Domain Decomposition Methods in Science and Engineering XXVI

Domain Decomposition Methods in Science and Engineering XXVI
Author: Susanne C. Brenner
Publisher: Springer Nature
Total Pages: 778
Release: 2023-03-15
Genre: Mathematics
ISBN: 3030950255

These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.

Domain Decomposition Methods in Science and Engineering XXIV

Domain Decomposition Methods in Science and Engineering XXIV
Author: Petter E. Bjørstad
Publisher: Springer
Total Pages: 556
Release: 2019-01-05
Genre: Mathematics
ISBN: 3319938738

These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2017.

Parallel Finite Element Computations

Parallel Finite Element Computations
Author: B. H. V. Topping
Publisher:
Total Pages: 328
Release: 1996
Genre: Mathematics
ISBN:

Describing the main procedures for the parallelization of the finite element method for distributed memory architectures, this book is for engineers, computer scientists and mathematicians working on the application of high performance computing to finite element methods. Its procedures are applicable to distributed memory computer architectures.

Numerical Methods for Mixed Finite Element Problems

Numerical Methods for Mixed Finite Element Problems
Author: Jean Deteix
Publisher: Springer Nature
Total Pages: 119
Release: 2022-09-24
Genre: Mathematics
ISBN: 3031126165

This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet’s boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.

Domain Decomposition Methods in Science and Engineering XX

Domain Decomposition Methods in Science and Engineering XX
Author: Randolph Bank
Publisher: Springer Science & Business Media
Total Pages: 702
Release: 2013-07-03
Genre: Mathematics
ISBN: 3642352758

These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.​

Massively Parallel Multifrontal Methods for Finite Element Analysis on MIMD Computer Systems

Massively Parallel Multifrontal Methods for Finite Element Analysis on MIMD Computer Systems
Author:
Publisher:
Total Pages: 18
Release: 1993
Genre:
ISBN:

The development of highly parallel direct solvers for large, sparse linear systems of equations (e.g. for finite element or finite difference models) is lagging behind progress in parallel direct solvers for dense matrices and iterative methods for sparse matrices. We describe a massively parallel (MP) multifrontal solver for the direct solution of large sparse linear systems, such as those routinely encountered in finite element structural analysis, in an effort to address concerns about the viability of scalable, MP direct methods for sparse systems and enhance the software base for MP applications. Performance results are presented and future directions are outlined for research and development efforts in parallel multifrontal and related solvers. In particular, parallel efficiencies of 25% on 1024 nCUBE 2 nodes and 36% on 64 Intel iPSCS60 nodes have been demonstrated, and parallel efficiencies of 60--85% are expected when a severe load imbalance is overcome by static mapping and dynamic load balance techniques previously developed for other parallel solvers and application codes.

A Massively Parallel Adaptive Finite Element Method with Dynamic Load Balancing

A Massively Parallel Adaptive Finite Element Method with Dynamic Load Balancing
Author:
Publisher:
Total Pages: 26
Release: 1993
Genre:
ISBN:

We construct massively parallel, adaptive finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We also present results using adaptive p-refinement to reduce the computational cost of the method. We describe tiling, a dynamic, element-based data migration system. Tiling dynamically maintains global load balance in the adaptive method by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. We demonstrate the effectiveness of the dynamic load balancing with adaptive p-refinement examples.

Innovative Approaches in Computational Structural Engineering

Innovative Approaches in Computational Structural Engineering
Author: George C. Tsiatas
Publisher: Frontiers Media SA
Total Pages: 266
Release: 2020-04-22
Genre:
ISBN: 2889636070

Nowadays, numerical computation has become one of the most vigorous tools for scientists, researchers and professional engineers, following the enormous progress made during the last decades in computing technology, in terms of both computer hardware and software development. Although this has led to tremendous achievements in computer-based structural engineering, the increasing necessity of solving complex problems in engineering requires the development of new ideas and innovative methods for providing accurate numerical solutions in affordable computing times. This collection aims at providing a forum for the presentation and discussion of state-of-the-art innovative developments, concepts, methodologies and approaches in scientific computation applied to structural engineering. It involves a wide coverage of timely issues on computational structural engineering with a broad range of both research and advanced practical applications. This Research Topic encompasses, but is not restricted to, the following scientific areas: modeling in structural engineering; finite element methods; boundary element methods; static and dynamic analysis of structures; structural stability; structural mechanics; meshless methods; smart structures and systems; fire engineering; blast engineering; structural reliability; structural health monitoring and control; optimization; and composite materials, with application to engineering structures.