Filters

2009 - 200912010 - 20153

More filters

20194
Reset filters

Settings

Version: publishedVersion × Subject: Maxwell’s equations ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Druet, Pierre-Étienne; Klein, Olaf; Sprekels, Jürgen
    This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations ...
  • Thumbnail Image
    Item
    Improved dual meshes using Hodge-optimized triangulations for electromagnetic problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Schlundt, Rainer
    Hodge-optimized triangulations (HOT) can optimize the dual mesh alone or both the primal and dual meshes. They make them more self-centered while keeping the primal-dual orthogonality. The weights are optimized in order to improve one or more of the discrete Hodge stars. Using the example of Maxwells equations we consider academic examples to demonstrate the generality of the approach.
  • Thumbnail Image
    Item
    Shifted linear systems in electromagnetics : part 1: Systems with intentical right-hand sides
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Schlundt, Rainer; Schmückle, Franz-Josef; Heinrich, Wolfgang
    We consider the solution of multiply shifted linear systems for a single right-hand side. The coefficient matrix is symmetric, complex, and indefinite. The matrix is shifted by different multiples of the identity. Such problems arise in a number of applications, including the electromagnetic simulation in the development of microwave and mm-wave circuits and modules. The properties of microwave circuits can be described in terms of their scattering matrix which is extracted from the orthogonal decomposition of the electric field. We discretize the Maxwell's equations with orthogonal grids using the Finite Integration Technique (FIT). Some Krylov subspace methods have been used to solve multiply shifted systems for about the cost of solving just one system. We use the QMR method based on coupled two-term recurrences with polynomial preconditioning.
  • Thumbnail Image
    Item
    Regular triangulation and power diagrams for Maxwell's equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Schlundt, Rainer
    We consider the solution of electromagnetic problems. A mainly orthogonal and locally barycentric dual mesh is used to discretize the Maxwell's equations using the Finite Integration Technique (FIT). The use of weighted duals allows greater flexibility in the location of dual vertices keeping the primal-dual orthogonality. The construction of the constitutive matrices is performed using either discrete Hodge stars or microcells. Hodge-optimized triangulations (HOT) can optimize the dual mesh alone to make it more self-centered while maintaining the primal-dual orthogonality, e.g., the weights are optimized in order to improve one or more of the discrete Hodge stars.