Lihong Feng

A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching

Parametric model order reduction (PMOR) has received a tremendous amount of attention in recent years. Among the first approaches considered, mainly in system and control theory as well as computational electromagnetics and nanoelectronics, are methods based on multi-moment matching. Despite numerous other successful methods, including the reduced-basis method (RBM), other methods based on (rational, matrix, manifold) interpolation, or Kriging techniques, multi-moment matching methods remain a reliable, robust, and flexible method for model reduction of linear parametric systems. Here we propose a numerically stable algorithm for PMOR based on multi-moment matching. Given any number of parameters and any number of moments of the parametric system, the algorithm generates a projection matrix for model reduction by implicit moment matching. The implementation of the method based on a repeated modified Gram-Schmidt-like process renders the method numerically stable. The proposed method is simple yet efficient. Numerical experiments show that the proposed algorithm is very accurate.

Parameter independent model order reduction

Several recently developed model order reduction methods for fast simulation of large-scale dynamical systems with two or more parameters are reviewed. Besides, an alternative approach for linear parameter system model reduction as well as a more efficient method for nonlinear parameter system model reduction are proposed in this paper. Comparison between different methods from theoretical elegancy to complexity of implementation are given. By these methods, a large dimensional system with parameters can be reduced to a smaller dimensional parameter system that can approximate the original large sized system to a certain degree for all the parameters.

Review of model order reduction methods for numerical simulation of nonlinear circuits

In this paper, we reviewed several newly presented nonlinear model order reduction methods, we analyze these methods theoretically and with experiments in detail. We show the problems exists in each method and future work needs to be done. Besides, we propose the two sided projection method which greatly improved the efficiency of the variational equation order reduction method.

Using surrogate models for efficient optimization of simulated moving bed chromatography

Abstract A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages.

System-level Modeling of MEMS

System-level modeling of MEMS microelectromechanical systems comprises integrated approaches to simulate, understand, and optimize the performance of sensors, actuators, and microsystems, taking into account the intricacies of the interplay between mechanical and electrical properties, circuitry, packaging, and design considerations. Thereby, system-level modeling overcomes the limitations inherent to methods that focus only on one of these aspects and do not incorporate their mutual dependencies.

A Fully Adaptive Scheme for Model Order Reduction Based on Moment Matching

A fully adaptive model order reduction scheme based on moment matching is proposed to derive the reduced-order models of linear time-invariant (LTI) systems. According to the given error tolerance, the order of the reduced-order model as well as the expansion points for the transfer function is automatically determined on the fly during the process of model reduction. In this sense, the reduced-order model is automatically obtained without assigning the number of moments and expansion points in a priori, which is a prerequisite for the standard implementation of model reduction based on moment matching. The proposed adaptive scheme is found to be efficient when it is tested on various LTI systems.

Parametric model order reduction accelerated by subspace recycling

Many model order reduction methods for parameterized systems need to construct a projection matrix V which requires computing several moment matrices of the parameterized systems. For computing each moment matrix, the solution of a linear system with multiple right-hand sides is required. Furthermore, the number of linear systems increases with both the number of moment matrices used and the number of parameters in the system. Usually, a considerable number of linear systems has to be solved when the system includes more than two parameters. The standard way of solving these linear systems in case sparse direct solvers are not feasible is to use conventional iterative methods such as GMRES or CG. In this paper, a fast recycling algorithm is applied to solve the whole sequence of linear systems and is shown to be much more efficient than the standard iterative solver GMRES as well as the newly proposed recycling method MKR-GMRES from [10]. As a result, the computation of the reduced-order model can be significantly accelerated.

Recycling BiCGSTAB with an Application to Parametric Model Order Reduction

Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming nonsymmetric matrices for recycling BiCG and recycling BiCGSTAB). As compared with other methods for solving sequences of single linear systems with nonsymmetric matrices (e.g., recycling variants of GMRES), BiCG-based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence and hence do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces. Using our algorithm for a parametr...

Nonlinear model reduction of a continuous fluidized bed crystallizer

This work considers a system of a fluidized bed crystallizer and an ultrasonic attenuator, which separates an enantiomer from a liquid solution. A population balance model of the system shows autonomous oscillations over a wide range of operation conditions. Proper orthogonal decomposition is applied to obtain nonlinear reduced models of low order. An a posteriori error estimator is used to assess the quality of the reduced model during run time.

A Note on Projection Techniques for Model Order Reduction of Bilinear Systems

In this paper we review two recently suggested projection techniques for model order reduction of bilinear systems. The first one is computationally more attractive, but so far it was assumed that this method does not yield a moment‐matching approximation. Here we show that the reduced‐order models computed by both of the two projection techniques match multi‐moments of the bilinear system. This leads to the conclusion that the first projection technique is preferable in applications.