C. Huber

Fast BEM computations with the adaptive multilevel fast multipole method

Since the storage requirements of the BEM are proportional to N/sup 2/, only relative small problems can be solved on a PC or a workstation. In this paper we present an adaptive multilevel fast multipole method for the solution of electrostatic problems with the BEM. We will show, that in practice the storage requirements and the computational costs are approximately proportional to N and therefore even large three dimensional problems can be solved on a relative small computer.

A boundary element formulation using higher order curvilinear edge elements

A boundary element method in terms of the field variable is applied to three-dimensional magnetostatic problems. We propose higher order edge elements of quadrilateral shape for the field approximation on curved surfaces. The tangential component of the unknown field variable is interpolated by the edge element. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by TEAM Workshop problem 13 assuming linear material properties.

A new method for the numerical calculation of Cauchy principal value integrals in BEM applied to electromagnetics

A new method for the evaluation of singular boundary element integrals over three-dimensional isoparametric boundary elements of higher order is presented. This new procedure represents a Gaussian quadrature technique using polar coordinates for the calculation of the Gaussian points and the weighting coefficients. This method permits an efficient integration of singular kernels of order O(1/r) on curved surfaces. For a numerical example the proposed integration scheme is compared with other methods (subdivision technique, double exponential formula method, modified Gauss-quadrature) showing high efficiency and accuracy. The actual computation can be easily included in any existing computer code.

Improvement of inverse scattering results by combining TM- and TE-polarized probing waves using an iterative adaptation technique

The inverse problem of reconstructing the starlike boundary /spl Lambda/ of an infinitely conducting, cylindrically shaped obstacle from its far field scattering data is investigated. The equivalent source method (ESM) is applied by defining an auxiliary curve /spl Gamma/ inside the unknown boundary /spl Lambda/ on which electric and magnetic current densities are sought to represent the measured fields. Compared to the case of a sole polarization the exploitation of scattering data of both TE and TM-polarization yields significant improvements on the reconstructed boundary /spl Lambda/.

Inverse electromagnetic medium scattering using a variable metric method

The 2D inverse electromagnetic scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed using scattering data from time-harmonic electromagnetic TM-polarized plane waves. The inverse scattering problem formulated as a nonlinear optimization problem is numerically solved using a variable metric method. This method is a quasi-Newton method and involves exact first-order gradients. Numerical examples are presented to show the efficiency of the algorithm.

A novel approach to the 2D-TM inverse electromagnetic medium scattering problem

The 2D inverse electromagnetic scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed using scattering data from time-harmonic TM-polarized electromagnetic plane waves. A novel method which ensures physically meaningful material properties is proposed to numerically solve this nonlinear optimization problem. Numerical examples illustrate the efficiency of the algorithm.

Application of curvilinear higher order edge elements to scattering problems using the boundary element method

A boundary element method in terms of the field variables is applied to three-dimensional electromagnetic scattering problems. We propose higher order edge elements of quadrilateral shape for the field approximation on curved surfaces. The tangential components of the unknown field variables are interpolated by the edge element. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by the comparison of numerical results with analytical solutions.

Application of a Novel Turbulence Generator to Multiphase Flow Computations

The application of a novel turbulent inflow generator is presented using a 3D Direct Numerical Simulation (DNS) method. For simulation the in-house 3D CFD program Free Surface 3D (FS3D) is applied, which solves the incompressible Navier Stokes Equations for flows with free surfaces using a Volume-of-Fluid (VOF) technique. Three different numerical setups are presented, demonstrating the wide range of application of the new inflow generator. For chosen cases qualitatively comparisons are made between the new and a former implemented turbulence generator. Another more general focus is put on the high influence of turbulent flow fields on simulation outcomes, which justifies the use of computationally intensive inflow generators. Further, information about the performance on the NEC SX-8 platform, where all the simulations were performed, are revealed.

A new approach to the 2D inverse electromagnetic medium scattering problem: reconstruction of anisotropic objects

A new method for reconstructing the material properties of inhomogeneous lossy dielectric biaxial cylindrical objects is presented. The material properties are reconstructed using scattering data from time-harmonic electromagnetic plane waves with the electric field vector perpendicular to the cylindrical object (TE-polarization). The inverse scattering problem formulated as a nonlinear optimization problem is numerically solved using a variable metric method. This method involves exact first-order gradients, Numerical examples illustrate the efficiency of the algorithm.

2D-TE inverse medium scattering: an improved variable metric method

The 2D inverse electromagnetic scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed using scattering data from time-harmonic electromagnetic plane waves with the electric field vector perpendicular to the cylinder axis (TE-polarization). An improved algorithm based on a variable metric method is presented to solve the inverse scattering problem. The new method ensures positive values of the reconstructed quantities. This method involves exact first-order gradients. Numerical examples illustrate the efficiency of the algorithm.