This paper presents new singular curl- and divergence-conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.

/pdf/singular-higher-order-complete-vector-bases-for-finite-rzlca5c2v9.pdf

Singular higher order complete vector bases for finite methods

A new oblique thin wire formalism based on Holland's approach is proposed in the FDTD method. The principal achievement of this new formalism is to enable us to model a junction correctly between several oblique wires. To this end, an important criterion is proposed: the continuity of the current traces in the grid must be maintained at each node of the Yee cell that contains a part of one or several wires. This condition prevents undamped parasite oscillations on the wire current responses. In addition, our approach offers versatility in its usage. First the extremities of the wire can be placed freely in a Yee cell. Second it operates in lossy medium and finally, the sensitivity of the wire is minimized when inclined or shifted. With regards to this last point, the in-cell inductance of a wire segment is formulated to take account of the segment position and its obliquity in the Yee cell.

New Oblique Thin Wire Formalism in the FDTD Method With Multiwire Junctions

A general-purpose algorithm such as the finite-difference-time-domain technique would be useful for analyzing discontinuity problems in classical waveguides. Its direct application, however, has been rendered difficult by the absence of exact termination conditions appropriate to the close waveguide environment. A rigorous termination condition specific to homogeneous waveguides is introduced. It is based on the convolution properties of the modal characteristic impedance of the accessible modes. This condition is straightforward to implement, as demonstrated by application to the nontrivial problem of a five cavity inductive post filter. Numerical results are compared to existing analytical and experimental data, showing excellent accuracy. >

A new termination condition for the application of FDTD techniques to discontinuity problems in close homogeneous waveguide

A number of different improvements to the analysis by finite-difference time-domain (FDTD) of small structures, such as wires, strips and slots have been proposed in the literature. One of these methods takes account of the fringing fields associated with metal edges and wires by empirically modifying the assigned material parameters in neighboring cells. In this contribution it is shown that, in many cases, it is possible to derive these modified assigned material parameters (MAMPs) analytically. In this form, the approach provides an alternative, and novel, way of incorporating Static Field Solutions into the FDTD method which has advantages of simplicity and robustness over existing techniques. Results are presented for a number of structures including wire transmission lines and a microstrip patch antenna.

/pdf/the-treatment-of-geometrically-small-structures-in-fdtd-by-2kv99dhw12.pdf

The treatment of geometrically small structures in FDTD by the modification of assigned material parameters

The authors present a correction of the finite-difference (FD) methods employing Yee's mesh, improving the accuracy when conductive edge corners are present in the analyzed structure. The algorithm allows the wedge to be arbitrarily located with respect to the grid points and yields significant error reduction.

A conductive wedge in Yee's mesh

When the electromagnetic-field equations are solved in a region with a corner, singularities in the field or in its spatial derivatives will be present at these corners. These singularities cause the load truncation error in a finite-difference approximation of the field equations to be unbounded. In this paper it is shown that failing to take these singularities into account leads to large errors in the finite-difference solution of the time-domain electromagnetic-field equations. A simple method is described to account for these singularities while retaining the simplicity of the finite-difference formulation. Numerical results are given that demonstrate the accuracy obtained when our technique is used.

The Modeling of Singularities in the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations

Finite difference method for the numerical solution of electromagnetic waveguide discontinuity problems is presented. The method of boundary relaxation is applied, using finite difference techniques in the nonuniform section of the waveguide and using a modal representation of the field in the uniform sections of the waveguide. To illustrate the process some two-dimensional diffraction problems in an electromagnetic waveguide with rectangular cross section are solved.

A Finite Dilyerence Method For The Solution Of Electromagnetic Waveguide Discontinuity Problems

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The Modeling of Singularities in the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations

A Finite Dilyerence Method For The Solution Of Electromagnetic Waveguide Discontinuity Problems