Wha Wil Schilders

Introduction to Model Order Reduction

In this first section we present a high level discussion on computational science, and the need for compact models of phenomena observed in nature and industry. We argue that much more complex problems can be addressed by making use of current computing technology and advanced algorithms, but that there is a need for model order reduction in order to cope with even more complex problems. We also go into somewhat more detail about the question as to what model order reduction is.

Simulation of Mutually Coupled Oscillators Using Nonlinear Phase Macromodels

Design of integrated RF circuits requires detailed insight in the behavior of the used components. Unintended coupling and perturbation effects need to be accounted for before production, but full simulation of these effects can be expensive or infeasible. In this paper, we present a method to build nonlinear phase macromodels of voltage-controlled oscillators. These models can be used to accurately predict the behavior of individual and mutually coupled oscillators under perturbation at a lower cost than full circuit simulations. The approach is illustrated by numerical experiments with realistic designs.

SparseRC: Sparsity Preserving Model Reduction for RC Circuits With Many Terminals

A novel model order reduction (MOR) method, SparseRC, for multiterminal RC circuits is proposed. Specifically tailored to systems with many terminals, SparseRC employs graph-partitioning and fill-in reducing orderings to improve sparsity during model reduction, while maintaining accuracy via moment matching. The reduced models are easily converted to their circuit representation. These contain much fewer nodes and circuit elements than otherwise obtained with conventional MOR techniques, allowing faster simulations at little accuracy loss.

Index-aware model order reduction for differential-algebraic equations

We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity.

Efficient Calculation of Uncertainty Quantification

We consider Uncertainty Quantification (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coefficients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more efficient for similar accuracy as obtained by SG. In SC the coefficients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to efficiently perform this sequence of deterministic simulations within SC.

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.

Modeling of passive-active device interactions

This paper deals with the modeling of the injection of electromagnetic fields into the active devices/circuits originating from integrated passive devices. It is shown that the impact of induced electromagnetic fields can be included as modified terminal conditions of the nearby devices.

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.

Reduction of large resistor networks

Electro Static Discharge (ESD) analysis is of vital importance during the design of large-scale integrated circuits, since it gives insight in how well the interconnect can handle unintended peak charges. Due to the increasing amount of interconnect and metal layers, ESD analysis may become very time consuming or even unfeasible. We propose an algorithm for the reduction of large resistor networks, that typically arise during ESD, to much smaller equivalent networks. Experiments show reduction and speed-ups up to a factor 10.

Robust Periodic Steady State Analysis of Autonomous Oscillators Based on Generalized Eigenvalues

In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector with the time derivative of the solution. It is dynamically updated within each Newton–Raphson iteration. The method is applied to an analytic benchmark problem and to an LC oscillator. It provides better convergence properties than when using the popular phase-shift condition. It also does not need additional information about the solution. The method can also easily be implemented within the Harmonic Balance framework.