Download or read book PETSc for Partial Differential Equations Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Download or read book Advanced Topics in Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2012-09-22 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Download or read book Stochastic Partial Differential Equations for Computer Vision with Uncertain Data written by Tobias Preusser and published by Springer Nature. This book was released on 2022-06-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: In image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be—and more and more frequently are—taken into account for further processing. This error and uncertainty propagation must be done for every processing step such that the final result comes with a reliable precision estimate. The goal of this book is to introduce the reader to the recent advances from the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). It presents a concept with which error propagation and sensitivity analysis can be formulated with a set of basic operations. The approach discussed in this book has the potential for application in all areas of quantitative computer vision, image processing, and image analysis. In particular, it might help medical imaging finally become a scientific discipline that is characterized by the classical paradigms of observation, measurement, and error awareness. This book is comprised of eight chapters. After an introduction to the goals of the book (Chapter 1), we present a brief review of PDEs and their numerical treatment (Chapter 2), PDE-based image processing (Chapter 3), and the numerics of stochastic PDEs (Chapter 4). We then proceed to define the concept of stochastic images (Chapter 5), describe how to accomplish image processing and computer vision with stochastic images (Chapter 6), and demonstrate the use of these principles for accomplishing sensitivity analysis (Chapter 7). Chapter 8 concludes the book and highlights new research topics for the future.

Download or read book Spectral and High Order Methods for Partial Differential Equations written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

Download or read book Computational Methods in Stochastic Dynamics written by Manolis Papadrakakis and published by Springer Science & Business Media. This book was released on 2012-10-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology. This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and represent some of the most recent developments in this field. The book consists of 21 chapters which can be grouped into several thematic topics including dynamic analysis of stochastic systems, reliability-based design, structural control and health monitoring, model updating, system identification, wave propagation in random media, seismic fragility analysis and damage assessment. This edited book is primarily intended for researchers and post-graduate students who are familiar with the fundamentals and wish to study or to advance the state of the art on a particular topic in the field of computational stochastic structural dynamics. Nevertheless, practicing engineers could benefit as well from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures.

Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

Download or read book ICIAM 07 written by Rolf Jeltsch and published by European Mathematical Society. This book was released on 2009 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organization of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The Sixth ICIAM Congress was held in Zurich, Switzerland, July 16-20, 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congress, the appreciations of the ICIAM Prize winners' achievements, and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers in their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives, and open problems. Topics embrace analysis of and numerical methods for: linear and nonlinear partial differential equations multiscale modeling nonlinear problems involving integral operators controllability and observability asymptotic solutions of Hamilton-Jacobi equations contact problems in solid mechanics topology optimization of structures dissipation inequalities in systems theory greedy algorithms sampling in function space order-value optimization parabolic partial differential equations and deterministic games Moreover, particular applications involve risk in financial markets, radar imaging, brain dynamics, and complex geometric optics applied to acoustics and electromagnetics.

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Following are 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.

Download or read book Frontiers in PDE Constrained Optimization written by Harbir Antil and published by Springer. This book was released on 2018-10-12 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Download or read book Recent Advances in Computational Engineering written by Michael Schäfer and published by Springer. This book was released on 2018-08-21 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the proceedings of the 4th International Conference on Computational Engineering (ICCE 2017), held in Darmstadt, Germany on September 28-29, 2017. The conference is intended to provide an interdisciplinary meeting place for researchers and practitioners working on computational methods in all disciplines of engineering, applied mathematics and computer science. The aims of the conference are to discuss the state of the art in this challenging field, exchange experiences, develop promising perspectives for future research and initiate further cooperation. Computational Engineering is a modern and multidisciplinary science for computer-based modeling, simulation, analysis, and optimization of complex engineering applications and natural phenomena. The book contains an overview of selected approaches from numerics and optimization of Partial Differential Equations as well as uncertainty quantification techniques, typically in multiphysics environments. Where possible, application cases from engineering are integrated. The book will be of interest to researchers and practitioners of Computational Engineering, Applied Mathematics, Engineering Sciences and Computer Science.

Download or read book Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications written by Massimiliano Vasile and published by Springer Nature. This book was released on 2022-01-27 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2020 International Conference on Uncertainty Quantification & Optimization gathered together internationally renowned researchers in the fields of optimization and uncertainty quantification. The resulting proceedings cover all related aspects of computational uncertainty management and optimization, with particular emphasis on aerospace engineering problems. The book contributions are organized under four major themes: Applications of Uncertainty in Aerospace & Engineering Imprecise Probability, Theory and Applications Robust and Reliability-Based Design Optimisation in Aerospace Engineering Uncertainty Quantification, Identification and Calibration in Aerospace Models This proceedings volume is useful across disciplines, as it brings the expertise of theoretical and application researchers together in a unified framework.

Download or read book Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Download or read book Probabilistic and Stochastic Methods in Analysis with Applications written by J.S. Byrnes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: