1,720,979 research outputs found
Interpolatory Curl-Conforming Vector Bases for Pyramid Cells
No full textWe have recently shown that hierarchical higher-order complete curl-conforming and divergence-conforming bases for pyramids can be obtained by multiplying the lowest-order basis functions by hierarchical scalar multipliers defined by Jacobi polynomials. This paper extends this technique and builds curl-conforming interpolatory bases for pyramids by replacing the hierarchical polynomials with appropriate combinations of interpolatory polynomials of Silvester. Our curl-conforming bases for the pyramid are tangentially continuous with those of adjacent differently shaped cells of the same order and type (i.e., hierarchical or interpolatory) available for years in the literature. This allows numerical electromagnetic solvers using zero-order vector basis functions to be transformed into higher order solvers that work with hybrid meshes simply by adding a few routines to compute the multiplicative polynomials and their first derivatives. Hierarchical bases, including ours of previous papers, are in general more convenient than interpolatory ones for using p-adaptive techniques, while the interpolatory bases such as those shown here are more easily implemented because the recurrence relations of Silvester polynomials are much simpler than those associated with hierarchical multipliers. Numerical results that verify the correctness of our new bases are also reported
Exploring Algebraic Preconditioning of EFIE Matrices Arising from Higher Order Additive Singular Bases
Get PDFCurrently there are no operator-dependent preconditioners (for example of the Calderón type) to handle matrices obtained using high-order singular vector bases. So this letter has a dual purpose. The first is to show that the electric field integral equation (EFIE) discretized by high-order singular bases can be quickly solved iteratively using special general-purpose algebraic preconditioners. The second is to demonstrate that the results obtained with the fast solver have the same accuracy as those obtained using classical direct solution methods. The algebraic preconditioner specifically considered here has been used elsewhere to efficiently solve problems with several million unknowns. Thus, in light of the dual purpose and without loss of generality, we use as benchmarks medium-sized test problems involving singular induced currents because, for these problems, the preconditioned solutions can be compared with those obtained by direct methods, which are notoriously unsuitable for solving very large, ill-conditioned problems. In particular, to demonstrate that our approach correctly models the singular behavior of fields in the near-field region, we report several numerical results for current components induced by plane waves on infinitely thin flat plates. On the edges of these plates the current component parallel to the edges can be unlimited (i.e. going to infinity), while the component normal to the edges must vanish. This behavior is correctly modeled by our singular bases when necessary and is not corrupted by the fast solver, which demonstrates the effectiveness and robustness of the singular bases and the preconditioner used
TE and TM modes in cylindrical metallic structures filled with homogeneous bianisotropic material
No full textModal propagation is studied for metallic circular waveguides, coaxial cables and sectoral waveguides filled with linear bianisotropic material. By representing the material constitutive tensors in cylindrical coordinates, the conditions under which TE and TM modal decoupling occurs are obtained, and second-order differential equations for the longitudinal field components are derived. Though the TE and TM longitudinal field components are expressible in terms of hypergeometric functions, a complete numerical solution scheme is, in general, more convenient. Conventional application of finite elements renders the differential problem numerically equivalent to a generalized eigenvalue matrix problem, whose solution yields the dispersion relation and cutoff frequencies of the waveguides together with the eigenfields expression. The effects one can obtain by varying the various coefficients of the constitutive tensors are illustrated by several numerical result
Hierarchical Divergence-Conforming Vector Bases for Pyramid Cells
Get PDFDivergence-conforming hierarchical vector bases for the pyramid consist of face- and volume-based functions obtained by a simple procedure that uses a new paradigm recently introduced by this author to produce pyramid bases. In order to define the bases' order, the procedure starts by mapping the pyramids into a cube of a new Cartesian space, which we call the grandparent space, where the basis functions and their divergences take on polynomial form. Then we get the face-based functions of zero polynomial order and the volume-based functions of the first order. Functions of arbitrarily high order are obtained by multiplying the vector functions of the lowest order by independent scalar polynomials of higher order. Our face-based functions conform to those of other differently shaped elements to allow the use of hybrid meshes, while the multiplicative construction technique generates right away the volume-based basis functions. The completeness of the bases is demonstrated and all the basis functions we obtain are suitably normalized; their expression involves orthogonal polynomials which are easy to implement and alleviate the loss of linear independence
Bending loss of modes in optical fibers - Pivotal aspects of a computational scheme
No full textTo compute the bending losses of modes in optical fibers, a full-vectorial analysis of the bent fiber is performed. For this analysis, we distinguish between field solutions inside and outside the fiber. For the interior region, a coupled system of ordinary differential equations is integrated numerically from the known regular solutions at the center to the boundary. For the exterior region, modified Bessel functions with large, complex order and argument play an important role. They are the key to an accurate solution and have to be computed to high relative precision (10-13). A program to compute a scaled version of these functions has been written and tested extensively in the parameter range of interest.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Bending loss of modes in optical fibers - Pivotal aspects of a computational scheme
No full textTo compute the bending losses of modes in optical fibers, a full-vectorial analysis of the bent fiber is performed. For this analysis, we distinguish between field solutions inside and outside the fiber. For the interior region, a coupled system of ordinary differential equations is integrated numerically from the known regular solutions at the center to the boundary. For the exterior region, modified Bessel functions with large, complex order and argument play an important role. They are the key to an accurate solution and have to be computed to high relative precision (10-13). A program to compute a scaled version of these functions has been written and tested extensively in the parameter range of interest.</p
A Space-Time Approach for the Time-Domain Simulation in a Rotating Reference Frame
No full textIn the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is important in order to guarantee the synchronization between the electromagnetic field and the accelerated particles. The main interest of this work is in the evaluation of eigenmode sensitivities with respect to geometrical changes using Monte Carlo simulations and stochastic collocation. The choice of an Isogeometric Analysis approach for the spatial discretization allows for an exact handling of the geometrical domains and their deformations, guaranteeing, at the same time, accurate and highly regular solutions
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