|
Showing 1 - 2 of
2 matches in All Departments
This book presents a detailed description of a robust
pseudomultigrid algorithm for solving (initial-)boundary value
problems on structured grids in a black-box manner. To overcome the
problem of robustness, the presented Robust Multigrid Technique
(RMT) is based on the application of the essential multigrid
principle in a single grid algorithm. It results in an extremely
simple, very robust and highly parallel solver with
close-to-optimal algorithmic complexity and the least number of
problem-dependent components. Topics covered include an
introduction to the mathematical principles of multigrid methods, a
detailed description of RMT, results of convergence analysis and
complexity, possible expansion on unstructured grids, numerical
experiments and a brief description of multigrid software, parallel
RMT and estimations of speed-up and efficiency of the parallel
multigrid algorithms, and finally applications of RMT for the
numerical solution of the incompressible Navier Stokes equations.
Potential readers are graduate students and researchers working in
applied and numerical mathematics as well as multigrid
practitioners and software programmers. Contents Introduction to
multigrid Robust multigrid technique Parallel multigrid methods
Applications of multigrid methods in computational fluid dynamics
The organization of the material is presented as follows: This
introductory chapter I represents a theoretical analysis of the
computational algorithms for a numerical solution of the basic
equations in continuum mechanics. In this chapter, the general
requirements for computational grids, discretization, and iterative
methods for black-box software are examined. Finally, a concept of
a two-grid algorithm for (de-)coupled solving multidimensional
non-linear (initial-)boundary value problems in continuum mechanics
(multiphysics simulation) in complex domains is presented. Chapter
II contains descriptions of the sequential Robust Multigrid
Technique which is developed as a general-purpose solver in
black-box codes. This chapter presents the main components of the
Robust Multigrid Technique (RMT) used in the two-grid algorithm
(Chapter I) to compute the auxiliary (structured) grid correction.
This includes the generation of multigrid structures, computation
of index mapping, and integral evaluation. Finite volume
discretization on the multigrid structures will be explained by
studying a 1D linear model problem. In addition, the algorithmic
complexity of RMT and black-box optimization of the
problem-dependent components of RMT are analysed. Chapter III
provides a description of parallel RMT. This chapter introduces
parallel RMT-based algorithms for solving the boundary value
problems and initial-boundary value problems in unified manner.
Section 1 presents a comparative analysis of the parallel RMT and
the sequential V-cycle. Sections 2 and 3 present a geometric and an
algebraic parallelism of RMT, i.e. parallelization of the smoothing
iterations on the coarse and the levels. A parallel multigrid cycle
will be considered in Section 4. A parallel RMT for the
time-dependent problems is given in Section 5. Finally, the basic
properties of parallel RMT will be summarized in Section 6.
Theoretical aspects of the used algorithms for solving
multidimensional problems are discussed in Chapters IV. This
chapter contains the theoretical aspects of the algorithms used for
the numerical solving of the resulting system of linear algebraic
equations obtained from discrete multidimensional
(initial-)boundary value problems.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.