Fast time- and frequency-domain finite-element methods for electromagnetic analysis

Fast electromagnetic analysis in time and frequency domain is of critical importance to the design of integrated circuits (IC) and other advanced engineering products and systems. Many IC structures constitute a very large scale problem in modeling and simulation, the size of which also continuously grows with the advancement of the processing technology. This results in numerical problems beyond the reach of existing most powerful computational resources. Different from many other engineering problems, the structure of most ICs is special in the sense that its geometry is of Manhattan type and its dielectrics are layered. Hence, it is important to develop structure-aware algorithms that take advantage of the structure specialties to speed up the computation. In addition, among existing time-domain methods, explicit methods can avoid solving a matrix equation. However, their time step is traditionally restricted by the space step for ensuring the stability of a time-domain simulation. Therefore, making explicit time-domain methods unconditionally stable is important to accelerate the computation. In addition to time-domain methods, frequency-domain methods have suffered from an indefinite system that makes an iterative solution difficult to converge fast. The first contribution of this work is a fast time-domain finite-element algorithm for the analysis and design of very large-scale on-chip circuits. The structure specialty of on-chip circuits such as Manhattan geometry and layered permittivity is preserved in the proposed algorithm. As a result, the large-scale matrix solution encountered in the 3-D circuit analysis is turned into a simple scaling of the solution of a small 1-D matrix, which can be obtained in linear (optimal) complexity with negligible cost. Furthermore, the time step size is not sacrificed, and the total number of time steps to be simulated is also significantly reduced, thus achieving a total cost reduction in CPU time. The second contribution is a new method for making an explicit time-domain finite-element method (TDFEM) unconditionally stable for general electromagnetic analysis. In this method, for a given time step, we find the unstable modes that are the root cause of instability, and deduct them directly from the system matrix resulting from a TDFEM based analysis. As a result, an explicit TDFEM simulation is made stable for an arbitrarily large time step irrespective of the space step. The third contribution is a new method for full-wave applications from low to very high frequencies in a TDFEM based on matrix exponential. In this method, we directly deduct the eigenmodes having large eigenvalues from the system matrix, thus achieving a significantly increased time step in the matrix exponential based TDFEM. The fourth contribution is a new method for transforming the indefinite system matrix of a frequency-domain FEM to a symmetric positive definite one. We deduct non-positive definite component directly from the system matrix resulting from a frequency-domain FEM-based analysis. The resulting new representation of the finite-element operator ensures an iterative solution to converge in a small number of iterations. We then add back the non-positive definite component to synthesize the original solution with negligible cost

Automated Construction of Equivalent Electrical Circuit Models for Electromagnetic Components and Systems

The description of electromagnetic components and systems by electrical circuit models is indispensable for a wide range of applications: In the field of EMC, electrical circuit models are ideally suited for the detection of EMC coupling paths, which are very difficult to track for 3D geometries. In the field of numerical optimization techniques, electrical circuit models offer short simulation times and allow the coupling of the electromagnetic domain to other physical domains. In the field of power electronics, electrical circuit models describe energy dissipation due to parasitic electromagnetic interactions. The construction of an equivalent electrical circuit model is in general cumbersome and less formalized than a description in terms of electromagnetic fields. No general and reliable technique for the automated construction of equivalent electrical circuit models exists. The aim of this thesis is the development of a technique that allows a fully automated construction of equivalent electrical circuit models from 3D geometry information. Instead of constructing the circuit directly from geometry data, our approach consists of reducing a field-theoretical model to an equivalent electrical circuit model. In this way, we exploit the generality of the field-theoretical approach, which can be applied for a wide range of geometries using state-of-the-art simulation techniques. The electromagnetic effects having the largest impact in the frequency range of interest are then used for the construction of the electrical circuit model. The circuit elements can be seen as condensed representations of these field-theoretical processes. The reduction process allows a very direct assessment of the accuracy of the electrical circuit model

Parameterized macromodeling of passive and active dynamical systems

L'abstract è presente nell'allegato / the abstract is in the attachmen

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed