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Meshfree Methods for Partial Differential Equations
Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.
Frontiers of Numerical Analysis
Contains lecture notes on four topics at the forefront of research in computational mathematics. This book presents a self-contained guide to a research area, an extensive bibliography, and proofs of the key results. It is suitable for professional mathematicians who require an accurate account of research in areas parallel to their own.
Meshfree Methods for Partial Differential Equations VII
Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. 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. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.
Meshfree Methods for Partial Differential Equations III
Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.
Meshfree Methods for Partial Differential Equations V
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.
Computational Methods
The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.
Meshfree Methods for Partial Differential Equations VI
Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering.
Meshfree Methods for Partial Differential Equations II
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.
Singular Phenomena and Scaling in Mathematical Models
The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.
High Performance Computing
This book constitutes revised selected papers from 7 workshops that were held in conjunction with the ISC High Performance 2016 conference in Frankfurt, Germany, in June 2016. The 45 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They stem from the following workshops: Workshop on Exascale Multi/Many Core Computing Systems, E-MuCoCoS; Second International Workshop on Communication Architectures at Extreme Scale, ExaComm; HPC I/O in the Data Center Workshop, HPC-IODC; International Workshop on OpenPOWER for HPC, IWOPH; Workshop on the Application Performance on Intel Xeon Phi – Being Prepared for KNL and Beyond, IXPUG; Workshop on Performance and Scalability of Storage Systems, WOPSSS; and International Workshop on Performance Portable Programming Models for Accelerators, P3MA.
