Gustavo Migoni

Linearly Implicit Quantization-Based Integration Methods for Stiff Ordinary Differential Equations

Abstract In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization-based integration (QBI), i.e., replacing the time discretization by state quantization, the proposed algorithms generalize the idea of linearly implicit algorithms. Also, the implementation of the new algorithms in a DEVS simulation tool is discussed. The efficiency of these new methods is verified by comparing their performance in the simulation of two benchmark problems with that of other numerical stiff ODE solvers. In particular, the advantages of these new algorithms for the simulation of electronic circuits are demonstrated.

Quantization-based new integration methods for stiff ordinary differential equations

In this paper we introduce new classes of numerical ordinary differential equation (ODE) solvers that base their internal discretization method on state quantization instead of time slicing. These solvers have been coined quantized state system (QSS) simulators. The primary result of the research described in this article is a first-order accurate QSS-based stiff system solver, called the backward QSS (BQSS). The numerical properties of this new algorithm are discussed, and it is shown that this algorithm exhibits properties that make it a potentially attractive alternative to the classical numerical ODE solvers. Some simulation examples illustrate the advantages of this method. As a collateral result, a first-order accurate QSS-based solver designed for solving marginally stable systems is briefly outlined as well. This new method, called the centered QSS (CQSS), is successfully applied to a challenging benchmark problem describing a high-order system that is simultaneously stiff and marginally stable. However, the primary emphasis of this article is on the BQSS method, that is, on a stiff system solver based on state quantization.

Quantization-based simulation of switched mode power supplies

In this article we study the performance of quantized state system algorithms in the simulation of switched mode power supplies. Under realistic modeling assumptions, these models are stiff and exhibit frequent discontinuities, making them difficult to simulate with classic solvers. However, there are linearly implicit quantized state system methods that can efficiently handle these types of systems, providing faster and more accurate results. In order to corroborate these features, we first built the models corresponding to the different topologies of switched mode power supplies, and then analyzed the resulting equation structures in order to establish whether they can be efficiently simulated by linearly implicit quantized state system algorithms. Finally, we compared the simulation performance of linearly implicit quantized state systems with the widely used DASSL solver. The results showed that the linearly implicit quantized state systems were 3–200 times faster and noticeably more accurate than the differential algebraic system solver.

Integración por Cuantificación de Sistemas Stiff

Este articulo presenta un nuevo metodo de integracion numerica de ecuaciones diferenciales ordinarias basado en la cuantificacion de las variables de estado. Utilizando conceptos de integracion implicita, el nuevo metodo denominado BQSS (Backward Quantized State Systems) permite integrar sistemas stiff de manera eficiente. Siendo el primer metodo de cuantificacion para sistemas stiff, BQSS es en si un metodo explicito, por lo que la contribucion es importante en el contexto general de los metodos de integracion numerica. Ademas de presentar el metodo, el articulo estudia las principales propiedades teoricas del mismo, aborda aspectos practicos de la implementacion del algoritmo y presenta resultados de simulacion sobre dos sistemas stiff.

Improving Linearly Implicit Quantized State System Methods

In this article we propose a modification to Linearly Implicit Quantized State System Methods (LIQSS), a family of methods for solving stiff Ordinary Differential Equations (ODEs) that replace the classic time discretization by the quantization of the state variables. LIQSS methods were designed to efficiently simulate stiff systems, but they only work when the system has a particular structure. The proposed modification overcomes this limitation, allowing the algorithms to efficiently simulate stiff systems with more general structures. Besides describing the new methods and their algorithmic descriptions, the article analyzes the algorithms performance in the simulation of some complex systems.

Improving a linearly implicit quantized state system method

In this article we propose a modification to the first order Linearly Implicit Quantized State System Method (LIQSS1), an algorithm for continuous system simulation that replaces the classic time discretization by the quantization of the state variables. LIQSS was designed to efficiently simulate stiff systems but it only works when the system has a particular structure. The proposed modification overcomes this limitation allowing the algorithm to efficiently simulate stiff systems with more general structures. Besides describing the new method and its software implementation, the article analyzes the algorithm performance in the simulation of a complex power electronic converter.