3,031 research outputs found
Eigenmodes of index-modulated layers with lateral PMLs
Maxwell equations are solved in a layer comprising a finite number of
homogeneous isotropic dielectric regions ended by anisotropic perfectly matched
layers (PMLs). The boundary-value problem is solved and the dispersion relation
inside the PML is derived. The general expression of the eigenvalues equation
for an arbitrary number of regions in each layer is obtained, and both
polarization modes are considered. The modal functions of a single layer ended
by PMLs are found, and their orthogonality relation is derived. The present
method is useful to simulate scattering problems from dielectric objects as
well as propagation in planar slab waveguides. Its potential to deal with more
complex problems such as the scattering from an object with arbitrary cross
section in open space using the multilayer modal method is briefly discussed.Comment: 17 pages, 4 figure
Analyzing the wave number dependency of the convergence rate of a multigrid preconditioned Krylov method for the Helmholtz equation with an absorbing layer
This paper analyzes the Krylov convergence rate of a Helmholtz problem
preconditioned with Multigrid. The multigrid method is applied to the Helmholtz
problem formulated on a complex contour and uses GMRES as a smoother substitute
at each level. A one-dimensional model is analyzed both in a continuous and
discrete way. It is shown that the Krylov convergence rate of the continuous
problem is independent of the wave number. The discrete problem, however, can
deviate significantly from this bound due to a pitchfork in the spectrum. It is
further shown in numerical experiments that the convergence rate of the Krylov
method approaches the continuous bound as the grid distance gets small
Multilayer metamaterial absorbers inspired by perfectly matched layers
We derive periodic multilayer absorbers with effective uniaxial properties
similar to perfectly matched layers (PML). This approximate representation of
PML is based on the effective medium theory and we call it an effective medium
PML (EM-PML). We compare the spatial reflection spectrum of the layered
absorbers to that of a PML material and demonstrate that after neglecting gain
and magnetic properties, the absorber remains functional. This opens a route to
create electromagnetic absorbers for real and not only numerical applications
and as an example we introduce a layered absorber for the wavelength of
~m made of SiO and NaCl. We also show that similar cylindrical
core-shell nanostructures derived from flat multilayers also exhibit very good
absorptive and reflective properties despite the different geometry
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
On the indefinite Helmholtz equation: complex stretched absorbing boundary layers, iterative analysis, and preconditioning
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz
problems that are formulated with absorbing boundary layers based on complex
coordinate stretching. The preconditioner problem is a Helmholtz problem where
not only the coordinates in the absorbing layer have an imaginary part, but
also the coordinates in the interior region. This results into a preconditioner
problem that is invertible with a multigrid cycle. We give a numerical analysis
based on the eigenvalues and evaluate the performance with several numerical
experiments. The method is an alternative to the complex shifted Laplacian and
it gives a comparable performance for the studied model problems
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
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
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