Comparing Attic Method with the Existing Techniques for Linear Programming

The aim of the work is to compare the performances of the novel Attic method for linear programming (Buzzi-Ferraris, 2011) with the existing algorithms of the simplex and interior point families. Potentialities of the new method are demonstrated and quantified on the linear programming problem of thermal cracking refinery

Performance Assessment of Existing Methodologies for Chemical Process Dynamic Simulation

The chemical engineer has nowadays a wide choice of tools, numerical libraries, and programming languages to perform computations. Actually, it is possible to use several well established commercial packages, implement dedicated solvers into specific programming languages, or use existing numerical libraries. Also, it is possible to combine these possibilities to get either superior performances or more robustness, according to the problem features through the so-called mixed-language approach, which is increasingly spreading in the scientific communities. Since there is no full clarity on their benefits in handling numerical problems and their performances have not been yet compared in the literature, this paper is aimed at analyzing efficiency and robustness of some of the most widespread methodologies adopted for numerical computations: the conventional methods, the implementation of numerical libraries, the mixed-language, and the commercial tools. Specifically, the common case of differential systems is selected as comparison field

Improving the selection of interior points for one-dimensional finite element methods

A new strategy to improve the selection of interior points inside an element of finite element methods is proposed. The novelty is to use the element boundary information in selecting the internal points. The new strategy is compared to the classical strategy in several examples and the main benefits are qualitatively and quantitatively explained

Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems

Engineers and other applied scientists are frequently faced with models of complex systems for which no rigorous mathematical solution can be calculated. To predict and calculate the behaviour of such systems, numerical approximations are frequently used, either based on measurements of real life systems or on the behaviour of simpler models. This is essential work for example for the process engineer implementing simulation, control and optimization of chemical processes for design and operational purposes. This fourth in a suite of five practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them. The volume focuses on differential and differential-algebraic systems, providing numerous real-life industrial case studies to illustrate this complex topic. It describes the methods, innovative techniques and strategies that are all implemented in a freely available toolbox called BzzMath, which is developed and maintained by the authors and provides up-to-date software tools for all the methods described in the book. Numerous examples, sample codes, programs and applications are taken from a wide range of scientific and engineering fields, such as chemical engineering, electrical engineering, physics, medicine, and environmental science. As a result, engineers and scientists learn how to optimize processes even before entering the laboratory. With additional online material including the latest version of BzzMath Library, installation tutorial, all examples and sample codes used in the book and a host of further examples

BzzMath: Library Overview and Recent Advances in Numerical Methods

This paper gives an overview of the numerical methods included in BzzMath library. The library is written in C++, exploits the features of object-oriented programming, and is free for non-commercial applications at www.chem.polimi.it/homes/gbuzzi