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A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
A fundamental and practical introduction to the finite element method, its variants, and their applications in engineering.
Jurassic Stratigraphy - Part 1, Volume Nine of the serial Stratigraphy and Timescales, showcases new advances in the field with a collection of engaging chapters. This volume spans a broad range of stratigraphic disciplines and offers insights into recent developments within the geoscientific research community. As a fully commissioned review, it aims to highlight progress in various areas of stratigraphy, including geochronology, magnetostratigraphy, lithostratigraphy, event-stratigraphy, isotope stratigraphy, astrochronology, climatostratigraphy, seismic stratigraphy, biostratigraphy, ice core chronology, cyclostratigraphy, palaeoceanography, sequence stratigraphy, and more. - Contains contributions from leading authorities in the field - Informs and updates on all the latest developments in the field - Aims to foster and convey progress in stratigraphy, including geochronology, magnetostratigraphy, lithostratigraphy, event-stratigraphy, and more
This book presents a novel approach to the classical scientific discipline of Structural Engineering, which is inspired by numerous current applications from domains of Civil, Mechanical or Aerospace Engineering. The main goal of this book is to help with making the best choice between accuracy and efficiency, when it comes to building the most suitable structural models by practising engineers using modern computational tools available in commercial software products (SAP, FEAP, ANSYS ...) for which we have carried out many developments that have been become the main reference in the field. Any development of this kind is not a mere modification of discrete approximation, but a thorough tre...
The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?
This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmet...
This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to give a detailed and self-contained presentation of these methods, including the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed that have not been covered in any monograph yet: the coupling of finite and boundary elements within the tearing and interconnecting framework including exterior problems, and the case of highly varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book offers a detailed view to an active and up-to-date area of research.
Master the techniques necessary to build and use computational models of porous media fluid flow In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation. Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fun...