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Author: Silvia Bertoluzza Publisher: Springer ISBN: 3642240798 Category : Mathematics Languages : en Pages : 324
Book Description
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author: Silvia Bertoluzza Publisher: Springer ISBN: 3642240798 Category : Mathematics Languages : en Pages : 324
Book Description
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author: Silvia Bertoluzza Publisher: Springer Science & Business Media ISBN: 364224078X Category : Mathematics Languages : en Pages : 324
Book Description
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author: Silvia Bertoluzza Publisher: Springer ISBN: 9783642240805 Category : Mathematics Languages : en Pages : 314
Book Description
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author: Publisher: World Scientific ISBN: Category : Languages : en Pages : 1131
Author: Siegfried Müller Publisher: Springer Science & Business Media ISBN: 9783540443254 Category : Mathematics Languages : en Pages : 214
Book Description
During the last decade enormous progress has been achieved in the field of computational fluid dynamics. This became possible by the development of robust and high-order accurate numerical algorithms as well as the construc tion of enhanced computer hardware, e. g. , parallel and vector architectures, workstation clusters. All these improvements allow the numerical simulation of real world problems arising for instance in automotive and aviation indus try. Nowadays numerical simulations may be considered as an indispensable tool in the design of engineering devices complementing or avoiding expen sive experiments. In order to obtain qualitatively as well as quantitatively reliable results the complexity of the applications continuously increases due to the demand of resolving more details of the real world configuration as well as taking better physical models into account, e. g. , turbulence, real gas or aeroelasticity. Although the speed and memory of computer hardware are currently doubled approximately every 18 months according to Moore's law, this will not be sufficient to cope with the increasing complexity required by uniform discretizations. The future task will be to optimize the utilization of the available re sources. Therefore new numerical algorithms have to be developed with a computational complexity that can be termed nearly optimal in the sense that storage and computational expense remain proportional to the "inher ent complexity" (a term that will be made clearer later) problem. This leads to adaptive concepts which correspond in a natural way to unstructured grids.
Author: Publisher: Elsevier ISBN: 0443294496 Category : Science Languages : en Pages : 446
Book Description
Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. - Covers multi-scale modeling - Includes updates on data-driven modeling - Presents the latest information on large deformations of multi-scale materials
Author: Rajendra Bhatia Publisher: World Scientific ISBN: 9814462934 Category : Mathematics Languages : en Pages : 4137
Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Author: Alexandre Ern Publisher: Springer Nature ISBN: 3030569233 Category : Mathematics Languages : en Pages : 491
Book Description
This book is the second 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 II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Author: Peter Benner Publisher: Springer ISBN: 3319152602 Category : Mathematics Languages : en Pages : 635
Book Description
This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Author: Silvia Bertoluzza
Author: Silvia Bertoluzza
Author: Silvia Bertoluzza
Author: Silvia Bertoluzza
Author: 
Author: Siegfried Müller
Author: 
Author: Rajendra Bhatia
Author: Alexandre Ern
Author: Weinan E
Author: Peter Benner