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computational Tool for a Mini-Windmill Study with SOFT

Computational Tool for a Mini-Windmill Study with SOFT

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18th International Conference on Domain Decomposition Methods

作者： Garbey, M. Smaoui, M. De Brye, N. Picard, C. Univ Houston Dept Comp Sci Houston TX 77204 USA

ISBN: (纸本)9783642026775;9783642026768

In this paper, we present a parallel computational framework for the completely automated design of a Vertical Axis Fluid Turbine (VAFT). Simulation, Optimum design, Fabrication and Testing (SOFT) of the VAFT is integrated into a hardware/software environment that can fit into a small office space. The components of the four steps design loop are as follows Simulation: We use a parallel CFD algorithm to run a direct simulation of the fluid structure interaction problem. We derive from that computation the torque and the average rotation speed for a given friction coefficient on the rotor shaft and an average flow speed. Our objective is to get the most power out of the windmill, consequently the highest rotation speed possible. Optimization: We optimize the shape of the blade section with a genetic algorithm and/or a surface response. The evaluation of the objective function (average rotation speed) corresponds to the direct simulation of the Navier Stokes flow interacting with the rotating turbine, until reaching a stationary regime. Because this simulation is compute-intensive, we distribute the evaluation of the objective function for the different shapes (gene or parameter combinations) on a network of computers using an embarrassingly parallel algorithm. Fabrication: The optimization procedure results in a supposedly optimum shape in the chosen design space. This shape is sent to a 3-D printer that fabricates the real turbine. This turbine is set up such that it can be easily mounted on a standard base equipped with an electric alternator/generator. Testing: The windmill is tested in a mini wind tunnel. The electric output is measured and a video camera can directly monitor the windmill rotation through the transparent wall of the wind tunnel. This information can be analyzed by the computer system and comparison with the simulation is assessed. Figure 1 gives a graphical overview of the SOFT concept. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： computational fluid dynamics

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Distributed Decomposition Over Hyperspherical Domains

Distributed Decomposition Over Hyperspherical Domains

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18th International Conference on Domain Decomposition Methods

作者： Ahmadia, Aron Keyes, David Melville, David Rosenbluth, Alan Tian, Kehan Columbia Univ Dept Appl Phys & Appl Math New York NY 10027 USA IBM Corp TJ Watson Res Ctr Yorktown Hts NY 10598 USA

ISBN: (纸本)9783642026775;9783642026768

We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at the origin of Euclidean space of arbitrary dimension. A decomposition of the feasible region into convex regions suggests a heuristic sampling approach to finding the global minimum. We describe a technique for decomposing the surface of a hypersphere of arbitrary dimension, both exactly and approximately, into a specific number of regions of equal area and small diameter. The decomposition generalizes to any problem posed on a spherical domain where regularity of the decomposition is an important concern. We specifically consider a storage-optimized decomposition and analyze its performance. We also show how the decomposition can parallelize the sampling process by assigning each processor a subset of points on the hypersphere to sample. Finally, we describe a freely available C++ software package that implements the storage-optimized decomposition.

关键词： Global optimization

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Parallelization of a Constrained Three-Dimensional Maxwell Solver

Parallelization of a Constrained Three-Dimensional Maxwell S...

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18th International Conference on Domain Decomposition Methods

作者： Assous, F. Segre, J. Sonnendruecker, E. Bar Ilan Univ Dept Math & Stat IL-52100 Ramat Gan Israel CEA DEN DM2S SFME Saclay France Univ Strasbourg CNRS IRMA F-67070 Strasbourg France

ISBN: (纸本)9783642026775;9783642026768

The numerical solution of very large 3D electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the 3D Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov-Maxwell equations, widely used to simulate complex devices like particle injectors or accelerators. This approach in particular leads to reuse without modification most of an existing sequential code.

关键词： Particle injectors

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Patch Smoothers for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems

Patch Smoothers for Saddle Point Problems with Applications ...

引用

18th International Conference on Domain Decomposition Methods

作者： Simon, Rene Zulehner, Walter Univ Linz SFB 013Altenbergerstr69 A-4040 Linz Austria Johannes Kepler Univ Linz Inst Computat Math A-4040 Linz Austria

ISBN: (纸本)9783642026775;9783642026768

We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of elliptic optimal control problems. A rigorous multigrid convergence analysis yields level-independent convergence rates. Numerical experiments indicate that the convergence rates are also independent of the involved regularization parameter.

关键词： Optimal control systems

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An Algorithm for Non-Matching Grid Projections with Linear Complexity

An Algorithm for Non-Matching Grid Projections with Linear C...

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18th International Conference on Domain Decomposition Methods

作者： Gander, Martin J. Japhet, Caroline Univ Geneva Sect Math 2-4 Rue LievreCP 64 CH-1211 Geneva 4 Switzerland Univ Paris 13 LAGA F-93430 Villetaneuse France

ISBN: (纸本)9783642026775;9783642026768

Non-matching grids are becoming more and more common in scientific computing. Examples are the Chimera methods proposed by [20] and analyzed in [2], the mortar methods in domain decomposition by [1], and the patch method for local refinement by [6], and [17], which is also known under the name 'numerical zoom', see [9]. In the patch method, one has a large scale solver for a particular partial differential equation, and wants to add more precision in certain areas, without having to change the large scale code. One thus introduces refined, possibly non-matching patches in these regions, and uses a residual correction iteration between solutions on the patches and solutions on the entire domain, in order to obtain a more refined solution in the patch regions. The mortar method is a domain decomposition method that permits an entirely parallel grid generation, and local adaptivity independently of neighboring subdomains, because grids do not need to match at interfaces. The Chimera method is also a domain decomposition method, specialized for problems with moving parts, which inevitably leads to non-matching grids, if one wants to avoid regridding at each step. Contact problems in general lead naturally to nonmatching grids. In all these cases, one needs to transfer approximate solutions from one grid to a non-matching second grid by projection. This operation is known in the literature under the name mesh intersection problem in [12], intergrid communication problem in [16], grid transfer problem in [18], and similar algorithms are also needed when one has to interpolate discrete approximations, see [13, Chap. 13]. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Domain decomposition methods

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On Preconditioners for Generalized Saddle Point Problems with an Indefinite Block

On Preconditioners for Generalized Saddle Point Problems wit...

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18th International Conference on Domain Decomposition Methods

作者： Krzyzanowski, Piotr Univ Warsaw PL-02097 Warsaw Poland

In many applications one needs to solve a discrete system of linear equations with a symmetric block matrix M (u/p) ≡ (A BT/B O) (u/p) = (f/g,) where the block A =AT is not necessarily positive definite and may even ... 详细信息

ISBN: (纸本)9783642026775

In many applications one needs to solve a discrete system of linear equations with a symmetric block matrix M (u/p) ≡ (A B^T/B O) (u/p) = (f/g,) where the block A =A^T is not necessarily positive definite and may even be singular. Such situation occurs, for example, after suitable finite element discretization of the generalized Stokes problem, cf. [5], -Delta;u -ωu + ∇_p = f, div u = 0, when for large enough ω one cannot preserve the ellipticity of -Δ -ω. Another example is the time-harmonicMaxwell equation, see [7], ∇ × ∇ × u -ωu + ∇_p = f, div u = 0, where large enough ω again results in an indefinite A. Although the whole system matrix (1) remains invertible when ω = 0, the matrix A which then corresponds to the discrete curl-curl operator, has a large kernel. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Artificial intelligence

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A FETI-2LM Method for Non-Matching Grids

A FETI-2LM Method for Non-Matching Grids

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18th International Conference on Domain Decomposition Methods

作者： Roux, Francois-Xavier Off Natl Etud & Rech Aerosp High Performance Comp Unit F-92320 Chatillon France

ISBN: (纸本)9783642026775

In this paper, a new solution methodology based on the FETI-2LM method for non conforming grids is introduced. Thanks to the regularizing properties of the Robin interface matching conditions of the FETI-2LM method, each non conforming condition can be localized inside one subdomain, in such a way that the FETI-2LM method applies exactly in the same way as in the conforming case. The paper is organized as follows: section 2 recalls the principle of FETI-2LM method, section 3 briefly describes the mortar method for non conforming domains, the new methodology for localizing the multi-point constraints on the non conforming interface derived from the mortar method is introduced in section 4 and section 5 generalizes the methodology in the case of multi-level splitting of a mesh including a non conforming interface. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Mortar

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A Maximum Principle for L²-Trace Norms with an Application to Optimized Schwarz Methods

A Maximum Principle for <i>L</i><SUP>2</SUP>-Trace Norms wit...

引用

18th International Conference on Domain Decomposition Methods

作者： Loisel, Sebastien Szyld, Daniel B. Temple Univ Philadelphia PA 19122 USA

ISBN: (纸本)9783642026775

Harmonic functions attain their pointwise maximum on the boundary of the domain. In this article, we analyze the relationship between various norms of nearly harmonic functions and we show that the trace norm is maximized on the boundary of the domain. One application is that the Optimized Schwarz Method with two subdomains converges for all Robin parameters alpha > 0.

关键词： Harmonic functions

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NKS for Fully Coupled Fluid-Structure Interaction with Application

NKS for Fully Coupled Fluid-Structure Interaction with Appli...

引用

18th International Conference on Domain Decomposition Methods

作者： Barker, Andrew T. Cai, Xiao-Chuan Univ Colorado Dept Appl Math Boulder CO 80309 USA Univ Colorado Dept Comp Sci Boulder CO 80309 USA

ISBN: (纸本)9783642026775;9783642026768

Newton-Krylov-Schwarz algorithms have been used in many areas and are often quite scalable and robust. In this paper we explore the application of Schwarz type domain decomposition preconditioners to some fully coupled systems for fluidstructure interaction. In particular, we are interested in developing a scalable parallel framework for the simulation of blood flow in human arteries [11]. In [2, 3], coupled fluid-structure problems are solved in 3D for patient-specific artery models, with emphasis on accurately representing vessel geometry, on constitutive model for the artery walls, and other physical concerns. In this paper we focus on a class of parallel domain decomposition algorithms for solving the coupled systems and report on the robustness and parallel scalability of the algorithms. Very often in the simulation of fluid-structure interaction, fluid and structure are iteratively coupled, as in [4, 5, 7]. That is, fluid and structure subproblems are solved alternately (or in parallel), passing boundary conditions between them, until the solutions are compatible at the fluid-structure interface, and then the simulation proceeds to the next time step. However, this approach often requires small timesteps, can become unstable, and can reduce the order of accuracy of the solution [8]. In contrast, we use fully monolithic coupling, where the fluid and the structure are solved together as one system. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Fluid structure interaction

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On the Convergence of Optimized Schwarz Methods by way of Matrix Analysis

On the Convergence of Optimized Schwarz Methods by way of Ma...

引用

18th International Conference on Domain Decomposition Methods

作者： Loisel, Sebastien Szyld, Daniel B. Temple Univ Philadelphia PA 19122 USA

ISBN: (纸本)9783642026775;9783642026768

Domain decomposition methods are widely used to solve in parallel large linear systems of equations arising in the discretization of partial differential equations. Optimized Schwarz Methods (OSM) have been the subject of intense research because they lead to algorithms that converge very quickly. The analysis of OSM has been a very challenging research area and there are currently no general proofs of convergence for the optimized choices of the Robin parameter in the case of overlap. In this article, we apply a proof technique developed for the analysis of Schwarz-type algorithms using matrix analysis techniques and specifically using properties of matrix splittings, to the Optimized Schwarz algorithms. We thus obtain new general convergence results, but they apply only to large Robin parameters, which may not be the optimal ones.

关键词： Domain decomposition methods

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