|
Showing 1 - 3 of
3 matches in All Departments
In this book the author sets out to answer two important questions:
1. Which numerical methods may be combined together? 2. How can
different numerical methods be matched together? In doing so the
author presents a number of useful combinations, for instance, the
combination of various FEMs, the combinations of FEM-FDM, REM-FEM,
RGM-FDM, etc. The combined methods have many advantages over single
methods: high accuracy of solutions, less CPU time, less computer
storage, easy coupling with singularities as well as the
complicated boundary conditions. Since coupling techniques are
essential to combinations, various matching strategies among
different methods are carefully discussed. The author provides the
matching rules so that optimal convergence, even superconvergence,
and optimal stability can be achieved, and also warns of the
matching pitfalls to avoid. Audience: The book is intended for both
mathematicians and engineers and may be used as text for advanced
students.
In this book the author sets out to answer two important questions:
1. Which numerical methods may be combined together? 2. How can
different numerical methods be matched together? In doing so the
author presents a number of useful combinations, for instance, the
combination of various FEMs, the combinations of FEM-FDM, REM-FEM,
RGM-FDM, etc. The combined methods have many advantages over single
methods: high accuracy of solutions, less CPU time, less computer
storage, easy coupling with singularities as well as the
complicated boundary conditions. Since coupling techniques are
essential to combinations, various matching strategies among
different methods are carefully discussed. The author provides the
matching rules so that optimal convergence, even superconvergence,
and optimal stability can be achieved, and also warns of the
matching pitfalls to avoid. Audience: The book is intended for both
mathematicians and engineers and may be used as text for advanced
students.
For a numerical method, its stability is a crucial issue in the
sense that an unstable algorithm can render it useless in practical
computation. For an over-determined linear algebraic equation , its
stability is typically evaluated by using the traditional condition
number, Cond= , where and are the maximal and the minimal singular
values of matrix , respectively. In this book, the concept of an
effective condition number, Cond_eff= , is introduced. Cond_eff is
smaller, and generally much smaller, than Cond, and is a better
stability criterion. The Cond_eff can be used as an estimation on
stability for the numerical solutions of partial differential
equations (PDEs) using algorithms, such as the collocation Trefftz
method, the spectral method, the finite difference method, and the
finite element method. An analysis of stability integrated with
errors is the focus of this book.
|
You may like...
Tenet
John David Washington, Robert Pattinson, …
DVD
R53
Discovery Miles 530
|