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Heinlein, A. (author), Rheinbach, Oliver (author), Röver, Friederike (author)The parallel performance of the three-level fast and robust overlapping Schwarz (FROSch) preconditioners is investigated for linear elasticity. The FROSch framework is part of the Trilinos software library and contains a parallel implementation of different preconditioners with energy minimizing coarse spaces of generalized Dryja--Smith--Widlund...journal article 2022
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Heinlein, A. (author), Klawonn, Axel (author), Knepper, Jascha (author), Rheinbach, Oliver (author), Widlund, Olof B. (author)A new reduced-dimension adaptive generalized Dryja-Smith-Widlund (GDSW) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be...journal article 2022
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Mororó, L. A. T. (author), van der Meer, F.P. (author)The thick level set (TLS) method has been proposed as a nonlocal damage model for the modeling of failure in solids being able to deal with crack initiation, branching, and merging. The nonlocality of the TLS is achieved by introducing a characteristic length into the problem. This way, the TLS does not suffer from spurious localization in the...journal article 2021
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Xiao, C. (author), Tian, Leng (author)This paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high-dimensional inversion problems. We fully replace the high-fidelity model with a set of subdomain linear models through integrating model linearization with smooth...journal article 2020
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Lloberas Valls, O. (author), Everdij, F.P.X. (author), Rixen, D.J. (author), Simone, A. (author), Sluys, L.J. (author)The multiscale framework presented in [1, 2] is assessed in this contribution for a study of random heterogeneous materials. Results are compared to direct numerical simulations (DNS) and the sensitivity to user-defined parameters such as the domain decomposition type and initial coarse scale resolution is reported. The parallel performance of...conference paper 2013
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Lloberas Valls, O. (author), Everdij, F.P.X. (author), Rixen, D.J. (author), Simone, A. (author), Sluys, L.J. (author)Concurrent multiscale analysis of quasi-brittle heterogeneous materials such as concrete and rock is conducted employing non-overlapping domain decomposition techniques. Initially a coarse discretization with effective properties is considered at each domain. A zoom-in technique is performed at those domains in which non-linearities take place....conference paper 2012
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Collignon, T.P. (author)This dissertation deals mainly with the design, implementation, and analysis of efficient iterative solution methods for large sparse linear systems on distributed and heterogeneous computing systems as found in Grid computing. First, a case study is performed on iteratively solving large symmetric linear systems on both a multi–cluster and a...doctoral thesis 2011
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Van Esch, J.M. (author)Natural geological formations generally show multiscale structural and functional heterogeneity evolving over many orders of magnitude in space and time. In subsurface hydrological simulations the geological model focuses on the structural hierarchy of physical sub units and the flow model addresses the functional hierarchy of the flow process....doctoral thesis 2010
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Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...journal article 2010
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Lloberas Valls, O. (author), Rixen, D.J. (author), Simone, A. (author), Sluys, L.J. (author)In this contribution we describe a methodology for the study of softening brittle materials at different scales of observation. The goal is to account for a higher resolution at those areas that undergo the non-linear processes. We apply the FETI (Finite Element Tearing and Interconnecting) technique to glue different domain resolutions during...conference paper 2009
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Tang, J.M. (author)The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite coefficient matrix. However, if the preconditioned coefficient matrix is ill-conditioned, the convergence of the PCG method typically deteriorates. Instead, a two-level PCG...doctoral thesis 2008
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Utzmann, J. (author), Munz, C.D. (author)This paper advances the idea of a heterogeneous domain decomposition for Computational Aeroacoustics (CAA). Direct simulations of aeroacoustic problems are accelerated by sub-dividing the computational domain into smaller domains. In each of these sub-domains the equations, the discretization, the mesh and the time step may be different and are...conference paper 2006
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Jund, S. (author), Sonnendrücker, E. (author)We develop a numerical method for solving the linearized acoustic equations on a grid involving zones with cells of very different sizes, in order for example to compute sources coming from the flow on a fine grid. The method is based on domain decomposition techniques which lead us to introduce two auxiliary problems and show theoretically how...conference paper 2006
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Gamnitzer, P. (author), Wall, W.A. (author)This note discusses a combination of the Chimera fixed grid approach and Arbitrary Lagrangean Eulerian ('ALE') based methods for large deformation fluid structure interaction ('FSI'). The governing equations for incompressible flows in an Eulerian framework, a rotating frame of reference and an ALE-setting are discussed in order to point out the...conference paper 2006
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Ivanov, E.G. (author), Andrä, H. (author), Kudryavtsev, A.N. (author)The desire to simulate more and more geometrical and physical features of technical structures and the availability of parallel computers and parallel numerical solvers which can exploit the power of these machines have lead to a steady increase in the number of grid elements used. Memory requirements and computational time are too large for...conference paper 2006
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Lovgren, A.E. (author), Maday, Y. (author), Ronquist, E.M. (author)The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations within domains belonging to a certain class. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into...conference paper 2006
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Bijl, H. (author), Van Zuijlen, A.H. (author), Bosscher, S. (author)In this paper we use the multigrid algorithm - commonly used to improve the efficiency of the flow solver - to improve the efficiency of partitioned fluid-structure interaction iterations. Coupling not only the structure with the fine flow mesh, but also with the coarse flow mesh (often present due to the multigrid scheme) leads to a significant...conference paper 2006
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Bijl, H. (author), Van Zuijlen, A.H. (author), Bosscher, S. (author)In this paper we use the multigrid algorithm - commonly used to improve the efficiency of the flow solver - to improve the efficiency of partitioned fluid-structure interaction iterations. Coupling not only the structure with the fine flow mesh, but also with the coarse flow mesh (often present due to the multigrid scheme) leads to a significant...conference paper 2006
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Erlangga, Y.A. (author)In this report, several numerical aspects and diculties for solving a linear system derived from the time-harmonic wave equations are overviewed. The presentation begins with the derivation of the governing equation for waves propagating in general inhomogeneous media. Due to the need of numerical solutions, various discretizations based on...report 2002
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- Brakkee, E. (author) doctoral thesis 1996