Bücher der Reihe Lecture Notes in Computational Science and Engineering

This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena.The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate approximation of solutions of singularly perturbed differential equations; that is, problems whose solutions exhibit boundary and/or interior layers.

Isogeometric Analysis is a groundbreaking computational approach that promises the possibility of integrating the finite element method into conventional spline-based CAD design tools.

This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers.

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.

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 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.

These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland.

This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic.

Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique.

The research and its outcomes presented in this collection focus on various aspects of high-performance computing (HPC) software and its development which is confronted with various challenges as today's supercomputer technology heads towards exascale computing.

This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium "Building bridges: connections and challenges in modern approaches to numerical partial differential equations".

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications.

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity.

This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015.

This book comprises the proceedings of the 4th International Conference on Computational Engineering (ICCE 2017), held in Darmstadt, Germany on September 28-29, 2017.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fourth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-"Finite Element for Flows" conference, held in Rome in spring 2017.

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 volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering.The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain.This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area.

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019.

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.

These are the proceedings of the 25th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in St. John's, Newfoundland, Canada in July 2018.

These are the proceedings of the 25th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in St. John's, Newfoundland, Canada in July 2018.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-"Finite Element for Flows" conference, held in Rome in spring 2017.

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018.

This book explores four guiding themes - reduced order modelling, high dimensional problems, efficient algorithms, and applications - by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs.

This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018.

This book is about solving partial differential equations (PDEs). Such equa- tions are used to model a wide range ofphenomena in virtually all fields ofsci- ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in- tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech- niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor- der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff- pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple- mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe- rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of- tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho- dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora- ted perfonnances for the corresponding closed-loop systems.