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About 7,163 papers for “Domain decomposition methods”

14. Domain Decomposition Methods

Yousef Saad · Society for Industrial and Applied Mathematics eBooks · 2003

As multiprocessing technology steadily gains ground, new classes of numerical methods that can take better advantage of parallelism are emerging. Among these techniques, domain decomposition methods are undoubtedly the best known and perhaps the most promising for certain types of problems. These methods combine ideas from partial differential equations (PDEs), linear algebra, and mathematical analysis, and techniques from graph theory. This chapter is devoted to decomposition methods, which are based on the general concepts of graph partitionings.

Cited by 30

Domain Decomposition Methods 10

International Conference on Domain Decomposition < 1997, Boulder, Colo.>, Mandel, Jan, Farhat, Charbel et al. · Contemporary mathematics - American Mathematical Society · 1998

Computational Fluid Dynamics codes based on the Reynolds averaged Navier-Stokes equations may be used to simulate the generation of sound waves along with the other features of the flow of air. For adequate acoustic modeling the information about the sound sources within the flow is passed to a linearized Euler solver that accurately resolves the propagation of sound through the non-uniformly moving medium. 
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\nAerodynamic sound is generated by the flow of air or results from the interaction of sound with airflow. Computation of aerodynamic noise implies direct simulation
\nof the sound field based on first principles [6]. It allows complex sound fields to be simulated such as those arising in turbulent flows. 
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\nWhen building a software tool for this simulation two options exist: (a) to develop a new code especially for this purpose, or (b) to use an existing Computational 
\nFluid Dynamics (CFD) code as much as possible. (As it will be shown later, due to numerical diffusion conventional CFD codes tend to smear the sound signal too close to its source, and cannot be used directly for aeroacoustic simulations.) 
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\nThe second option is considered here as it seems to require less work and makes use of the vast amount of experience accumulated in flow modeling. CFD codes have built-in capabilities of handling non-linearities, curved boundaries, boundary layers, turbulence, and thermal effects. They are based on optimized, efficient, readily converging algorithms. If no CFD code is used as a basis, all these features have to be implemented again in the new code developed for the simulation of the sound field.

Cited by 42

ALGEBRAIC DOMAIN DECOMPOSITION METHODS

Mikolaj Szydlarski, These De Doctorat, De Paris Centre et al. · 2010

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Cited by 0

Heterogeneous Domain Decomposition Methods

Alfio Quarteroni, Alberto Valli · 1999

Abstract In this chapter we address the case of heterogeneous domain decomposition, arising whenever, in the approximation of certain physical phenomena, two different kinds of (initial-) boundary value problems hold within two disjoined subregions of the computational domain.

Cited by 1

Domain Decomposition and Variational Methods

O. Pironneau · 2015

There are several reasons to study Domain Decomposition Methods (DDM) • For Parallel Processing, because it is an easy way to allocate tasks to processors in a multi-processor machine. • For local mesh refinements, by putting a numerical zoom around the re-gions in which one wants a better precision. • For new applications such as thermal studies in buildings, or preliminary studies for car for instance in the art design departments where construc-tive solid geometry is prefered to engineering CAD systems. For the second item Professor J.L. Lions suggested a method where by the space of the variational formulation is decomposed. For example for the Dirichlet problem in Ω ∫ Ω

Cited by 0