Numerical Solutions of PDEs Involving Interfaces and Irregular Domains
Author: Zhilin Li,Kazufumi Ito
"This book will be a useful resource for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems, particularly problems with fixed and moving interfaces, free boundary problems, and problems on regular domains."--BOOK JACKET.
Author: Ali R. Ansari
This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was mathematical biology, including a keynote address by Professor Philip Maini. The second theme was computational science/numerical analysis, including a keynote address by Professor Grigorii Shishkin. The conference also addressed more general applications topics, with papers in business applications, fluid mechanics, optimization, scheduling problems and engineering applications, as well as a keynote by Professor Ali Nayfeh.
In Honor of Yoshikazu Giga's 60th Birthday, Sapporo, Japan, August 2015
Author: Yasunori Maekawa,Shuichi Jimbo
This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
Program on Moving Interface Problems and Applications in Fluid Dynamics, January 8-March 31, 2007, Institute for Mathematical Sciences, National University of Singapore
Author: Boo Cheong Khoo,Zhilin Li,Ping Lin
Publisher: American Mathematical Soc.
This volume is a collection of research papers presented at the program on Moving Interface Problems and Applications in Fluid Dynamics, which was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences (IMS) of the National University of Singapore. The topics discussed include modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications including biological treatments with experimental verification, multi-medium flow or multi-phase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas. Readers can benefit from some recent research results in these areas.
33rd international conference, Sozopol, Bulgaria, 8-14 June 2007
Author: Michail D. Todorov,Tekhnicheski universitet--Sofii︠a︡
Publisher: Amer Inst of Physics
Category: Business & Economics
All papers have been peer-reviewed. The main goal of this series of Conferences is to bring together experts and young talented scientists from Bulgaria and abroad to discuss modern trends, and to ensure exchange of views in various applications of mathematics in the fields of engineering, physics, economics, biology, etc. Keeping the main topics of the previous AMEE conferences, the 33rd issue was subject to the motto "Nonlinear phenomena - mathematical theory and environmental reality". The Organizing Committee encouraged students and postgraduates to take part in the sessions of the Conference. The invited speakers organized special sessions. An integral part of the Conference is the publishing and distribution the proceedings among mathematical and related societies who have an interest in the topics of applied mathematics. Topics discussed include: Mathematical modeling in engineering, physics, astrophysics, heat conductivity, hydrodynamics, queuing, numerical methods and simulations, computational techniques and algorithms, spectral methods, optimal control, and scientific computing.
Modeling, Analysis, and Control
Author: Jerry J. Batzel,Franz Kappel,Daniel Schneditz,Hien T. Tran
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted. Researchers and graduate students in mathematical biology and biomedical engineering will find this book useful. It will also appeal to researchers in the physiological and life sciences who are interested in mathematical modeling.
Numerical Methods in a Unified Object-Oriented Approach, Second Edition
Author: Yair Shapira
In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.
Computer Algebra, Numerics, Visualization
Author: Friedrich W. Hehl,Roland A. Puntigam,Hanns Ruder
Publisher: Springer Science & Business Media
For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.
Author: Philippe Gourbesville,Jean Cunge,Guy Caignaert
This book is a collection of extended papers based on presentations given during the SIMHYDRO 2014 conference, held in Sophia Antipolis in June 2014. It focuses on the modeling and simulation of fast hydraulic transients, on 3D modeling, and on uncertainties and multiphase flows. The book explores both the limitations and performance of current models and presents the latest developments based on new numerical schemes, high-performance computing, multiphysics and multiscale methods, and better interaction with field or scale model data. It addresses the interests of practitioners, stakeholders, researchers and engineers active in this field.
Author: Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Publisher: Springer Science & Business Media
Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
Author: Suvranu De,Farshid Guilak,Mohammad Mofrad
Publisher: Springer Science & Business Media
Category: Technology & Engineering
Availability of advanced computational technology has fundamentally altered the investigative paradigm in the field of biomechanics. Armed with sophisticated computational tools, researchers are seeking answers to fundamental questions by exploring complex biomechanical phenomena at the molecular, cellular, tissue and organ levels. The computational armamentarium includes such diverse tools as the ab initio quantum mechanical and molecular dynamics methods at the atomistic scales and the finite element, boundary element, meshfree as well as immersed boundary and lattice-Boltzmann methods at the continuum scales. Multiscale methods that link various scales are also being developed. While most applications require forward analysis, e.g., finding deformations and stresses as a result of loading, others involve determination of constitutive parameters based on tissue imaging and inverse analysis. This book provides a glimpse of the diverse and important roles that modern computational technology is playing in various areas of biomechanics including biofluids and mass transfer, cardiovascular mechanics, musculoskeletal mechanics, soft tissue mechanics, and biomolecular mechanics.
Portable Parallel Programming with the Message-Passing Interface
Author: William Gropp,Ewing Lusk,Anthony Skjellum
Publisher: MIT Press
This book offers a thoroughly updated guide to the MPI (Message-Passing Interface) standard library for writing programs for parallel computers. Since the publication of the previous edition of Using MPI, parallel computing has become mainstream. Today, applications run on computers with millions of processors; multiple processors sharing memory and multicore processors with multiple hardware threads per core are common. The MPI-3 Forum recently brought the MPI standard up to date with respect to developments in hardware capabilities, core language evolution, the needs of applications, and experience gained over the years by vendors, implementers, and users. This third edition of Using MPI reflects these changes in both text and example code. The book takes an informal, tutorial approach, introducing each concept through easy-to-understand examples, including actual code in C and Fortran. Topics include using MPI in simple programs, virtual topologies, MPI datatypes, parallel libraries, and a comparison of MPI with sockets. For the third edition, example code has been brought up to date; applications have been updated; and references reflect the recent attention MPI has received in the literature. A companion volume, Using Advanced MPI, covers more advanced topics, including hybrid programming and coping with large data.