Journal: BIT Numerical Mathematics

Abbreviation

BIT

Publisher

Springer

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ISSN

0006-3835
1572-9125

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Publications 1 - 10 of 20
  • Sparse tensor edge elements
    Item type: Journal Article
    Hiptmair, Ralf; Jerez-Hanckes, Carlos; Schwab, Christoph (2013)
    BIT Numerical Mathematics
    We consider the tensorized operator for the Maxwell cavity source problem in frequency domain. Such formulations occur when computing statistical moments of the fields under a stochastic volume excitation. We establish a discrete inf-sup condition for its Ritz-Galerkin discretization on sparse tensor product edge element spaces built on nested sequences of meshes. Our main tool is a generalization of the edge element Fortin projector to a tensor product setting. The techniques extend to the surface boundary edge element discretization of tensorized electric field integral equation operators.
  • Generating numerical algorithms using a computer algebra system
    Item type: Journal Article
    Gander, Walter (2006)
    BIT Numerical Mathematics
  • A second-kind Galerkin boundary element method for scattering at composite objects
    Item type: Journal Article
    Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke (2015)
    BIT Numerical Mathematics
    We consider the scattering of time-harmonic acoustic waves at objects composed of several homogeneous parts with different material properties. In Claeys (A single trace integral formulation of the second kind for acoustic scattering, 2011), a novel second-kind boundary integral formulation for this scattering problem was proposed, that relies on skeleton Cauchy data as unknowns. We recast it into a variational problem set in 𝐿2 and investigate its Galerkin boundary element discretization from a theoretical and algorithmic point of view. Empiric studies demonstrate the competitive accuracy and superior conditioning of the new approach compared to a widely used Galerkin boundary element approach based on a first-kind boundary integral formulation.
  • A weak second-order split-step method for numerical simulations of stochastic differential equations
    Item type: Journal Article
    Perret, C.; Petersen, Wesley P. (2014)
    BIT Numerical Mathematics
    In an analogy from symmetric ordinary differential equation numerical integrators, we derive a three-stage, weak 2nd-order procedure for Monte-Carlo simulations of Itô stochastic differential equations. Our composite procedure splits each time step into three parts: an h/2-stage of trapezoidal rule, an h-stage martingale, followed by another h/2-stage of trapezoidal rule. In n time steps, an h/2-stage deterministic step follows another n−1 times. Each of these adjacent pairs may be combined into a single h-stage, effectively producing a two-stage method with partial overlap between successive time steps.
  • Preface to BIT 55:1
    Item type: Other Journal Item
    Hiptmair, Ralf (2015)
    BIT Numerical Mathematics
  • Computing periodic deflating subspaces associated with a specified set of eigenvalues
    Item type: Journal Article
    Granat, Robert; Kågström, Bo; Kressner, Daniel (2007)
    BIT Numerical Mathematics
  • Fast construction of the Fejer and Clenshaw-Curtis quadrature rules
    Item type: Journal Article
    Waldvogel, Jörg (2006)
    BIT Numerical Mathematics
  • Multilevel Monte Carlo front-tracking for random scalar conservation laws
    Item type: Journal Article
    Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska (2016)
    BIT Numerical Mathematics
    We consider random scalar hyperbolic conservation laws in spatial dimension $d ≥ 1$ with bounded random flux functions which are Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution. We present a convergence analysis of a multilevel Monte Carlo front-tracking algorithm. It is based on “pathwise” application of the front-tracking method for deterministic conservation laws. Due to the first order convergence of front tracking, we obtain an improved complexity estimate in one space dimension.
  • Stable finite difference schemes for the magnetic induction equation with Hall effect
    Item type: Journal Article
    Corti, Pablo; Mishra, Siddhartha (2012)
    BIT Numerical Mathematics
  • On stability of numerical schemes via frozen coefficients and the magnetic induction equations
    Item type: Journal Article
    Mishra, Siddhartha; Svaerd, Magnus (2010)
    BIT Numerical Mathematics
Publications 1 - 10 of 20