Implicit local refinement for evanescent layers combined with classical FDTD

In this letter we hybridize the well-known FDTD method with the fully implicit method of [1]. In effect, this enables local space refinement without necessitating a smaller time step. In particular, this is very useful for thin layers of highly conducting material or to treat complex media, such as plasma, allowing evanescent waves

Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DIN) operator is a useful tool in the characterization of interconnect structures. in. combination with the Method of Moments; it con. be used for the calculation, of the per-unit length transmission line parameters of multi-conductor Or to directly determine the interval impedance of conductors. This paper presents a new and fast calculation method for the DIN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples

Time-domain formulation of cold plasma based on mass-lumped finite elements

Recent advances in FDTD simulations of simple dielectrics have opened the possibility of various forms of local refinement [1]. These possibilities are based on writing FDTD as a special case of a finite element technique. We have shown [3] that these techniques can be extended to Body-Of-Revolution (BOR) FDTD which is well-suited for modelling toroidal cavities. Further extending this technique to the time-domain modelling of plasmas presents difficulties: The classical "Whitney" basis-functions (and their analogues in toroidal geometries) are insufficiently smooth to be used as "testing" functions the time-domain constitutive equations of cold plasma [2]. In this paper, we present a set of basis-functions that can be used to write time-domain cold plasma as a mass lumped finite element scheme

Construction of the dirichlet to neumann boundary operator for triangles and applications in the analysis of polygonal conductors

This paper introduces a fast and accurate method to investigate the broadband inductive and resistive behavior of conductors with a nonrectangular cross section. The presented iterative combined waveguide mode (ICWM) algorithm leads to an expansion of the longitudinal electric field inside a triangle using a combination of parallel-plate waveguide modes in three directions, each perpendicular to one of the triangle sides. This expansion is used to calculate the triangle's Dirichlet to Neumann boundary operator. Subsequently, any polygonal conductor can be modeled as a combination of triangles. The method is especially useful to investigate current crowding effects near sharp conductor corners. In a number of numerical examples, the accuracy of the ICWM algorithm is investigated, and the method is applied to some polygonal conductor configurations

Eigenmode-based capacitance calculations with applications in passivation layer design

The design of high-speed metallic interconnects such as microstrips requires the correct characterization of both the conductors and the surrounding dielectric environment, in order to accurately predict their propagation characteristics. A fast boundary integral equation approach is obtained by modeling all materials as equivalent surface charge densities in free space. The capacitive behavior of a finite dielectric environment can then be determined by means of a transformation matrix, relating these charge densities to the boundary value of the electric potential. In this paper, a new calculation method is presented for the important case that the dielectric environment is composed of homogeneous rectangles. The method, based on a surface charge expansion in terms of the Robin eigenfunctions of the considered rectangles, is not only more efficient than traditional methods, but is also more accurate, as shown in some numerical experiments. As an application, the design and behavior of a microstrip passivation layer is treated in some detail

High precision evaluation of the selfpatch integral for linear basis functions on flat triangles

The application of integral equations for the frequency domain analysis of scattering problems requires the accurate evaluation of interaction integrals. Generally speaking, the most critical integral is the selfpatch. However, due to the non-smoothness of the Green function, this integral is also the toughest to calculate numerically. In previous work, the source and test integrals have been determined analytically for the 1/R singularity, i.e., the static kernel. In this work we extend this result to the terms of the form R-n, for all n is an element of {0, 1, 2, 3, 4} that occur in the Taylor expansion of the Green function. Numerical testing shows that truncating the Taylor series beyond n = 4 yields a highly accurate result for lambda/7 and lambda/10 discretizations. These analytical formulas are also very robust when applied to highly irregular triangles