1,721,078 research outputs found
A parallel algorithm for the solution of large-scale nonconforming fluid-structure interaction problems in hemodynamics
No full textIn this work we address the numerical solution of large scale fluid-structure interaction problems when nonconforming grids and/or nonconforming finite elements discretizations are used at the interface separating the fluid and structure physical domains. To deal with nonconforming fluid-structure discretizations we use the INTERNODES method (INTER-polation for Nonconforming DEcompositionS) formerly introduced in [6] for the solution of elliptic PDEs on nonconforming domain decomposition. To cope with the high computational complexity of the three dimensional FSI problem obtained after spatial and temporal discretization, we use the block parallel preconditioner FaCSI [7]. A numerical investigation of the accuracy properties of INTERNODES applied to the nonconforming FSI problem is carried out for the simulation of the pressure wave propagation in a straight elastic cylinder. Finally, we study the scalability performance of the FaCSI preconditioner in the nonconforming case by solving a large-scale nonconforming FSI problem in a patient-specific arterial bypass
Multi space reduced basis preconditioners for large-scale parametrized PDEs
Full text linkIn this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, which plays the role of coarse component, and a 'traditional"" fine-grid preconditioner, such as one-level additive Schwarz, block Gauss-Seidel, or block Jacobi preconditioners. The coarse component is built upon a new multi space reduced basis (MSRB) method that we introduce for the first time in this paper, where a reduced basis space is built through the proper orthogonal decomposition algorithm at each step of the iterative method at hand, like the flexible GMRES method. MSRB strategy consists in building reduced basis spaces that are well suited to perform a single iteration, by addressing the error components which have not been treated yet. The Krylov iterations employed to solve the resulting preconditioned system target small tolerances with a very small iteration count and in a very short time, showing good optimality and scalability properties. Simulations are carried out to evaluate the performance of the proposed preconditioner in different large-scale computational settings related to parametrized advection diffusion equations and compared with the current state-of-the-art algebraic multigrid preconditioners
A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations
Full text linkWe analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameter-dependent elliptic partial differential equations (PDEs). In order to exploit the parametric dependence of thePDE, the proposed preconditioner takes advantage of the reduced basis (RB) method within the preconditioned iterative solver employed to solve the linear system, and combines a RB solver, playing the role of coarse component, with a traditional fine grid (such as Additive Schwarz or block Jacobi) preconditioner. A sequence of RB spaces is required to handle the approximation of the error-residual equation at each step of the iterative method at hand, whence the name of Multi Space Reduced Basis (MSRB) method. In this paper, a numerical investigation of the proposed technique is carried on in the case of a Richardson iterative method, and then extended to the flexible GMRES method, in order to solve parameterized advection-diffusion problems. Particular attention is payed to the impact of anisotropic diffusion coefficients and (possibly dominant) transport terms on the proposed preconditioner, by carrying out detailed comparisons with the current state of the art algebraic multigrid preconditionersCMCSSCI-SB-SDThis article is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Licens
FaCSI: A block parallel preconditioner for fluid–structure interaction in hemodynamics
No full textModeling Fluid–Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate that it exploits the Factorized form of the linearized FSI matrix, the use of static Condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for saddle-point problems. FaCSI is built upon a block Gauss–Seidel factorization of the FSI Jacobian matrix and it uses ad-hoc preconditioners for each physical component of the coupled problem, namely the fluid, the structure and the geometry. In the fluid subproblem, after operating static condensation of the interface fluid variables, we use a SIMPLE preconditioner on the reduced fluid matrix. Moreover, to efficiently deal with a large number of processes, FaCSI exploits efficient single field preconditioners, e.g., based on domain decomposition or the multigrid method. We measure the parallel performances of FaCSI on a benchmark cylindrical geometry and on a problem of physiological interest, namely the blood flow through a patient-specific femoropopliteal bypass. We analyze the dependence of the number of linear solver iterations on the cores count (scalability of the preconditioner) and on the mesh size (optimality)
INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces
No full textWe are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used from the two sides, or even to a geometrical mismatch. Across each interface, one subdomain is identified as master and the other as slave. We consider Galerkin methods for the discretization (such as finite element or spectral element methods) that make use of two interpolants for transferring information across the interface: one from master to slave and another one from slave to master. The former is used to ensure continuity of the primal variable (the problem solution), while the latter that of the dual variable (the normal flux). In particular, since the dual variable is expressed in weak form, we first compute a strong representation of the dual variable from the slave side, then interpolate it, transform the interpolated quantity back into weak form and eventually assign it to the master side. In case of slightly non-matching geometries, we use a radial-basis function interpolant instead of Lagrange interpolant. The proposed method is named INTERNODES (INTERpolation for NOnconforming DEcompositionS): it can be regarded as an alternative to the mortar element method and it is simpler to implement in a numerical code. We show on two dimension al problems that by using the Lagrange interpolation we obtain at least as good convergence results as with the mortar element method with any order of polynomials. When using low order polynomials, the radial-basis interpolant leads to the same convergence properties as the Lagrange interpolant. We conclude with a comparison between INTERNODES and a standard conforming approximation in a three dimensional case
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Parameter estimates for the Relaxed Dimensional Factorization preconditioner and application to hemodynamics
Full text linkWe present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems from incompressible flow simulations, first introduced in Benzi et al. (2011). This method contains a parameter α > 0, to be chosen by the user. Previous works provided an estimate of α in the 2D case using Local Fourier Analysis. A novel algebraic estimation technique for finding a suitable value of the RDF parameter in both the 2D and the 3D case with arbitrary geometries is proposed. This technique is tested on a variety of discrete saddle point problems arising from the approximation of the Navier-Stokes equations using a Marker-and-Cell scheme and a finite element one. We also show results for a large-scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
