A series of transverse electromagnetic transmission cells (TEM cells) developed at the National Bureau of Standards (NBS) is three-dimensional analyzed using a mixed discretization based on both of constant and linear elements in a boundary element method (mixed BEM). Mixed BEM presented here is generalized in order to be usable in two and three dimensions. Conductor surface of TEM cell models is discretized using non-uniform elements so that the flux distribution can be approximated more accurately in the less number of elements. The distributed characteristic impedance, which is important to design the cell, in the main line section is evaluated through the flux induced in the center conductor. The calculated results are in good agreement with those in two dimensions in spite of the small number of elements. As a result, it is proved that three-dimensional cell models are effectively and accurately solved by using mixed BEM and non-uniform elements together. The present work plays a preliminary part in an analysis of more realistic NBS cell models taken into account a tapered section. In future, therefore, we will be able perform a reliable analysis of TEM cells using mixed BEM and non-uniform elements.

A new boundary integral formulation is presented in order to solve a general Laplace-Poisson's equation, which is one of the basic equations of semiconductor devices. As this formulation is based on Green's second identity or Gauss' divergence theorem, no conventional volume integral is needed, regardless of arbitrary distributions of space charge. The potentials and electric field intensities at interface nodes put between a Laplace and a Poisson domain are analytically calculated, because interface nodes are treated as same as internal points. It is effective and powerful to device analysis of such a junction-gate field effect transistor with interfaces movable according to operation bias conditions. On the basis of simple numerical experiments, the present method is applied to a simplified device models. It is shown that device analysis can be easily obtained for a more small discretized model. In consequence, numerical results also demonstrate the effectiveness of this approach.

We have presented a formulation of convective diffusion equations based on the method of sub-regions and the boundary element method, especially in three dimensions, in order to analyze very long and narrow convection-diffusion fields which we frequently encounter. In this formulation, we have introduced mixed-type boundary elements, which have more advantages in boundary element computation, and the weighted conservation law of mass in each sub-boundary model so as to be conservative in itself. In addition we have proposed a coupling technique at interface boundaries in order to equalize the number of equations to that of interface unknowns. As a result, it is found that the present method will give more accurate and stable solutions and also have more merits even on the basis of the method of sub-regions, and so is suitable and applicable particularly to a three-dimensional problem. The present formulation for mixed elements is also usable not only to convective diffusion problems, but also to Laplace and Helmholtz-type equations in steady and unsteady state.

A term rewriting system is said to be rpoterminating if it's termination is proved with the recursive path ordering method. The direct sum R1M2 of term rewriting systems R1 and R2 is rpo-terminating iff both R1 and R2 are so.

Boundary-element solutions of an unsteady-state convective diffusion equation are investigated using a mixed boundary-element method with both constant and linear elements. Transient numerical solutions at each discrete time are compared with exact solutions so that the dependence of their relative errors on time and space are demonstrated. It is shown that the present method is applicable to an electromagnetic field analysis governed by the partial differential equation of convective-diffusion type as in a steady state problem.

Numerical characteristics of mixed element solutions are studied in comparison with constant and linear elements'. It is shown that mixed elements give accurate solutions as similar to the previous investigations and also the system of equations is better-conditioned than other elements'.

A steady-state convective diffusion problem is analyzed using a mixed boundary element method with both of constant and linear elements in three dimensions. The usefulness of the present method is shown as compared with a boundary element method with only constant elements.