# Numerical Electromagnetics and Field Calculation

Unfortunately most problems of practical use can not be solved analytically, because their geometry is too complex. In these cases, one has to resort to numerical methods. Fortunately there exists a proven uniqueness theorem which states that any solution which can be found for such a system, is the solution of the system, irrespective of the method which was used to find it. This is the basis for the field of Numerical Electromagnetics.

There are two categories of Numerical Methods to solve electromagnetic systems. There are the methods in the time domain and the methods in the frequency, or Fourier domain. Both methods have their merits and a combination of both methods often yields the best results. The most famous methods in the frequency domain are the **Method of Moments (MoM)** and the **Finite Element Method (FEM)**.

The **MoM** is especially well suited for Problems which have their boundaries in infinity, like the computation of an antenna radiation pattern in open space. Not so well suited it is for problems which include dielectric parts within the structure.

The** FEM **is very efficient for Computations of systems within closed spaces, like wave guides or a microwave oven. This method also deals very good with different matters. It is often not the method of choice for radiation problems, like an antenna in open space, because an infinite space can not be partitioned into small volume elements. In such cases, the volume has to be bounded artificially and a near to far field converter has to be used to compute the radiation patterns.

The **Finite Difference Time Domain (FDTD)** method is the classical method in time domain. The volume of interest is partitioned into small volume elements or cells. Each cell has its material constants, which define the matter within the cell. The field equations are solved directly for each cell in time steps. Hence one gets the evolution of the fields in time as a result of this method. The advantages and disadvantages are similar to the FEM.

Both method categories exist in similar form in computational fluid dynamics.

More and more, hybrid solvers enter the stage. hybrid solvers combine different methods, thus combining the advantages of both methods. So it is possible to combine FEM and MoM. The volume within the structure is computed by FEM, while the interaction between structure elements which are far apart, are computed by using the MoM, as well as the boundaries.

We have the necessary tools and the necessary experience to perform all types of calculations and we offer this service to companies in the business of electrical engineering which want to out-source this task cost efficiently in order to be able to concentrate on their core-competency. Since a calculation of this type is a very complex procedure, details have to be discussed before the time requirements and costs can be estimated. **Please contact us for further details.**

## Publications

### First author

Oswald, T.H.,W. Macher, G.Fischer, and H. Rucker (2004), |

Oswald, T.H. (2005), |

Oswald, T.H., W. Macher, G. Fischer, H. Rucker, J. Bougeret, M. Kaiser, and K. Goetz (2005), |

Oswald, T.H., W. Macher, G.Fischer, and H. Rucker (2005), |

Oswald, T.H., H. Rucker, W. Macher, G.Fischer, and U. Taubenschuss (2005), |

Oswald, T.H., W. Macher, G. Fischer, H. O. Rucker, U. Taubenschuss, J. L. Bougeret, M. L. Kaiser, K. Goetz (2005), |

Oswald, T.H., H. Rucker, W. Macher, G.Fischer, and U. Taubenschuss (2006), |

Oswald, T.H., W. Macher, G. Fischer, H. O. Rucker, U. Taubenschuss, J. L. Bougeret, A. Lecacheux, M. L. Kaiser, K. Goetz (2006), |

Oswald, T.H., H.O. Rucker, W. Macher (2006), |

Oswald, T.H., H.O. Rucker, W. Macher (2006), |

Oswald, T.H., W. Macher, G. Fischer, H.O. Rucker, J.-L. Bougeret, M.L. Kaiser, K. Goetz (2006), Planetary Radio Emissions VI; 01/2006. |

Oswald, T.H., H. Rucker, W. Macher, and the SOLAR ORBITER RPW team (2007), |

Oswald, T.H., W. Macher, H. O. Rucker (2007), |

Oswald, T.H., W. Macher, H. O. Rucker (2007), |

Oswald, T.H., W. Macher, H. Rucker, G. Fischer, U. Taubenschuss, J. Bougeret, A. Lecacheux, M. Kaiser, and K. Goetz (2009), |

Oswald, T.H. (2010), |

Oswald, T.H., H. O. Rucker, W. Macher, G. Fischer, M. Sampl and (submitted 2010) |

Oswald, T.H., |

Oswald, T.H., M. Sampl, H. O. Rucker, D. Plettemeier, M. Maksimovic (2012), |

Oswald, T.H., M. Sampl, H.O. Rucker, W. Macher, G. Fischer, M. Maksimovic (2011), |

### Co-author

Bale, S., R. Ullrich, K. Goetz, B. Cecconi, M. Dekkali, W. Macher, R. E. Manning, T. H. Oswald, and M. Pulupa (2007), |

Bougeret, J.L., K. Goetz, M. L. Kaiser, S. D. Bale, P. J. Kellogg, M. Maksimovic, N. Monge, S. J. Monson, P. L. Astier, S. Davy, M. Dekkali, J. J. Hinze, R. E. Manning, E. Aguilar-Rodriguez, X. Bonnin, C. Briand, I. H. Cairns, C. A. Cattell, B. Cecconi, J. Eastwood, R. E. Ergun, J. Fainberg, S. Hoang, K. E. J. Huttunen, S. Krucker, A. Lecacheux, R. J. MacDowall, W. Macher, A. Mangeney, C. A. Meetre, X. Moussas, Q. N. Nguyen, T. H. Oswald, M. Pulupa, M. J. Reiner, P. A. Robinson, H. Rucker, C. Salem, O. Santolik, J. M. Silvis, R. Ullrich, P. Zarka, I. Zouganelis (2008), |

Khodachenko, M., T. H. Oswald, W. Macher, H. O. Rucker (2006), |

Macher, W., T.H. Oswald, H. Rucker, and G. Fischer (2006), |

Macher, W., T.H. Oswald, G. Fischer, and H. Rucker (2007), |

Macher, W., and T.H. Oswald (2011), |

Panchenko, M., H. O. Rucker, W. Macher, B. Cecconi, T. H. Oswald, G. Fischer (2010), |

Panchenko, M., W. Macher, H.O. Rucker, G. Fischer, T. H. Oswald, B. Cecconi, M. Maksimovic (2014), |

Plettemeier, D., H. O. Rucker, T.H. Oswald, M. Sampl, G. Fischer, W. Macher, M. Maksimovic (2009), |

Rucker, H.O., W. Macher, G. Fischer, T.H. Oswald, J.-L. Bougeret, M. Kaiser, and K. Goetz (2005), |

Rucker, H.O., T.H. Oswald, W. Macher (2006), |

Rucker, H.O., T.H. Oswald, W. Macher, and the SOLAR ORBITER RPW team (2007) , |

Rucker, H.O., T.H. Oswald, M. Sampl, W. Macher, D. Plettemeier (2009), |

Rucker, H.O., M. Sampl, M. Panchenko, T. Oswald, D. Plettemeier, M. Maksimovic, G. Fischer (2010), |

Rucker, H.O., M. Sampl, M. Panchenko, G. Fischer, W. Macher, D. Plettemeier, T.H. Oswald (2010), |

Rucker, H.O., M. Sampl, M. Panchenko, T.H. Oswald, D. Plettemeier, M. Maksimovic, W. Macher (2011), |

Sampl, M., W. Macher, C. Gruber, T.H. Oswald, H.O. Rucker, and M. Mogilevsky (2009), |

Sampl, M., W. Macher, C. Gruber, T.H. Oswald, H.O. Rucker (2009), |

Sampl, M., W. Macher, Ch. Gruber, T.H. Oswald, H.O. Rucker (2009), |

M. Sampl, T. H. Oswald, H. O. Rucker, D. Plettemeier, M. Maksimovic, W. Macher (2010), |

Sampl, M., W. Macher, C. Gruber, T.H. Oswald, H.O. Rucker (2010), |

Sampl, M., W. Macher, C. Gruber, T.H. Oswald, H.O. Rucker (2010), |

Sampl, M., H.O. Rucker, T.H. Oswald, D. Plettemeier, M. Maksimovic, W. Macher (2011), |

Sampl, M., T.H. Oswald, H.O. Rucker, R Karlsson, D. Plettemeier, W. S. Kurth (2011), |

Sampl, M., T.H. Oswald, H.O. Rucker, G. Fischer, D. Plettemeier, W.S. Kurth, W. Macher (2011), |

Sampl, M., T.H. Oswald, M. Kapper, D. Plettemeier, H.O. Rucker, W.S. Kurth (2012), |

Sampl, M., T.H. Oswald, H.O. Rucker (2012), |

Sampl, M., W. Macher, C. Gruber, T. Oswald, H.O. Rucker, M. Mogilevsky (2012), |