CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011

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ITERATIVE METHODS AND PRECONDITIONING 5.12 A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. P. Jiránek : TECHNICAL UNIVERSITY OF LIBEREC AND CERFACS, Czech Republic and France ; Z. Strakos : ACADEMY OF SCIENCES OF THE CZECH REPUBLIC, Czech Republic ; M. Vohralík : UPMC UNIV. PARIS VI AND CNRS, France For the finite volume discretization of a second-order elliptic model problem, we derive a posteriori error estimates which take into account an inexact solution of the associated linear algebraic system. We show that the algebraic error can be bounded by constructing an equilibrated RaviartThomasNédélec discrete vector field whose divergence is given by a proper weighting of the residual vector. Next, claiming that the discretization error and the algebraic one should be in balance, we construct stopping criteria for iterative algebraic solvers. An attention is paid, in particular, to the conjugate gradient method which minimizes the energy norm of the algebraic error. Using this convenient balance, we also prove the efficiency of our a posteriori estimates ; i.e., we show that they also represent a lower bound, up to a generic constant, for the overall energy error. A local version of this result is also stated. This makes our approach suitable for adaptive mesh refinement which also takes into account the algebraic error. Numerical experiments illustrate the proposed estimates and construction of efficient stopping criteria for algebraic iterative solvers. For further details, see [ALG31]. 5.13 Estimating the backward error in LSQR. P. Jiránek : TECHNICAL UNIVERSITY OF LIBEREC AND CERFACS, Czech Republic and France ; D. Titley-Peloquin : MCGILL UNIVERSITY, SCHOOL OF COMPUTER SCIENCE, Canada In [ALG30], we propose practical stopping criteria for the iterative solution of sparse linear least squares (LS) problems. Although we focus our discussion on the algorithm LSQR of Paige and Saunders, the ideas discussed here may also be applicable to other algorithms. We review why the 2-norm of the projection of the residual vector onto the range of A is a useful measure of convergence, and show how this projection can be estimated efficiently at every iteration of LSQR. We also give practical and cheaply-computable estimates of the backward error for the LS problem. 5.14 A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics. X. Pinel : CERFACS, France The topic of [ALG66] is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown effcient for two-dimensional applications and the purpose of this thesis 20 Jan. 2010 – Dec. 2011
PARALLEL ALGORITHMS PROJECT is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver. CERFACS ACTIVITY REPORT 21
Page 1 and 2: CERFACS Scientific Activity Report
Page 3 and 4: Table des matières 1 Foreword xiii
Page 5 and 6: 9 Publications 40 9.1 Books . . . .
Page 7 and 8: 3 The OpenPALM coupler 104 3.1 Intr
Page 9 and 10: Table des figures CERFACS chart as
Page 11 and 12: TABLE DES FIGURES 6 Computational F
Page 13 and 14: Foreword Welcome to the 2010-2011 S
Page 15 and 16: CERFACS STRUCTURE CERFACS organizat
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Page 33 and 34: 3 List of Members of HiePACS HiePAC
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1 Introduction Data assimilation is
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DATA ASSIMILATION 2.3 Calibrating o
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3 Data assimilation for atmospheric
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DATA ASSIMILATION BECM using or not
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DATA ASSIMILATION the potential vor
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DATA ASSIMILATION A two years simul
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DATA ASSIMILATION FIG. 4.1: Reducti
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DATA ASSIMILATION FIG. 4.3: April 2
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DATA ASSIMILATION by a surface mode
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6 Data assimilation with EDF neutro
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DATA ASSIMILATION demonstrate that
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DATA ASSIMILATION [DA13] S. Massart
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4 Coupling tools and HPC Climate Mo
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2 The OASIS coupler The OASIS coupl
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THE OASIS COUPLER 2.3 OASIS4 Since
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3 The OpenPALM coupler 3.1 Introduc
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THE OPENPALM COUPLER In the NitroEu
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4 HPC Climate modelling 4.1 General
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5 Publications 5.1 Conference Proce
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5 Climate Variability and Global Ch
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2 Climate variability and predictab
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CLIMATE VARIABILITY AND PREDICTABIL
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CLIMATE VARIABILITY AND PREDICTABIL
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CLIMATE CHANGE AND IMPACT STUDIES a
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CLIMATE CHANGE AND IMPACT STUDIES b
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PUBLICATIONS [CM15] Y. Kwon, C. Des
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1 Introduction The CFD (Computation
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2 Combustion The research activity
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COMPUTATIONAL FLUID DYNAMICS rate-o
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COMPUTATIONAL FLUID DYNAMICS FIG. 2
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COMPUTATIONAL FLUID DYNAMICS an iss
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COMPUTATIONAL FLUID DYNAMICS TU Ber
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COMPUTATIONAL FLUID DYNAMICS design
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COMPUTATIONAL FLUID DYNAMICS (a) (b
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5 Publications 5.1 Conferences Proc
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COMPUTATIONAL FLUID DYNAMICS [CFD34
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7 Aviation and Environment
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INTRODUCTION instead of regular ker
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SIMULATIONS OF AIRCRAFT WAKES AND R
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LARGE SCALE ATMOSPHERIC COMPOSITION
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LARGE SCALE ATMOSPHERIC COMPOSITION
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PUBLICATIONS 4.2 Technical Reports
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CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011

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CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011