Finite Difference Computing With Exponential Decay Models
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Finite Difference Computing With Exponential Decay Models
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Author : Hans Petter Langtangen
language : en
Publisher: Springer
Release Date : 2016-06-10
Finite Difference Computing With Exponential Decay Models written by Hans Petter Langtangen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with Computers categories.
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.
Finite Difference Computing With Pdes
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Author : Hans Petter Langtangen
language : en
Publisher: Springer
Release Date : 2017-06-21
Finite Difference Computing With Pdes written by Hans Petter Langtangen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-21 with Computers categories.
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Computing Characterizations Of Drugs For Ion Channels And Receptors Using Markov Models
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Author : Aslak Tveito
language : en
Publisher: Springer
Release Date : 2016-04-19
Computing Characterizations Of Drugs For Ion Channels And Receptors Using Markov Models written by Aslak Tveito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.
Scientific Computing
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Author : John A. Trangenstein
language : en
Publisher: Springer
Release Date : 2018-05-14
Scientific Computing written by John A. Trangenstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-14 with Mathematics categories.
This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 49 examples, 110 exercises, 66 algorithms, 24 interactive JavaScript programs, 77 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.
Multiscale Models In Mechano And Tumor Biology
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Author : Alf Gerisch
language : en
Publisher: Springer
Release Date : 2018-03-16
Multiscale Models In Mechano And Tumor Biology written by Alf Gerisch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-16 with Mathematics categories.
This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.
Advanced Finite Element Methods With Applications
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Author : Thomas Apel
language : en
Publisher: Springer
Release Date : 2019-06-28
Advanced Finite Element Methods With Applications written by Thomas Apel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-28 with Mathematics categories.
Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
Scientific Computing
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Author : Bertil Gustafsson
language : en
Publisher: Springer
Release Date : 2018-10-03
Scientific Computing written by Bertil Gustafsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods’ journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing – making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.
Geometrically Unfitted Finite Element Methods And Applications
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Author : Stéphane P. A. Bordas
language : en
Publisher: Springer
Release Date : 2018-03-13
Geometrically Unfitted Finite Element Methods And Applications written by Stéphane P. A. Bordas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Mathematics categories.
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
Bem Based Finite Element Approaches On Polytopal Meshes
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Author : Steffen Weißer
language : en
Publisher: Springer
Release Date : 2019-07-18
Bem Based Finite Element Approaches On Polytopal Meshes written by Steffen Weißer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Numerical Geometry Grid Generation And Scientific Computing
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Author : Vladimir A. Garanzha
language : en
Publisher: Springer Nature
Release Date : 2021-09-25
Numerical Geometry Grid Generation And Scientific Computing written by Vladimir A. Garanzha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-25 with Mathematics categories.
The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.