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The Mimetic Finite Difference Method for Elliptic Problems
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
Proceedings of the 16th International Meshing Roundtable
This volume contains the articles presented at the 16th International Meshing Roundtable (IMR) organized, in part, by Sandia National Laboratories and held in Seattle, Washington, U.S.A. in October, 2007. The volume presents recent results of mesh generation and adaptation which has applications to finite element simulation. It introduces theoretical and novel ideas with practical potential.
Current Trends in Scientific Computing
This volume contains 36 research papers written by prominent researchers. The papers are based on a large satellite conference on scientific computing held at the International Congress of Mathematics (ICM) in Xi'an, China. Topics covered include a variety of subjects in modern scientific computing and its applications, such as numerical discretization methods, linear solvers, parallel computing, high performance computing, and applications to solid and fluid mechanics, energy, environment, and semiconductors. The book will serve as an excellent reference work for graduate students and researchers working with scientific computing for problems in science and engineering.
Computational Science – ICCS 2009
The two-volume set LNCS 5544-5545 constitutes the refereed proceedings of the 9th International Conference on Computational Science, ICCS 2009, held in Baton Rouge, LA, USA in May 2008. The 60 revised papers of the main conference track presented together with the abstracts of 5 keynote talks and the 138 revised papers from 13 workshops were carefully reviewed and selected for inclusion in the three volumes. The general main track of ICSS 2009 was organized in about 20 parallel sessions addressing the following topics: e-Science Applications and Systems, Scheduling, Software Services and Tools, New Hardware and Its Applications, Computer Networks, Simulation of Complex Systems, Image Processing, Optimization Techniques, and Numerical Methods.
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
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”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.
Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems
The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many ...
Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems
This volume comprises the second part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023. The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or ...
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is...
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems
This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, ...
