Solution of indefinite linear systems using an LQ decomposition for the linear constraints

In this paper, indefinite linear systems with linear constraints are considered. We present a special decomposition that makes use of the LQ decomposition, and retains the constraints in the factors. The resulting decomposition is of a structure similar to that obtained using the Bunch-Kaufman-Parlett algorithm. The decomposition can be used in a direct solution algorithm for indefinite systems, but it can also be used to construct effective preconditioners. Combinations of the latter with conjugate gradient type methods have been demonstrated to be very useful

Micro- and macro-block factorizations for regularized saddle point systems

We present unique and existing micro-block and induced macro-block Crout-based factorizations for matrices from regularized saddle-point problems with semi-positive de¿nite regularization block. For the classical case of saddle-point problems we show that the induced macro-block factorizations mostly reduces to the factorization presented in [24]. The presented factorization can be used as a direct solution algorithm for regularized saddle-point problems as well as it can be used a basis for the construction of preconditioners

Simulation of electromagnetic descriptor models using projectors

Electromagnetic descriptor models are models which lead to differential algebraic equations (DAEs). Some of these models mostly arise from electric circuit and power networks. The most frequently used modeling technique in the electric network design is the modified nodal analysis (MNA) which leads to differential algebraic equations in descriptor form. DAEs are known to be very difficult to solve numerically due to the sensitivity of their solutions to perturbations. We use the tractability index to measure this sensitivity since it can be computed numerically. Simulation of DAEs is a very difficult task especially for those with index greater than one. To solve higher-index DAEs, one needs to use multistep methods such as Backward difference formulas (BDFs). In this paper, we present an easier method of solving DAEs numerically using special projectors. This is done by first splitting the DAE system into differential and algebraic parts. We then use the existing numerical integration methods to approximate the solutions of the differential part and the solutions of the algebraic parts are computed explicitly. The desired solution of the DAE system is obtained by taking the linear combination of the solutions of the differential and algebraic parts. Our method is robust and efficient, and can be used on both small and very large systems

Evaluation and comparison of FEM and BEM for extraction of homogeneous substrates

In the design and fabrication of micro-electronic circuits, it is necessary to simulate and predict many kinds of effects, such as substrate crosstalk, interconnect delays and others. In order to simulate and predict properly these effects, accurate and efficient substrate modeling methods are required. Substrate resistance extraction involves finding a resistance network between ports correctly describing the behaviour of the substrate. In this report we consider the problem of resistance extraction of a substrate with a homogeneous doping profile. We solve the problem by means of two discretization methods, namely the finite element method (FEM) and the boundary element method (BEM) and discuss the advantages and disadvantages of each of these methods. We particularly addresses the problem of achieving grid-independent results and characterize the cases in which one technique is better than the other

De wiskundige leest in bedrijf

Wil Schilders zal bij veel ITW-lezers bekend zijn als voormalig redactielid van ITW Nieuws en bestuurslid van ITW. Sinds vier jaar slaat hij als buitengewoon hoogleraar aan de Technische Universieit Eindhoven een brug tussen zijn praktische werkzaamheden als numeriek wiskundige bij Philips Research en de theorie op de universiteit. Op 24 oktober van het vorige jaar hield Wil zijn intreerede, die hier enigszins ingekort is weergegeven

Stability and passivity of the super node algorithm for EM modeling of IC's

The super node algorithm performs model order reduction based on physical principles. Although the algorithm provides us with compact models, its stability and passivity have not thoroughly been studied yet. The loss of passivity is a serious problem because simulations of the reduced network may encounter artificial behavior which render the simulations useless. In this paper we explain why the algorithm delivers not passive reduced order models and present a way in order to overcome this problem

Efficient simulation of power MOS transistors

In this report we present a few industrial problems related to modeling of MOS transistors. We suggest an efficient algorithm for computing output current at the top ports of power MOS transistors for given voltage excitations. The suggested algorithm exploits the connection between the resistor and transistor networks and benefits from the sparsity of the conductance matrix. We also investigate a large resistor network which is a part of the power MOS transistor model and find out which existing reduction methods for resistor networks deliver significant reduction in the amount of resistors

Simulation of three mutually coupled oscillators

In a practical multipurpose high frequency circuit, different oscillators are not completely isolated from each other. Instead, they interact with the environment, or with other oscillator. The interference between different oscillators may lead to generation of undesired signals. Therefore, the effect of oscillators on each other must be considered in the circuit design. As oscillators have nonlinear behavior, simulation of some of them which are coupled to each other needs more attention. In this report we present a mathematical model for three mutually coupled voltage controlled oscillators and solve it by a numerical method. The approach is illustrated by numerical experiments on realistic designs