W. Rieger

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.

BEM computations using the fast multipole method in combination with higher order elements and the Galerkin method

A new approach to the adaptive multilevel fast multipole method in combination with higher order elements and the Galerkin method is presented. As the computational costs and the memory requirements are approximately proportional to the number of unknowns, very large static problems with complex geometrical configuration can be solved on a small computer.

Fast field computations with the fast multipole method

The application of the fast multipole method reduces the computational costs and the memory requirements of the boundary element method from O(N2) to approximately O(N). In this paper we present that the computational costs can be strongly shortened, when the multipole method is not only used for the solution of the system of linear equations but also for the field computation in arbitrary points.

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.

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.

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.