Conform Time Solving of surface structure and cable for Maxwell’s equations – CONFORME

Recently, the team EMC (ElectroMagnetic Compatibility) of the Institute XLIM has developed new thin oblique wire formalism in the FDTD method applied for Maxwell’s equations. This formalism exhibits robustness, flexibility and enable us to model complex topology of cables as demonstrated with the Falcon 7x airplane of DASSAULT AVIATION. Hence, we have shown the ability of our solver (called TEMSI-FD) to handle all the complexity of an airplane with an electromagnetic model projected in a Cartesian grid including all bundles in a common mode model.
The Finite Difference Time Domain method is a versatile approach with a strong ability to easily incorporate different models such as materials, sub-cell, circuit, etc. Applications impact all electromagnetic domains. However, the modelling of curve structure or inclined structure is done by a projection in a Cartesian grid. That is the staircase approximation. It may introduce inaccuracy in the results or shift frequency resonance of structure. Besides, the gap between a cable and the inclined conductor surface is uncertain, the original points of the junction cable – plate no longer correspond with the staircase approximation.
The first objective of the project aim to free oneself from the staircase meshing by using a new approach based on the conform-FDTD method. It consists in cutting the FDTD cells at the boundary of a structure plate. In fact, the FDTD method can be generalized for unstructured meshing, conform meshing or curved meshing. Here, we propose to study and to develop the more efficient approach that enables us to keep the Cartesian grid and all tools existing for this one, and then to locally modify the FDTD cell shapes in the close vicinity of the structure boundary. The meshing problem cannot be neglected. In our project this part is addressed by AXESSIM partner who has a large experience in this domain.
It is well known that cables run along the walls. Therefore, we have need to generalise the thin oblique wire formalism to the conform cells. It will be necessary especially to maintain the properties of the current trace continuity in the conform-grid in order to avoid parasitic oscillation or instability. This property is inherent to the oblique wire formalism.
Finally, The FDTD method presents another underestimated drawback that we propose to correct: the fast variation of the electromagnetic in the vicinity of the metal plate discontinuity is truncated by the numerical scheme of the FDTD method. Even the mesh refinement gives a slow convergence to the reference solution. The consequences are an inaccuracy both in the structure frequency resonance and in the results coming from the modelling of printed conductors as in PCB or from antenna structures.
The different steps of our project are extended over a period of 3 years. At the end, we will aim to propose a global solution to the EMC complex system where uncertainties due to the meshing approximation and to electromagnetic solving will become negligible. In our project we will perform some tests coming from airplane EMC problem to evaluate the relevance of our approach.