Large Scale FD-TD, A PSCI project

Note:This project has now been concluded. It has been succeeded by the GEMS project.

Project goal

The goal of this PSCI-project is to develop methods for numerical simulation of electromagnetic phenomena in complex systems, for instance an aircraft. Within the time frame of this project a 3D Finite-Difference Time-Domain (FD-TD) method will be implemented on the IBM SP-2, Strindberg, at the Center for Parallel Computers (PDC) at KTH. In parallel, new alternative types of time domain methods, such as finite volume or finite element approaches on unstructured grids, will be considered for the future. Small geometrical details and fast field variations, compared with the exciting wavelength, can be resolved by an unstructured grid. The memory size and speed of todays computers makes it necessary for the traditional FD-TD method to introduce subcell models to model thin structures (thin compared with the overall resolution). Examples of such structures are wires, gaps, coatings, and semiconducting walls. The project will also study such subcell models as well as developing new ones. Particularly it will study the possibility to use Wavelet homogenization as a general technique to produce subcell models.


Electromagnetic fields are governed by the Maxwell equations, a first order hyperbolic system of PDE:s. These can not be solved analytically except for a few simple geometries, such as spheres and cylinders. For more complex structures one has to rely on numerical methods, i.e. Computational Electromagnetics (CEM), and/or experiments.

There is a wide range of applications for CEM. Some of the more important are:

The methods developed in this project are general and will have impact on all the CEM areas mentioned above. They are well suited for a modern industrial computational environment. There automatic geometrical input and meshing from a CAD description of the object and advanced data visualization are necessary both from a feasibility and cost effectiveness point of view.

The main interests of the industrial participants Ericsson Space Avionics, FOA and SP are EMC, RCS and antenna analysis. Regarding EMC there are several threats that an aircraft has to be verified against where some examples are lightning, radio and radar fields, electrostatic discharge, fields emitted by the electronic equipment and directed high power microwave weapons. All these threats can, if the electronic equipment of the aircraft is not sufficiently protected, disturb or damage the electronic equipment causing EMC problems which would jeopardize flight safety. A well known example is the prohibition of using cellular phones during take off and landing. The position of the antennas on an aircraft has to be optimized so that the antenna-antenna coupling is minimized and the desired coverage is achieved. Minimizing the RCS will make an aircraft harder to detect by radar.

The Yee Method

In 1966 an FD-TD method for the Maxwell equations was introduced by K. S. Yee. This method uses a Leapfrog scheme on staggered Cartesian grids. Calculating the electromagnetic field outside an object usually leads to an open problem, i.e. an infinite computational domain. Therefore, some artificial boundary conditions (ABC) is needed to truncate the computational domain. These boundary conditions must be such that they minimize the reflection of waves trying to leave the computational domain. One common way is to use the so called Mur boundary condition. These are the electromagnetic version of the Engquist-Majda boundary condition. A more modern approach is to use the Perfectly Matched Layer (PML) introduced by Berenger in 1994. Incident plane waves can be generated by Huygens' surfaces.

The Yee method has several advantages. It is robust, fast and simple to understand. Furthermore it is possible to achieve the response in a chosen frequency band in one calculation by using a pulse excitation. This can not be achieved with a frequency domain method. On the other hand the Cartesian grid conforms badly to the real geometry, thus introducing so called stair stepping errors. Furthermore, the absence of a general subgridding scheme means that structures smaller than the resolution have to be treated by subcell models. These models are limited to relatively simple geometrical structures such as wires, gaps, layers, etc. In spite of these disadvantages we believe that the Yee method will remain in use for many years. Therefore the subcell models have to be improved and new subcell models must be developed. Some of the areas in need of (better) subcell models are:

The project will also consider the possibility to use wavelet homogenization as a general subgridding scheme.

The project is also interested in many other topics related to time-domain methods. Some of these are related to the Yee method, but others are entirely new methods. Such topics are:

High Frequency Methods

When using FD-TD methods one has to resolve the waves with at least 10 points per wavelength and sometimes with as many as 30 points per wavelength. Memory size and execution times increases with frequency and with the ``electrical size'' of the object. With ``electrical size'' we mean the quotient between the physical size and the wavelength. FD-TD methods can not be used for arbitrarily large objects. One must instead use high frequency methods such as Geometrical Theory of Diffraction (GTD). The CEM program within PSCI is also interested in looking at such methods.

Persons involved

The following persons was involved in the project during its later stages:


Nearest activities

This project have now been concluded. It has been succeeded by the GEMS project. The GEMS project began 1998-01-01. These two projects ran in parallel for a while before it was decided to conclude the Large Scale FD-TD project.

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