BzzMath library

The book describes numerical methods, high-performance algorithms, specific devices, and innovative techniques and strategies, all of which are implemented in a well-established numerical library the BzzMath library, developed by Prof. Guido Buzzi-Ferraris at the Politecnico di Milano and downloadable from http // www.chem.polimi.it/homes/gbuzzi. 

The BzzMath library can be used in any scientific field in which there is a need to solve numerical problems. Its primary use is in engineering, but it can also be used in statistics, medicine, economics, physics, management, environmental sciences, biosciences, and so on. 

This book deals with the solution of differential and differential-algebraic systems. Analogously to the aforementioned companion books, it proposes a series of robust and high-performance algorithms implemented in the BzzMath library to tackle these multifaceted and notoriously difficult issues. 

Definite integrals are solved in Chapter 1. Existing methods and novel alternatives are proposed, implemented in the BzzMath library, and adopted to solve some well-established literature-based tests. Parallel computations are also introduced. 

Ordinary differential equation systems are broached in Chapter 2. Conditioning, stability, and stiffness are described in detail by giving specific information on how to handle them whenever they arise. The BzzMath library also implements a wide set of algorithms to solve classical problems and chemical/process engineering problems. 

Differential-algebraic systems are explored in greater depth in Chapter 4. Special algorithms to handle this family of problems are described and implemented in the BzzMath library. Classes to handle the sparsity and structure of such systems typical of chemical engineering are also described. 

Caveat, risk of making sneaky mistakes, and spread errors. Description of some BzzMath library classes or functions. Definitions and properties. 

The style adopted in the BzzMath library is described hereinafter ... 

New Types of Object This is similar to the function identifier, but in order to distinguish it from functions, it is useful to add a prefix. All the classes belonging to the BzzMath library are characterized by the prefix Bzz. 

A third important style-based decision concerned the criterion to pass variables of a function either by value or by reference. In the BzzMath library, we adopt the following criteria ... 

BzzMath library, release 7.0, was designed for a Microsoft Windows environment... 

Moreover, FORTRAN users can either adopt all the classes belonging to the BzzMath library using opportune interfaces or directly use pieces of C++ codes in FORTRAN, by means of the so-called mixed language (see Appendix A of Vol. 2, Buzzi-Ferraris and Manenti, 2010b). 

The previous version of the BzzMath library (release 6.0) is updated until May 20, 2011 and will not undergo any further development. Moreover, the new release 7.0 has been extended quite significantly, particularly for classes dedicated to optimization and exploitation of openMP directives and to differential, differential-algebraic, and boundary value problems. 

Windows users must follow these general tasks to use the BzzMath library on a computer ... 

When at least an object of BzzMath library is used, it is necessary to select the appropriate compiler by choosing one of the following alternatives ... 

Moreover, whenever even one BzzMath library object is used, it is always necessary to introduce the statement... 

In the BzzMath library, the BzzIntegralGaussLobatto class uses the algorithms of Gauss-Lobatto with 5 and 7 internal points. Points and weights are reported in Tables 1.3 and 1.4. 

In the BzzMath library, the Bzz Integra IGauss class adopts this philosophy. 

In the BzzMath library, the Bzz Integra IGaussLobatto class adopts a different strategy to the ones used to solve the same problem with the classes Bzz Integra 1 and Bzz Integra IGaussBF. 

In the BzzMath library, all the classes for the calculation of definite integrals automatically exploit the openMP directives when the compiler allows it... 

Classes Based on Runge-Kutta Algorithms in the BzzMath Library 61... 

The following classes for the solution of nonstiff problems, which are based on Runge-Kutta explicit algorithms, are implemented in the BzzMath library ... 

In the BzzMath library, classes based on implicit and diagonally implicit Runge-Kutta methods are not implemented to handle ODE problems with initial conditions. 

The latter alternative was adopted in release 6 of BzzMath library and is now considered obsolete since the new way adopts a more efficient linear system solver. 

In the BzzMath library, these algorithms have not been implemented in dedicated classes. 

In the BzzMath library, the BzzOdeStiff and BzzOdeSparseStlff classes contain several functions that make it easy to move from a system to another one of different nature. 

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