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Reinhold Pregla - One of the best experts on this subject based on the ideXlab platform.

  • Numerical analysis of couplers and novel filters with the Method of Lines
    Proceedings of 2004 6th International Conference on Transparent Optical Networks (IEEE Cat. No.04EX804), 2004
    Co-Authors: A. Barcz, Stefan F. Helfert, Reinhold Pregla
    Abstract:

    The paper presents the results of the numerical analysis of various kinds of photonic crystal structures, such as 3 dB couplers and meander-Lines, connected to photonic crystal waveguides and dielectric waveguides. The devices are modelled by the Method of Lines (MoL) with Floquet's theorem.

  • New high-accuracy subgridding technique for the Method of Lines
    2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535), 2004
    Co-Authors: L.a. Greda, Reinhold Pregla
    Abstract:

    A new high-accurate subgridding technique for the Method of Lines is proposed. It is the first paper dealing with subgridding in the Method of Lines. The proposed algorithm involves interpolation of the missing field components on the discontinuity between a coarse and a fine grid with second-order accuracy. All refinement factors can be used. The algorithm is substantiated with numerical results.

  • Modeling of 2D photonic crystals by using the Method of Lines
    Proceedings of 2002 4th International Conference on Transparent Optical Networks (IEEE Cat. No.02EX551), 2002
    Co-Authors: A. Barcz, Stefan F. Helfert, Reinhold Pregla
    Abstract:

    In our work we examined 2-dimensional photonic crystals. For modeling we used the Method of Lines (MoL). We analyzed waveguides, filters and concatenation of two bends. Results are in good agreement with results presented in the literature.

  • Analysis of Coplanar T-junctions by the Method of Lines
    Aeu-international Journal of Electronics and Communications, 2001
    Co-Authors: Łukasz A. Grda, Reinhold Pregla
    Abstract:

    Summary A novel Method for the analysis of a wide range of coplanar and microwave T-junctions is presented. The concept is based on the Method of Lines. Two crossed two-dimensional discretization schemes are combined with the impedance transformation for modelling the central region of the structure. This approach is validated by comparison with results obtained by FDTD Method and Sonnet software.

  • The Method of Lines for the analysis of dielectric waveguide bends
    Journal of Lightwave Technology, 1996
    Co-Authors: Reinhold Pregla
    Abstract:

    The analysis of a wide class of waveguide bends using the Method of Lines is suggested. The discretization is performed in radial direction. The cross section of the waveguide may consist of many inhomogeneous layers. Loss can be taken into account by using complex permittivities. The radiation loss is calculated by the use of absorbing boundary conditions. The presented algorithm is verified by the analysis of a rib waveguide bend. The results are in good agreement with those published in the literature.

Stefan F. Helfert - One of the best experts on this subject based on the ideXlab platform.

  • The Method of Lines in the time domain
    Advances in Radio Science, 2013
    Co-Authors: Stefan F. Helfert
    Abstract:

    Abstract. The Method of Lines (MoL) is a semi-analytical numerical algorithm that has been used in the past to solve Maxwell's equations for waveguide problems. It is mainly used in the frequency domain. In this paper it is shown how the MoL can be used to solve initial value problems in the time domain. The required expressions are derived for one-dimensional structures, where the materials may be dispersive. The algorithm is verified with numerical results for homogeneous structures, and for the concatenation of standard dielectric and left handed materials.

  • Applying Oblique Coordinates in the Method of Lines
    Progress in Electromagnetics Research-pier, 2006
    Co-Authors: Stefan F. Helfert
    Abstract:

    Oblique coordinates are introduced into the Method of Lines. For the purpose of analysis, suitable equations are derived. The formulas are applied to compute the transmission in a waveguide device consisting of straight waveguides connected by a tilted one. Furthermore, the band structure of a hexagonal photonic bandgap structure was computed using these oblique coordinates.

  • Numerical analysis of couplers and novel filters with the Method of Lines
    Proceedings of 2004 6th International Conference on Transparent Optical Networks (IEEE Cat. No.04EX804), 2004
    Co-Authors: A. Barcz, Stefan F. Helfert, Reinhold Pregla
    Abstract:

    The paper presents the results of the numerical analysis of various kinds of photonic crystal structures, such as 3 dB couplers and meander-Lines, connected to photonic crystal waveguides and dielectric waveguides. The devices are modelled by the Method of Lines (MoL) with Floquet's theorem.

  • The Method of Lines for the calculation of band structures in photonic crystals
    Proceedings of 2003 5th International Conference on Transparent Optical Networks 2003., 2003
    Co-Authors: Stefan F. Helfert
    Abstract:

    The Method of Lines a semivectorial algorithm is applied to the computation of band-structures in photonic crystals. The algorithm is used for the examination of square lattices of rods in air. The determined results are compared with other Methods showing a good agreement.

  • Modeling of 2D photonic crystals by using the Method of Lines
    Proceedings of 2002 4th International Conference on Transparent Optical Networks (IEEE Cat. No.02EX551), 2002
    Co-Authors: A. Barcz, Stefan F. Helfert, Reinhold Pregla
    Abstract:

    In our work we examined 2-dimensional photonic crystals. For modeling we used the Method of Lines (MoL). We analyzed waveguides, filters and concatenation of two bends. Results are in good agreement with results presented in the literature.

Zdzisław Kamont - One of the best experts on this subject based on the ideXlab platform.

  • Method of Lines for Quasilinear Functional Differential Equations
    Ukrainian Mathematical Journal, 2014
    Co-Authors: W. Czernous, Zdzisław Kamont
    Abstract:

    UDC 517.9 We give a theorem on the estimation of error for approximate solutions to ordinary functional differential equations. The error is estimated by a solution of an initial problem for a nonlinear functional differential equation. We apply this general result to the investigation of convergence of the numerical Method of Lines for evolution functional differential equations. The initial boundary-value problems for quasilinear equations are transformed (by means of discretization in spatial variables) into systems of ordinary functional differential equations. Nonlinear estimates of the Perron-type with respect to functional variables for given operators are assumed. Numerical examples are given. The numerical Method of Lines for partial differential or functional differential equations consists in replacing the derivatives with respect to spatial variables by difference expressions. This leads to systems of ordinary differential or functional differential equations. They satisfy consistency conditions on classical solutions of the original problems. The main task in these considerations is to find sufficient conditions for the stability of differential difference problems. There is an ample literature on the Method of Lines. The classical papers are [7, 8, 22, 23], where parabolic equations were considered. The existence results based on the Method of Lines can be found in [3, 14, 19, 24, 25]. Parabolic problems and first-order partial differential equations and boundary-value problems for nonlinear elliptic equations were considered. The papers [1, 2, 4, 13, 29, 30] initiated the theory of the Method of Lines for the evolution functional differential equations. Initial problems on the Haar pyramid for Hamilton–Jacobi-type equations and parabolic equations with initial or initial-boundary conditions of the Dirichlet-type were investigated. For further bibliographic information concerning the Method of Lines, see [9, 11, 17, 21, 28]. The results obtained by the Method of Lines for the evolution functional differential equations are based on the following ideas. The comparison theorems for differential difference inequalities generated by nonlinear functional differential equations are obtained. These theorems state that the functions satisfying differential difference inequalities can be estimated by using the solutions of ordinary differential or functional differential equations. The comparison theorems are used to prove the existence of approximate solutions. The results on the convergence of sequences of approximate solutions are also based on the comparison theorems for differential difference inequalities. The theorems on the numerical Method of Lines for nonlinear first partial functional differential equations [1, 2, 12, 29] and for parabolic problems [15, 30] were obtained by using the comparison Methods mentioned above. The aim of the present paper is to propose a new Method for the investigation of the numerical Method of Lines for the evolution functional-differential equations. It is shown that the results on the existence of approximate solutions and the theorems on convergence of the Methods are obtained as consequences of simple theorems for ordinary functional-differential equations.

  • Numerical Method of Lines
    Hyperbolic Functional Differential Inequalities and Applications, 1999
    Co-Authors: Zdzisław Kamont
    Abstract:

    The Method of Lines for partial differential equations consists in replacing spatial derivatives by difference expressions. Then the partial equation is transformed into a system of ordinary differential equations. The Method is used for approximation of solutions of nonlinear differential problems of parabolic type by solutions of ordinary equations ([91, 153, 219, 220, 222, 225, 238]). The Method is also treated as a tool for proving of existence theorems for differential problems corresponding to parabolic equations [223, 224, 227] or first-order hyperbolic systems [101, 157]. Simple examples of the Method of Lines for nonlinear functional differential equations were considered in [29, 108, 128]. The Method for equations of higher orders is studied in [91]. The book [189] demonstrates lots of examples of the use of the numerical Method of Lines. Convergence analysis of one step difference Methods generated by the numerical Method of Lines was investigated in [186].

William E Schiesser - One of the best experts on this subject based on the ideXlab platform.

  • Method of Lines solutions of the extended Boussinesq equations
    Journal of Computational and Applied Mathematics, 2005
    Co-Authors: Samir Hamdi, Wayne H. Enright, Y. Ouellet, William E Schiesser
    Abstract:

    A numerical solution procedure based on the Method of Lines for solving the Nwogu one-dimensional extended Boussinesq equations is presented. The numerical scheme is accurate up to fifth-order in time and fourth-order accurate in space, thus reducing all truncation errors to a level smaller than the dispersive terms retained by most extended Boussinesq models. Exact solitary wave solutions and invariants of motions recently derived by the authors are used to specify initial data for the incident solitary waves in the numerical model of Nwogu and for the verification of the associated computed solutions. The invariants of motions and several error measures are monitored in order to assess the conservative properties and the accuracy of the numerical scheme. The proposed Method of Lines solution procedure is general and can be easily modified to solve a wide range of Boussinesq-like equations in coastal engineering. .

  • Upwinding in the Method of Lines
    Mathematics and Computers in Simulation, 2001
    Co-Authors: Philippe Saucez, William E Schiesser, Alain Vande Wouwer
    Abstract:

    The Method of Lines (MOL) is a procedure for the numerical integration of partial differential equations (PDEs). Briefly, the spatial (boundary value) derivatives of the PDEs are approximated algebraically using, for example, finite differences (FDs). If the PDEs have only one initial value variable, typically time, then a system of initial value ordinary differential equations (ODEs) results through the algebraic approximation of the spatial derivatives.

  • adaptive Method of Lines
    2001
    Co-Authors: Vande A Wouwer, Ph Saucez, William E Schiesser
    Abstract:

    Introduction Application of the Adaptive Method of Lines to Nonlinear Wave Propagation Problems Adaptive MOL for Magneto-Hydrodynamic PDE Models Development of a 1-D Error-Minimizing Moving Adaptive Grid Method An Adaptive Method of Lines Approach for Modelling Flow and Transport in Rivers An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries, M. Sussman The Solution of Steady PDEs on Adjustable Meshes in Multidimensions Using Local Descent Methods Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems Linearly Implicit Adaptive Schemes for Singular Reaction-Diffusion Equations Unstructured Mesh MOL Solvers for Reacting Flow Problems Two-Dimensional Model of a Reaction Bonded Aluminum Oxide Cylinder Method of Lines within the Simulation Environment DIVA for Chemical Processes.

  • the numerical Method of Lines integration of partial differential equations
    1991
    Co-Authors: William E Schiesser
    Abstract:

    What Is the Numerical Method of Lines? Some Applications of the Numerical Method of Lines. Spatial Differentiation. Initial Value Integration. Stability of Numerical Method of Lines Approximations. Additional Applications: Multidimensional Pdes and Adaptive Grids. Appendix A: The Laplacian Operator in Various Coordinate Systems. Appendix B: Spatial Differentiation Routines. Appendix C: Library of ODE and ODE/PDE Applications. Index.

A. Barcz - One of the best experts on this subject based on the ideXlab platform.