Multi Scale And High Contrast Pde

Author : Habib Ammari,Yves Capdeboscq,Hyeonbae Kang
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 40,6 Mb
Release : 2012
Category : Computers
ISBN : 9780821869291

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Multi-Scale and High-Contrast PDE by Habib Ammari,Yves Capdeboscq,Hyeonbae Kang Pdf

Contains the proceedings of the conference Multi-Scale and High-Contrast PDE: From Modelling, to Mathematical Analysis, to Inversion, held June, 2011. The volume focuses on recent progress towards a complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. It also includes contributions on the inverse problem, both on its analysis and on numerical reconstructions.

Author : Habib Ammari, Yves Capdeboscq,Hyeonbae Kang, Imbo Sim
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 51,9 Mb
Release : 2016-03-23
Category : Differential equations, Partial
ISBN : 9781470419233

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Imaging, Multi-scale and High Contrast Partial Differential Equations by Habib Ammari, Yves Capdeboscq,Hyeonbae Kang, Imbo Sim Pdf

This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.

Author : Habib Ammari,Yves Capdeboscq,Hyeonbae Kang
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 45,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 9780821891018

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Multi-scale and High-contrast PDE by Habib Ammari,Yves Capdeboscq,Hyeonbae Kang Pdf

Author : Clemens Pechstein
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 53,9 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9783642235887

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Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems by Clemens Pechstein Pdf

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.

Author : Eric Chung,Yalchin Efendiev,Thomas Y. Hou
Publisher : Springer Nature
Page : 499 pages
File Size : 48,8 Mb
Release : 2023-06-07
Category : Mathematics
ISBN : 9783031204098

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Multiscale Model Reduction by Eric Chung,Yalchin Efendiev,Thomas Y. Hou Pdf

This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.

Author : Patrizia Pucci
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 40,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821898611

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Recent Trends in Nonlinear Partial Differential Equations by Patrizia Pucci Pdf

This book is the second of two volumes that contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Patrizia Pucci on the field of nonlinear analysis and partial differential equations. In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume. The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolution problems in nonlinear partial differential equations.

Author : James B. Serrin,Enzo L. Mitidieri,Vicenţiu D. Rădulescu
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 55,8 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9780821887363

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Recent Trends in Nonlinear Partial Differential Equations I by James B. Serrin,Enzo L. Mitidieri,Vicenţiu D. Rădulescu Pdf

This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer
Page : 863 pages
File Size : 48,9 Mb
Release : 2013-08-19
Category : Computers
ISBN : 9783642400209

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Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.

Author : Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang
Publisher : American Mathematical Soc.
Page : 509 pages
File Size : 44,8 Mb
Release : 2018-10-15
Category : Photonics
ISBN : 9781470448004

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Mathematical and Computational Methods in Photonics and Phononics by Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang Pdf

The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.

Author : Bogdan D. Suceavă,Alfonso Carriazo,Yun Myung Oh,Joeri Van der Veken
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 47,8 Mb
Release : 2016-09-14
Category : Differential geometry -- Local differential geometry -- Local submanifolds
ISBN : 9781470422981

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Recent Advances in the Geometry of Submanifolds by Bogdan D. Suceavă,Alfonso Carriazo,Yun Myung Oh,Joeri Van der Veken Pdf

This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25–26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963–2013), held from March 14–15, 2015, at Michigan State University, East Lansing, Ml. The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and contact manifolds. Some of these use techniques in classical differential geometry, while others use methods from ordinary differential equations, geometric analysis, or geometric PDEs. By brainstorming on the fundamental problems and exploring a large variety of questions studied in submanifold geometry, the editors hope to provide mathematicians with a working tool, not just a collection of individual contributions. This volume is dedicated to the memory of Franki Dillen, whose work in submanifold theory attracted the attention of and inspired many geometers.

Author : Joseph Auslander,Aimee Johnson,Cesar E. Silva
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 55,5 Mb
Release : 2016-11-29
Category : Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Non-Archimedean Fatou and Julia sets
ISBN : 9781470422998

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Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby by Joseph Auslander,Aimee Johnson,Cesar E. Silva Pdf

This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.

Author : Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 48,7 Mb
Release : 2016-10-25
Category : Differential geometry -- Classical differential geometry -- Classical differential geometry
ISBN : 9781470422059

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Real and Complex Singularities by Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas Pdf

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

Author : Catherine Bénéteau:,Alberto A. Condori,Constanze Liaw,William T. Ross,Alan A. Sola
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 47,9 Mb
Release : 2016-12-22
Category : Analytic functions
ISBN : 9781470423056

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Catherine Beneteau, Alberto A. Condori, Constanze Liaw, William T. Ross, and Alan A. Sola by Catherine Bénéteau:,Alberto A. Condori,Constanze Liaw,William T. Ross,Alan A. Sola Pdf

This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.

Author : Luis M. Pardo,Jose Luis Montaña
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 52,7 Mb
Release : 2014-11-12
Category : Computers
ISBN : 9780821891506

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Recent Advances in Real Complexity and Computation by Luis M. Pardo,Jose Luis Montaña Pdf

This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.

Author : Robert S. Doran,Efton Park
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 43,9 Mb
Release : 2016-07-28
Category : Operator algebras
ISBN : 9781470419486

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Operator Algebras and Their Applications by Robert S. Doran,Efton Park Pdf

his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.