Accurate and efficient algorithms for boundary element methods in electromagnetic scattering: a tribute to the work of F. Olyslager

Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry's boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from F. Olyslager's scientific endeavors are included in the survey

Recent advances in boundary element methods applied to conducting and dielectric electromagnetic scattering problems

Boundary element methods (BEMs) are an increasingly popular approach to the modeling of electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullu-lated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes the BEM's computational bottleneck. In particular, dedicated FMMs have been conceived for the computation of the electromagnetic scattering at complex metallic and/or dielectric objects in free space and in layered background media. Caldero n preconditioning of the BEM's system matrix lowers the number of matrix-vector products required to reach an accurate solution, and thus the time to reach it. Parallelization distributes the remaining workload over a battery of affordable computational nodes, diminishing the wall-clock computation time. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of some dedicated BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from Prof. Olyslager's scientific endeavors are included in the survey

Efficient computation of TM- and TE-polarized leaky modes in multilayered circular waveguides

In combination with the perfectly matched layer (PML)-paradigm, eigenmode expansion techniques have become increasingly important in the analysis and design of cylindrical and planar waveguides for photonics applications. To achieve high accuracy, these techniques rely on the determination of many modes of the modal spectrum of the waveguide under consideration. In this paper, we focus on the efficient computation of TM- and TE-polarized leaky modes for multilayered cylindrical waveguides. First, quasi-static estimates are derived for the propagation constants of these modes. Second, these estimates are used as a starting point in an advanced Newton iteration scheme after they have been subjected to an adaptive linear error correction. To prove the validity of the computation technique, it is applied to technologically important cases: vertical-cavity surface-emitting lasers and a monomode fiber

A hybrid MLFMM-UTD method for the solution of very large 2-D electromagnetic problems

The multilevel fast multipole method (MLFMM) is combined with the uniform theory of diffraction (UTD) to model two-dimensional (2-D) scattering problems including very large scatterers. The discretization of the very large scatterers is avoided by using ray-based methods. Reflections are accounted for by image source theory, while for diffraction a new MLFMM translation matrix is introduced. The translation matrix elements are derived based on a technique that generalizes the use of UTD for arbitrary source configurations and that efficiently describes the field over extended regions of space. O(n) scaling of the computational time and memory requirements is achieved for relevant structures, such as large antenna arrays in the presence of a wedge. The theory is validated by means of several illustrative numerical examples and is shown to remain accurate for non-line-of-sight (NLoS) scattering problems

An efficient 1-D periodic boundary integral equation technique to analyze radiation onto straight and meandering microstrip lines

A modeling technique to analyze the radiation onto arbitrary 1-D periodic metallizations residing on a microstrip substrate is presented. In particular, straight and meandering lines are being studied. The method is based on a boundary integral equation, more specifically on a mixed potential integral equation (MPIE), that is solved by means of the method of moments. A plane wave excites the microstrip structure, and according to the Floquet-Bloch theorem, the analysis can be restricted to one single unit cell. Thereto, the MPIE must be constructed using the pertinent 1-D periodic layered medium Green's functions. Here, these Green's functions are obtained in closed form by invoking the perfectly matched layer paradigm. The proposed method is applied to assess the radiation onto 1) a semi-infinite plate, 2) a straight microstrip line, and 3) a serpentine delay line. These three types of examples clearly illustrate and validate the method. Also, its efficiency, compared to a previously developed fast microstrip analysis technique, is demonstrated

Perfectly Matched Layer based modelling of layered media: Overview and perspective

Whereas the Perfectly Matched Layer (PML) was originally conceived to serve as a reflectionless absorbing boundary condition, terminating the infinite simulation domain in finite difference or finite element electromagnetic field solvers, unexpected applications of the PML arose by using it to close down open layered waveguide configurations. As a tribute to our former colleague, Prof. F. Olyslager, in this contribution, the PML-paradigm for layered media is explained and an overview of this paradigm's applications is presented. A novel illustrative example, focussing on the modelling of periodic microstrip structures, is also provided

Combining the Ultra-Weak Variational Formulation and the Multilevel Fast Multipole Method

International audienceBecause of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxwell's equations, a volume based method using plane wave basis functions, and an overlapping integral representation of the unknown field to obtain an exact artificial boundary condition on an auxiliary surface that can be very close to the scatterer. Combining the new algorithm with a multilevel fast multipole method we obtain an efficient volume based solver with an exact auxiliary boundary condition, but without the need for singular integrals