problems efficiently one usually confines the spatial domain to a bounded computational domain (i.e. in a neighborhood of the region of physical interest). Hereby, the usual strategy is to introduce so-called artificial boundaries and impose suitable boundary conditions. For wave-like equations, the ideal boundary conditions should not only lead to w ell-posed problems, but also mimic the perfect absorption of waves traveling out of the computational domain through the artificial boundaries ...
    Type of Medium: Online Resource
    Pages: Online-Ressource (34 S., 1,81 MB) , graph. Darst.
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1441
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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  • 7
    Keywords: Forschungsbericht
    Description / Table of Contents: A new approach for simulating the solution of the time-dependent Schrödinger equation with a general variable potential will be proposed. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a rational function with respect to a suitable spectral parameter. With the proposed method we can overcome the usual high-frequency restriction for absorbing boundary conditions of general variable potential problems. We end up with a fast computational algorithm for absorbing boundary conditions that are accurate for the full frequency band
    Type of Medium: Online Resource
    Pages: Online-Ressource (23 S., 809 KB) , graph. Darst.
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1426
    DDC: 510
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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  • 8
    Keywords: Forschungsbericht
    Description / Table of Contents: In this work we present a new numerical technique for solving periodic structure problems. This new approach possesses several advantages. First, it allows for a fast evaluation of the Robin-to-Robin operator for periodic array problems. Secondly, this computational method can also be used for bi-periodic structure problems with local defects. Our strategy is an improvement of the recently developed recursive doubling process by Yuan and Lu. In this paper we consider several problems, such as the exterior elliptic problems with strong coercivity, the time-dependent Schrödinger equation and finally the Helmholtz equation with damping.
    Type of Medium: Online Resource
    Pages: Online-Ressource (29 S., 1,75 MB)
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1323
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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  • 9
    Keywords: Forschungsbericht
    Description / Table of Contents: This chapter is a review of the research of the authors from the last decade and focuses on the mathematical analysis of the Schrödinger model for nano-scale semiconductor devices. We discuss transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation on a two dimensional domain. First we derive the two dimensional discrete TBCs in conjunction with a conservative Crank-Nicolson-type finite difference scheme and a compact nine-point scheme. For this difference equations we derive discrete transparent boundary conditions (DTBCs) in order to get highly accurate solutions for open boundary problems. The presented discrete boundary-valued problem is unconditionally stable and completely reflection-free at the boundary. Then, since the DTBCs for the Schrödinger equation include a convolution w.r.t. time with a weakly decaying kernel, we construct approximate DTBCs with a kernel having the form of a finite sum of exponentials, which can be efficiently evaluated by recursion. In several numerical tests we illustrate the perfect absorption of outgoing waves independent of their impact angle at the boundary, the stability, and efficiency of the proposed method. Finally, we apply inhomogeneous DTBCs to the transient simulation of quantum waveguides with a prescribed electron inflow.
    Type of Medium: Online Resource
    Pages: Online-Ressource (28 S., 4,60 MB)
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1339
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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  • 10
    Keywords: Forschungsbericht
    Description / Table of Contents: Periodic arrays are structures consisting of geometrically identical subdomains, usually called periodic cells. In this paper, by taking the Helmholtz equation as a model, we consider the definition and evaluation of the exact boundary mappings for general one-dimensional semi-infinite periodic arrays for any real wavenumber. The well-posedness of the Helmholtz equation is established via the limiting absorption principle. An algorithm based on the doubling procedure and extrapolation technique is proposed to derive the exact Sommerfeld-to-Sommerfeld boundary mapping. The advantages of this algorithm are the robustness and simplicity of implementation. But it also suffers from the high computational cost and the resonance wave numbers. To overcome these shortcomings, we propose another algorithm based on a conjecture about the asymptotic behaviour of limiting absorption principle solutions. The price we have to pay is the resolution of two generalized eigenvalue problems, but still the overall computational cost is significantly reduced. Numerical evidences show that this algorithm presents theoretically the same results as the first algorithm. Moreover, some quantitative comparisons between these two algorithms are given.
    Type of Medium: Online Resource
    Pages: Online-Ressource (19 S., 400 KB)
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1358
    Language: English
    Note: Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden , Systemvoraussetzungen: Acrobat reader.
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