TIME-DOMAIN ELECTROMAGNETIC-FIELD COMPUTATION WITH FINITE-DIFFERENCE METHODS

The solution of Maxwell's equations in the time domain has now been in use for almost three decades and has had great success in many differ ent applications. The main attraction of the time domain approach, ori ginating in a paper of Yee (1966), is its simplicity. Compared with co nventional frequency domain methods it takes only marginal effort to w rite a computer code for solving a simple scattering problem. However, when applying the time domain approach in a general way to arbitraril y complex problems, many seemingly simple additional problems add up. We describe a theoretical framework for solving Maxwell's equations in integral form, resulting in a set of matrix equations, each of which is the discrete analogue to one of the original Maxwell equations. Thi s approach is called Finite Integration Theory and was first developed for frequency domain problems starting about two decades ago. The key point in this formulation is that it can be applied to static, harmon ic and time dependent fields, mainly because it is nothing but a compu ter-compatible reformulation of Maxwell's equations in integral form. When specialized to time domain fields, the method actually contains Y ee's algorithm as a subset. Further additions include lossy materials and fields of moving charges, even including fully relativistic analys is. For many practical problems the pure time domain algorithm is not sufficient. For instance a waveguide transition analysis requires the knowledge of the incoming and outgoing mode patterns for proper excita tion in the time domain. This is a typical example where both frequenc y and time domain analysis are essential and only the combination yiel ds the successful result. Typical engineers may wonder why at all one should apply time domain analysis to basically monochromatic field pro blems. The answer is simple: it is much faster, needs less computer me mory, is more general and typically more accurate. Speed-up factors of over 200 have been reached for realistic problems in filter and waveg uide design. The small core space requirement makes time domain method s applicable on desktop computers using millions of cells, and six unk nowns per cell - a dimension that has not yet been reached by frequenc y domain approaches. This enormous amount of mesh cells is absolutely necessary when complex structures or structures with spatial dimension s of many wavelengths are to be studied. Our personal record so far is a waveguide problem in which we used 72,000,000 unknowns.