Some Examples


  • Exterior solution of the Laplace Equation

    Two different boundary integral formulations for an exterior Laplace equation are implemented. the approximate solutions are compared against a known exact solution.
    scriptLaplace2bie.m       Documentation



  • Different Boundary Integral Formulations for Helmholtz Equation

    This script implements eight different Boundary Integral Formulations for Helmholtz equation and compares the numerical approximation with an exact solution. It features the basic use of geometry and Calderón Calculus operators.
    scriptHelmholtz8bie.m       Documentation

  • Time-harmonic scattering by two PENETRABLE obstacles with different material properties

    A transmission problem for the Helmholtz equation. Two bounded obstacles with different acoustic coefficients interact with a plane acoustic wave. The script features the merging of geometries and the "decoupled" Calderón Calculus operators to deal with several independent obstacles.
    simulationTransmissionProblem.m       Documentation

  • Time-Harmonic Scattering of Elastic Waves by impenetrable obstacles

    A plane pressure wave is scattered by three disk-shaped impenetrable objects. The script features the use of the time-harmonic Navier-Lamé Calderón Calculus.
    simulationFDelasticity.m       Documentation

  • Acousting scattering from obstaces with different boundary conditions

    An acoustic wave is scattered off a sound-hard and a sound-soft obstacle.
    scriptMixedBVP.m       Documentation

  • Transient scattering of a plane wave

    An acoustic plane wave is scattered by a single kite-shaped obstacle. Here, we make use the BDF(2) based Convolution Quadrature for the computation of densities and the potential postprocessing.
    simulationPlanewave.m       Documentation

  • Transient scattering of a cylindrical wave

    A wave due to a point source is scattered by two elliptical obstacles. This script also demonstrates the use of CQ to approximate cylindrical waves.
    simulationCylindricalWave.m       Documentation

  • Convergence studies with RKCQ

    This script generates convergence studies for two different acoustic scattering problems. We couple Radau IIa CQ with deltaBEM and see order three convergence in the potential postprocessing of both examples.
    scriptRKCQComprehensiveTests.m       Documentation

  • Four integral formulations with BDF-CQ

    This script generates convergence studies for four different acoustic scattering problems from an ellipse. We demonstrate the use of deltaBEM and BDF-CQ with two direct and two indirect integral formulations.
    scriptHowToUseBDFCQ.m       Documentation


REMARK. All scripts named scriptSomethingElse.m work with known exact solutions and compute errors of the deltaBEM approximation. (They are designed in a way that it is easy to wrap another script around them for convergence analysis purposes.) Scripts named simulationSomethingElse.m perform experiments on different physical problems.

The research leading to the deltaBEM suite has been partially funded by the National Science Foundation through the grant NSF-DMS 1216356. Numerical simulation and analysis of transient waves in unbounded domains.