Gianluca Iaccarino's Books

Computational Modeling by Case Study

All Models Are Uncertain

By: Zachary del Rosario,Gianluca Iaccarino

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Computational Modeling by Case Study

All Models Are Uncertain

By: Zachary del Rosario,Gianluca Iaccarino

Mathematical models power the modern world; they allow us to design safe buildings, investigate changes to the climate, and study the transmission of diseases through a population. However, all models are uncertain: building contractors deviate from the planned design, humans impact the climate unpredictably, and diseases mutate and change. Modern advances in mathematics and statistics provide us with techniques to understand and quantify these sources of uncertainty, allowing us to predict and design with confidence. This book presents a comprehensive treatment of uncertainty: its conceptual nature, techniques to quantify uncertainty, and numerous examples to illustrate sound approaches. Several case studies are discussed in detail to demonstrate an end-to-end treatment of scientific modeling under uncertainty, including framing the problem, building and assessing a model, and answering meaningful questions. The book illustrates a computational approach with the Python package Grama, presenting fully reproducible examples that students and practitioners can quickly adapt to their own problems.

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849

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1036402924

ISBN 13

9781036402921

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

By: Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström

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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

By: Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

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Page Count

217

Publisher

Springer

Published Date

ISBN 10

3319107143

ISBN 13

9783319107141

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

By: Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström

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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

By: Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström

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Solve jigsaw puzzle

Age

Page Count

217

Publisher

Springer

Published Date

ISBN 10

3319107143

ISBN 13

9783319107141

Computational Modeling by Case Study

All Models Are Uncertain

By: Zachary del Rosario,Gianluca Iaccarino

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Computational Modeling by Case Study

All Models Are Uncertain

By: Zachary del Rosario,Gianluca Iaccarino

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

849

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1036402924

ISBN 13

9781036402921

Book's by Gianluca Iaccarino

Computational Modeling by Case Study

Computational Modeling by Case Study

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Computational Modeling by Case Study

Computational Modeling by Case Study

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