Mathematical software

About: Mathematical software is a research topic. Over the lifetime, 676 publications have been published within this topic receiving 13541 citations.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Abstract: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

Abstract: From the Publisher: Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included. Audience This book is appropriate for senior undergraduate or beginning graduate students with a computational focus and practicing engineers and scientists who want to learn about computational differential equations. A beginning course in numerical analysis is needed, and a beginning course in ordinary differential equations would be helpful. About the Authors Uri M. Ascher is a Professor in the Department of Computer Science at the University of British Columbia, Vancouver. He is also Director of the Institute of Applied Mathematics there. Linda R. Petzold is a Professor in the Departments of Mechanical and Environmental Engineering and Computer Science at the University of California at Santa Barbara. She is also Director of the Computational Science and Engineering Program there.

An overview of the Trilinos project

Abstract: The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software.Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking.Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates high-quality software engineering practices that are increasingly required from simulation software.

Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology

Abstract: Summary: We present a Systems Biology Toolbox for the widely used general purpose mathematical software MATLAB. The toolbox offers systems biologists an open and extensible environment, in which to explore ideas, prototype and share new algorithms, and build applications for the analysis and simulation of biological and biochemical systems. Additionally it is well suited for educational purposes. The toolbox supports the Systems Biology Markup Language (SBML) by providing an interface for import and export of SBML models. In this way the toolbox connects nicely to other SBML-enabled modelling packages. Models are represented in an internal model format and can be described either by entering ordinary differential equations or, more intuitively, by entering biochemical reaction equations. The toolbox contains a large number of analysis methods, such as deterministic and stochastic simulation, parameter estimation, network identification, parameter sensitivity analysis and bifurcation analysis. Availability: The Systems Biology Toolbox for MATLAB is open source and freely available from http://www.sbtoolbox.org. The website also contains a tutorial, extensive documentation and examples. Contact: henning@fcc.chalmers.se

Solving Linear Systems on Vector and: Shared Memory Computers

Abstract: Vector and parallel processing overview of current high-performance computers implementation details and overhead performance - analysis, modeling and measurements building blocks in linear algebra direct solution of sparse linear systems iterative solution of sparse linear systems. Appendices: acquiring mathematical software information on various high-performance computers level 1,2, and 3 BLAS quick reference operation counts for various BLAS and decompositions.