Numerical Analysis
Numerical Analysis

Author: Timo Heister

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-03-18

Total Pages: 194

ISBN-13: 3110573326

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Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.

A Tutorial on Elliptic PDE Solvers and Their Parallelization
A Tutorial on Elliptic PDE Solvers and Their Parallelization

Author: Craig C. Douglas

Publisher: SIAM

Published: 2003-01-01

Total Pages: 153

ISBN-13: 9780898718171

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This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.

Finite Elements and Fast Iterative Solvers
Finite Elements and Fast Iterative Solvers

Author: Howard Elman

Publisher: OUP Oxford

Published: 2014-06-19

Total Pages: 495

ISBN-13: 0191667927

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This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Multiphysics Phase-Field Fracture
Multiphysics Phase-Field Fracture

Author: Thomas Wick

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-10-12

Total Pages: 411

ISBN-13: 3110494191

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This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.

Mantle Convection and Surface Expressions
Mantle Convection and Surface Expressions

Author: Hauke Marquardt

Publisher: John Wiley & Sons

Published: 2021-07-07

Total Pages: 32

ISBN-13: 1119528615

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A multidisciplinary perspective on the dynamic processes occurring in Earth's mantle The convective motion of material in Earth's mantle, powered by heat from the deep interior of our planet, drives plate tectonics at the surface, generating earthquakes and volcanic activity. It shapes our familiar surface landscapes, and also stabilizes the oceans and atmosphere on geologic timescales. Mantle Convection and Surface Expressions brings together perspectives from observational geophysics, numerical modelling, geochemistry, and mineral physics to build a holistic picture of the deep Earth. It explores the dynamic processes occurring in the mantle as well as the associated heat and material cycles. Volume highlights include: Perspectives from different scientific disciplines with an emphasis on exploring synergies Current state of the mantle, its physical properties, compositional structure, and dynamic evolution Transport of heat and material through the mantle as constrained by geophysical observations, geochemical data and geodynamic model predictions Surface expressions of mantle dynamics and its control on planetary evolution and habitability The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

Abuse of Dominant Position: New Interpretation, New Enforcement Mechanisms?
Abuse of Dominant Position: New Interpretation, New Enforcement Mechanisms?

Author: Mark-Oliver Mackenrodt

Publisher: Springer Science & Business Media

Published: 2008-07-25

Total Pages: 210

ISBN-13: 3540699651

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As part of its review of competition law that started in the late 1990s, the European Commission proposes to revise its interpretation and application of the Treaty’s prohibition of abuses of dominant positions. Also, it has instigated a debate about the promotion of private enforcement of EC competition law. On the former subject, the Commission published a Discussion Paper in 2005; on the latter, a Green Paper in 2005, followed by a White Paper in 2008. The chapters in this volume critically appraise the Commission’s proposals, including the most recent ones. The authors also highlight the repercussions of the proposed ‘more economic approach’ to abuses of dominant positions on private litigants’ opportunities to bring damages actions in national courts for such abuses.

Spectral, Photon Counting Computed Tomography
Spectral, Photon Counting Computed Tomography

Author: Katsuyuki Taguchi

Publisher: CRC Press

Published: 2020-07-14

Total Pages: 446

ISBN-13: 0429942001

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Spectral, Photon Counting Computed Tomography is a comprehensive cover of the latest developments in the most prevalent imaging modality (x-ray computed tomography (CT)) in its latest incarnation: Spectral, Dual-Energy, and Photon Counting CT. Disadvantages of the conventional single-energy technique used by CT technology are that different materials cannot be distinguished and that the noise is larger. To address these problems, a novel spectral CT concept has been proposed. Spectral Dual-Energy CT (DE-CT) acquires two sets of spectral data, and Spectral Photon Counting CT (PC-CT) detects energy of x-ray photons to reveal additional material information of objects by using novel energy-sensitive, photon-counting detectors. The K-edge imaging may be a gateway for functional or molecular CT. The book covers detectors and electronics, image reconstruction methods, image quality assessments, a simulation tool, nanoparticle contrast agents, and clinical applications for spectral CT.

Software for Exascale Computing - SPPEXA 2016-2019
Software for Exascale Computing - SPPEXA 2016-2019

Author: Hans-Joachim Bungartz

Publisher: Springer Nature

Published: 2020-07-30

Total Pages: 624

ISBN-13: 3030479560

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This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

Mirror Symmetry
Mirror Symmetry

Author: Kentaro Hori

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 954

ISBN-13: 0821829556

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This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.