Velocity Estimation in Mixtures using Tomography

In oil production a lot of water is usually pumped up together with the oil. For many reasons the reduction of the water production is a very important issue. The method presented in this paper is meant to provide a necessary tool for this. Most drilling wells consist of a network of bore holes. Some of them may produce water, others oil or a mixture. At the moment the net flow of all bore holes together is brought to the surface. It is desirable to be able to detect how much water a specific bore hole contributes. If this amount surpasses a critical value one could then consider to close that bore hole. This leads to the question how the composition of the flow in a pipe can be determined in situ. In this paper we analyze how tomography techniques, well-known from medical applications, can be applied in the case of a bore hole. These techniques allow to measure instantaneously the mass distribution over a cross section of the pipe. For velocity estimation, the idea is to detect the mass distributions at two neighbouring cross sections at successive times. Correlating the obtained time series, one might be able to estimate the local velocity profile. The basic idea was already mentioned in literature before, but it was believed that the number of correlations to be evaluated is so huge, that the approach would fail in practice. In this paper we describe the mathematical details of the method and conclude that the number of time consuming calculations is not necessarily a limiting factor. In addition, suggestions are made to facilitate the use of tomography for velocity estimation

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

Snapshot-Based Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

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

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