|
Showing 1 - 4 of
4 matches in All Departments
This IMA Volume in Mathematics and its Applications MODELING, MESH
GENERATION, AND ADAPTIVE NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL
EQUATIONS is based on the proceedings of the 1993 IMA Summer
Program "Modeling, Mesh Generation, and Adaptive Numerical Methods
for Partial Differential Equations." We thank Ivo Babuska, Joseph
E. Flaherty, William D. Hen- shaw, John E. Hopcroft, Joseph E.
Oliger, and Tayfun Tezduyar for orga- nizing the workshop and
editing the proceedings. We also take this oppor- tunity to thank
those agencies whose financial support made the summer program
possible: the National Science Foundation (NSF), the Army Re-
search Office (ARO) the Department of Energy (DOE), the Minnesota
Su- percomputer Institute (MSI), and the Army High Performance
Computing Research Center (AHPCRC). A vner Friedman Willard Miller,
Jr. xiii PREFACE Mesh generation is one of the most time consuming
aspects of com- putational solutions of problems involving partial
differential equations. It is, furthermore, no longer acceptable to
compute solutions without proper verification that specified
accuracy criteria are being satisfied. Mesh gen- eration must be
related to the solution through computable estimates of
discretization errors. Thus, an iterative process of alternate mesh
and so- lution generation evolves in an adaptive manner with the
end result that the solution is computed to prescribed
specifications in an optimal, or at least efficient, manner. While
mesh generation and adaptive strategies are becoming available,
major computational challenges remain. One, in particular, involves
moving boundaries and interfaces, such as free-surface flows and
fluid-structure interactions.
This book shows the latest frontiers of the research by the most active researchers in the field of numerical mathematics. The papers in the book were presented at a symposium held in Yamaguchi, Japan. The subject of the symposium was mathematical modeling and numerical simulation in continuum mechanics. The topics of the lectures ranged from solids to fluids and included both mathematical and computational analysis of phenomena and algorithms. The reader can study the latest results on shells, plates, flows in various situations, fracture of solids, new ways of exact error estimates and many other topics.
With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.
This book deals with the impact of uncertainty in input data on the
outputs of mathematical models. Uncertain inputs as scalars,
tensors, functions, or domain boundaries are considered. In
practical terms, material parameters or constitutive laws, for
instance, are uncertain, and quantities as local temperature, local
mechanical stress, or local displacement are monitored. The goal of
the worst scenario method is to extremize the quantity over the set
of uncertain input data.
A general mathematical scheme of the worst scenario method,
including approximation by finite element methods, is presented,
and then applied to various state problems modeled by differential
equations or variational inequalities: nonlinear heat flow,
Timoshenko beam vibration and buckling, plate buckling, contact
problems in elasticity and thermoelasticity with and without
friction, and various models of plastic deformation, to list some
of the topics. Dozens of examples, figures, and tables are
included.
Although the book concentrates on the mathematical aspects of the
subject, a substantial part is written in an accessible style and
is devoted to various facets of uncertainty in modeling and to the
state of the art techniques proposed to deal with uncertain input
data.
A chapter on sensitivity analysis and on functional and convex
analysis is included for the reader's convenience.
-Rigorous theory is established for the treatment of uncertainty in
modeling
- Uncertainty is considered in complex models based on partial
differential equations or variational inequalities
- Applications to nonlinear and linear problems with uncertain data
are presented in detail: quasilinear steady heat flow, buckling of
beams and plates, vibration of beams, frictional contact of bodies,
several models of plastic deformation, and more
-Although emphasis is put on theoretical analysis and approximation
techniques, numerical examples are also present
-Main ideas and approaches used today to handle uncertainties in
modeling are described in an accessible form
-Fairly self-contained book
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|