A 3-D numerical field solver based on the finite-volume time-domain method

Numerical electromagnetic (EM) simulations are an important tool for the design, anal¬ ysis and optimization of electronic devices; simulations assist an engineer to minimize time and cost necessary to reach the maturity phase of a device. Thereby, the goal of the computational electromagnetics (CEM) tool is to guarantee accurate simulation results as well as an easy and faultless operation. Nowadays, many simulation tools based on different numerical techniques are commercially available. Nevertheless there are still more promising numerical methods to be explored in the frame of EM. In order to ful¬ fill the requirements imposed on the CEM tool, the employed numerical method has to provide the following characteristics: The basic requirement in order to achieve accurate simulation results is the precise modeling of the investigated problem. Not less impor¬ tant however is the error introduced and the stability provided by the approximation of the Maxwell's equations in the numerical method. In this scope, the Finite-Volume Time-Domain (FVTD) method shows very promis¬ ing prospects: On the one hand, the method exploits an unstructured, inhomogeneous polyhedral mesh capable of accurate approximation of complex geometries. Curved and oblique surfaces can be modeled with a high accuracy, and small details in close prox¬ imity to a large overall structure as well as high dielectric contrasts can be modeled without difficulties. On the other hand, the chosen FVTD formulation is second order accurate both in time and in space, and the explicit time domain (TD) formulation of the method allows for a comfortable treatment of inter-cell relations such as boundary conditions, excitation schemes and ports. The FVTD method takes its origin in computational fluid dynamics (CFD) and is applied to the solution of the Maxwell's equations since the beginning of the 1990s. Many implementations of the method exist, all of which show different characteristics and advantages. Nevertheless, FVTD is still in its infancy for the application in CEM, and only a few groups worldwide perform investigations of the method. In this thesis, the implementation of the FVTD method and the application of FVTD to the analysis of complex, real-world EM problems are presented. Relevant aspects in order to yield a practical CEM tool are discussed and verified: Among other things, the definition of a source plane with a built-in absorbing boundary condition (ABC) and a novel field-based scheme for the extraction of a generalized scattering matrix are proposed. In the beginning of this thesis, the hyperbolic Maxwell's equations are written in a conservative-law form and the explicit update equation used in FVTD is derived. Special attention is paid to the flux-splitting procedure which separates the flux through a cell face into an incoming and an outgoing part. The flux splitting is one of the main cha¬ racteristics of the FVTD method: As demonstrated in the continuative parts of the thesis, the separated fluxes are exploited for important numerical procedures such as for example the extraction of scattering parameters.