Almost all physical phenomena can be mathematically described in terms of differential equations. The finite element method is a tool for the appro- mate solution of differential equations. However, despite the extensive use of the finite element method by engineers in the industry, understanding the principles involved in its formulation is often lacking in the common user. As an approximation process, the finite ele~ent method can be for- lated with the general technique of weighted resi...

This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transce...

Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel’s doctoral descendant tree 1983–2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants.This book starts with a perso...

Recent Advances in Numerical Methods features contributions from distinguished researchers focused on significant aspects of current numerical methods and computational mathematics. This volume meets the need in the community for new computational methods that can solve complex scientific and engineering problems by presenting innovative methods that provide numerical solutions in effective computing times. Each chapter presents new and advanced methods and modern variations of known techn...

This book constitutes the revised selected papers of the 43rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2017, held in Eindhoven, The Netherlands, in June 2017.The 31 full papers presented in this volume were carefully reviewed and selectedfrom 71 submissions. They cover a wide range of areas, aiming at connecting theory and applications by demonstrating how graph-theoretic concepts can be applied in various areas of computer science. Another ...

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact soluti...

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finall...

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delon...

This book constitutes the proceedings of the 10th International Workshop on Algorithms and Computation, WALCOM 2016, held in Kathmandu, Nepal, in March 2016.The 27 full papers presented together with 4 invited talks were carefully reviewed and selected from 68 submissions. The papers cover a wide range of topics such as approximation algorithms, computational complexity, computational geometry, data structures, graph algorithms, graph coloring, graph exploration, and online algorit...

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area.This three-volume set, Walter Gautschi: Selected Works with Commentaries...

This book constitutes the thoroughly refereed proceedings of the 24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017, held in Porquerolles, France, in June 2017.The 21 full papers presented were carefully reviewed and selected from 41 submissions. They are devoted to the study of the interplay between structural knowledge, communications, and computing in decentralized systems of multiple communicating entities. They are organized arou...

Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods – a Consumer Guide