**Contemporary Mathematics**

Volume: 157;
1994;
484 pp;
Softcover

MSC: Primary 65;

Print ISBN: 978-0-8218-5158-6

Product Code: CONM/157

List Price: $45.00

AMS Member Price: $36.00

MAA Member Price: $40.50

**Electronic ISBN: 978-0-8218-7748-7
Product Code: CONM/157.E**

List Price: $45.00

AMS Member Price: $36.00

MAA Member Price: $40.50

# Domain Decomposition Methods in Science and Engineering

Share this page *Edited by *
*Alfio Quarteroni; Jacques Periaux; Yuri A. Kuznetsov; Olof B. Widlund*

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

#### Readership

Applied mathematicians, numerical analysts, computer scientists, engineers, graduate students, and researchers.

# Table of Contents

## Domain Decomposition Methods in Science and Engineering

- Contents vii8 free
- Preface xiii14 free
- List of Participants xv16 free
- Part I: Theory 124 free
- Invited Lectures 326
- Domain decomposition methods using modified basis functions 326
- Uniform convergence estimates for multigrid V-cycle algorithms with less than full elliptic regularity 1740
- A three-field domain decomposition method 2750
- Self-adaptive coupling of mathematical models and/or numerical methods 3558
- Noniterative domain decomposition for second order hyperbolic problems 4568
- Some recent results on Schwarz type domain decomposition algorithms 5376
- Overlapping domain decomposition methods for parabolic problems 6386
- Domain decomposition and multilevel PCG method for solving 3-D fourth order problems 7194
- Some two-grid finite element methods 79102

- Contributed Lectures 89112
- Interface conditions for a kind of non linear elliptic-hyperbolic problems 89112
- A domain decomposition for the transport equation 97120
- Hybrid domain decomposition with unstructured subdomains 103126
- Some Schwarz algorithms for the p-version finite element method 113136
- On the robustness and efficiency of the fully adaptive multigrid method 121144
- Finite volume variational formulation. Application to domain decomposition methods 127150

- Part II: Algorithms 133156
- Invited Lectures 135158
- Multigrid solvers on decomposed domains 135158
- Domain decomposition preconditioners for convection diffusion problems 157180
- A domain decomposition approach to solving the Helmholtz equation with a radiation boundary condition 177200
- The dual Schur complement method with well-posed local Neumann problems 193216
- Implicit domain decomposition algorithms for steady, compressible aerodynamics 203226
- A new mixed preconditioning method based on the clustered element-by element preconditioners 215238

- Contributed Lectures 223246
- Domain decomposition methods with local Fourier basis for parabolic problems 223246
- A domain decomposition method for the polar factorization of vector fields 231254
- An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation 237260
- An iterative finite-element collocation method for parabolic problems using domain decomposition 245268
- A domain decomposition method using sparse grids 255278
- Domain decomposition for the Stokes equations in streamfunction formulation 263286
- Overlapping domain decomposition methods for the obstacle problem 271294
- An iteration scheme for non-symmetric interface operators 279302
- Factorization of the convection-diffusion operator and a (possibly) non overlapping Schwarz method 287310
- Domain decomposition method coupling fmite elements and preconditioned Chebyshev collocation to solve elliptic problems 293316
- Additive Schwarz methods and acceleration with variable weights 299322

- Part III: Parallelism 311334
- Invited Lectures 313336
- Contributed Lectures 345368
- Implementation of domain decomposition techniques on nCUBE2 parallel machine 345368
- A class of domain decomposition preconditioners for massively parallel computers 353376
- A domain decomposition environment for local time dependent problems 361384
- A parallel element-by-element method for large-scale computations with h – p -finite elements 367390

- Part IV: Applications 375398
- Invited Lectures 377400
- Coupling Boltzmann and Euler equations without overlapping 377400
- On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Application to scattering 399422
- A fictitious domain method for unsteady incompressible viscous flow modelled by Navier-Stokes equations 421444

- Contributed Lectures 433456
- Introduction of domain decomposition techniques in time-dependent flow problems 433456
- The Schur complement algorithm for the solution of contact problems 441464
- Spectral multidomain methods for the simulation of wave propagation in heterogeneous media 447470
- Domain decomposed preconditioning for faulted geological blocks 457480
- A domain decomposition method for simulating 2D external viscous flows 463486
- Interface conditions for heterogeneous domain decomposition: coupling of different hyperbolic systems 469492
- Simulation of 3D Navier-Stokes flows via domain decomposition by the modified discrete vector potential model 477500

- Author Index 483506