His current research focus is on the design and analysis of accurate multiscale adaptive discretization techniques mixed finite elements, finite volumes, finite differences and efficient linear and nonlinear iterative solvers domain decomposition, multigrid, Newton-Krylov methods for massively parallel simulations of coupled multiphase porous media and surface flows. Other areas of research interest include estimation of uncertainty in stochastic systems and mathematical and computational modeling for biomedical applications.
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Accuracy and precision
Numerical Analysis and Scientific Computing The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces. Layton's Research Professor William J. Neilan's Research Assoc. Unfortunately, developing accurate and reliable scientific software is notoriously difficult.
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This book investigates some of the difficulties related to scientific computing and provides insight into how to overcome them and obtain dependable results. The tools to assess existing scientific applications are described, and a variety of techniques that can improve the accuracy and reliability of newly developed applications is discussed.
Accuracy and Reliability in Scientific Computing can be considered a handbook for improving the quality of scientific computing. It will help computer scientists address the problems that affect software in general as well as the particular challenges of numerical computation: approximations occurring at all levels, continuous functions replaced by discretized versions, infinite processes replaced by finite ones, and real numbers replaced by finite precision numbers. Divided into three parts, it starts by illustrating some of the difficulties in producing robust and reliable scientific software.
Well-known cases of failure are reviewed and the what and why of numerical computations are considered. The second section describes diagnostic tools that can be used to assess the accuracy and reliability of existing scientific applications.
In the last section, the authors describe a variety of techniques that can be employed to improve the accuracy and reliability of newly developed scientific applications. This book has an accompanying website, with codes, links, color versions of some illustrations, and additional material. Vouk Bibliography Index. Write Your Own Review Only registered users can write reviews.
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Boisvert, Ronald Cools and Bo Einarsson-- 3. Approximating integrals, estimating errors and giving the wrong solution for a deceptively easy problem Ronald Cools-- 4. An introduction to the quality of computed solutions Sven Hammarling-- 5. Diagnostic Tools: 6. Tools for the verification of approximate solutions to differential equations Wayne H.
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Enright-- Part III. Technology for Improving Accuracy and Reliability: 8. General methods for implementing reliable and correct software Bo Einarsson-- 9.
C-XSC - A C++ Class Library for Extended Scientific Computing: Main Page
The use and implementation of interval data types G. William Walster-- Computer-assisted proofs and self-validating methods Siegfried M. Rump-- Hardware assisted algorithms Craig C. Douglas and Hans Petter Langtangen-- Issues in accurate and reliable use of parallel computing in numerical programs William D. Gropp-- Software reliability engineering of numerical systems Mladen A. Vouk-- Bibliography-- Index.