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• Performance of mixed formulations for the particle finite element method in soil mechanics problems

  L. Monforte, J. Carbonell, M. Arroyo, A. Gens

  Comp. Part. Mech (2016). (Preprint) Vol. 4 (3), pp. 269-284

  
  

  Abstract

  This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy’s law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

  Abstract
  This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle [...]

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• Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM)

  J. Rodríguez, J. Carbonell, J. Cante, J. Oliver

  Int. J. Solids and Structures (2017). Vol. 120, pp. 81-120

  
  

  Abstract

  This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools.

  Abstract
  This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration [...]

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• Coronal advanced flap in combination with a connective tissue graft. Is the thickness of the flap a predictor for root coverage? A prospective clinical study

  T. Garces-McIntyre, J. Carbonell, L. Vallcorba, A. Santos, C. Valles, J. Nart

  Journal of Clinical Periodontology (2017). Vol. 44 (9), pp. 933-940

  
  

  Abstract

  Aim Evaluate if there is any relationship between the flap thickness (FT) and the presence of complete root coverage (CRC) when performing coronally advanced flaps in combination with a connective tissue graft (CTG). Materials and methods Prospective clinical study, in which multiple Miller class I and II recessions were treated with a coronally advanced flap and a CTG standardized at 1 mm of thickness. Individual stents permitted repeated measurements of conventional periodontal parameters at the same point. The primary outcome variable was CRC. Secondary outcomes were recession reduction, gingival thickness and width of keratinized tissue (KT) achieved at 6 months post‐surgery. Results Forty‐five recessions (2.4 ± 0.75 mm) were treated in 20 patients. Mean root coverage was 93.4 ± 10.98%; 65% achieved CRC. The mean FT was 1.01 mm ± 0.64 mm and 1.01 ± 0.61 mm at 2 and 5 mm from the gingival margin, respectively. No relationship could be found between FT and CRC (p > .05). Statistical significant changes (p < .05) were observed for recession depth, clinical attachment level, KT and soft tissue thickness at the end of the study. Conclusions Flap thickness seems not to be a predictor for CRC when performing a coronally advanced flap plus a CTG. This technique may be of choice when treating thin biotypes.

  Abstract
  Aim Evaluate if there is any relationship between the flap thickness (FT) and the presence of complete root coverage (CRC) when performing coronally advanced flaps in [...]

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• Generation of segmental chips in metal cutting modeled with the PFEM

  J. Prieto, J. Carbonell, J. Cante, J. Oliver, P. Jonsén

  Computational Mechanics (2018). Vol. 61 (6), pp. 639-655

  
  

  Abstract

  The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

  Abstract
  The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining [...]

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• FEMPAR: an object-oriented parallel finite element framework

  S. Badia, A. Martín, J. Principe

  Archives of Comp. Meths. Engng. (2018). Vol. 25 (2), pp. 195-271

  
  

  Abstract

  FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting state-of-the-art supercomputing resources. It is a highly modularized, flexible, and extensible library, that provides a set of modules that can be combined to carry out the different steps of the simulation pipeline. FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted finite element techniques on cut cells, combined with h-adaptivity. The linear solver module relies on state-of-the-art bulk-asynchronous implementations of multilevel domain decomposition solvers for the different discretization alternatives and block-preconditioning techniques for multiphysics problems. FEMPAR is a framework that provides users with out-of-the-box state-of-the-art discretization techniques and highly scalable solvers for the simulation of complex applications, hiding the dramatic complexity of the underlying algorithms. But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework. In this work, the first one in a series of articles about FEMPAR, we provide a detailed introduction to the software abstractions used in the discretization module and the related geometrical module. We also provide some ingredients about the assembly of linear systems arising from finite element discretizations, but the software design of complex scalable multilevel solvers is postponed to a subsequent work.

  Abstract
  FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by [...]

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• Driving mechanisms and streamwise homogeneity in molecular dynamics simulations of nanochannel flows

  J. Principe, V. Bitrián

  Physical review fluids (2018). (Preprint) Vol. 3 (1), pp. 1-16

  
  

  Abstract

  In molecular dynamics simulations, nanochannel flows are usually driven by a constant force, that aims to represent a pressure difference between inlet and outlet, and periodic boundary conditions are applied in the streamwise direction resulting in an homogeneous flow. The homogeneity hypothesis can be eliminated adding reservoirs at the inlet and outlet of the channel which permits us to predict streamwise variation of flow properties. It also opens the door to drive the flow by applying a pressure gradient instead of a constant force. We analyze the impact of these modeling modifications in the prediction of the flow properties, and we show when they make a difference with respect to the standard approach. It turns out that both assumptions are irrelevant when low pressure differences are considered, but important differences are observed at high pressure differences. They include the density and velocity variation along the channel (the mass flow rate is constant) but, more importantly, the temperature increase and slip length decrease. Because viscous heating is important at high shear rates, these modeling issues are also linked to the use of thermostating procedures. Specifically, selecting the region where the thermostat is applied has a critical influence on the results. Whereas in the traditional homogeneous model the choices are limited to the fluid and/or the wall, in the inhomogeneous cases the reservoirs are also available, which permits us to leave the region of interest, the channel, unperturbed.

  Abstract
  In molecular dynamics simulations, nanochannel flows are usually driven by a constant force, that aims to represent a pressure difference between inlet and outlet, and periodic [...]

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• Multilevel balancing domain decomposition at extreme scales

  S. Badia, A. Martín, J. Principe

  SIAM J. Numer. Anal. (2016). (preprint) Vol. 38 (1), pp. C22-C52

  
  

  Abstract

  In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition by constraints (MLBDDC) preconditioner. The implementation highly relies on subcommunicators in order to achieve the desired effect of coarse-grain overlapping of computation and communication, and communication and communication among levels in the hierarchy (namely, interlevel overlapping). Essentially, the main communicator is split into as many nonoverlapping subsets of message-passing interface (MPI) tasks (i.e., MPI subcommunicators) as levels in the hierarchy. Provided that specialized resources (cores and memory) are devoted to each level, a careful rescheduling and mapping of all the computations and communications in the algorithm lets a high degree of overlapping be exploited among levels. All subroutines and associated data structures are expressed recursively, and therefore MLBDDC preconditioners with an arbitrary number of levels can be built while re-using significant and recurrent parts of the codes. This approach leads to excellent weak scalability results as soon as level-1 tasks can fully overlap coarser-levels duties. We provide a model to indicate how to choose the number of levels and coarsening ratios between consecutive levels and determine qualitatively the scalability limits for a given choice. We have carried out a comprehensive weak scalability analysis of the proposed implementation for the three-dimensional Laplacian and linear elasticity problems on structured and unstructured meshes. Excellent weak scalability results have been obtained up to 458,752 IBM BG/Q cores and 1.8 million MPI being, being the first time that exact domain decomposition preconditioners (only based on sparse direct solvers) reach these scales. (An erratum is attached.)

  Abstract
  In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition [...]

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• Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows

  O. Colomés, S. Badia, J. Principe

  Comput. Methods Appl. Mech. Engrg., (2016). Vol. 304 (1), pp. 294-318

  
  

  Abstract

  The variational multiscale method thought as an implicit large eddy simulation model for turbulent flows has been shown to be an alternative to the widely used physical-based models. This method is traditionally combined with equal-order velocity–pressure pairs, since it provides pressure stabilization. In this work, we consider a different approach, based on inf–sup stable elements and convection-only stabilization. In order to do so, we consider a symmetric projection stabilization of the convective term using an orthogonal subscale decomposition. The accuracy and efficiency of this method compared with residual-based algebraic subgrid scales and orthogonal subscales methods for equal-order interpolation is assessed in this paper. Moreover, when inf–sup stable elements are used, the grad–div stabilization term has been shown to be essential to guarantee accurate solutions. Hence, a study of the influence of such term in the large eddy simulation of turbulent incompressible flows is also performed. Furthermore, a recursive block preconditioning strategy has been considered for the resolution of the problem with an implicit treatment of the projection terms. Two different benchmark tests have been solved: the Taylor–Green Vortex flow with Re=1600, and the Turbulent Channel Flow at Reτ=395 and Reτ=590.

  Abstract
  The variational multiscale method thought as an implicit large eddy simulation model for turbulent flows has been shown to be an alternative to the widely used physical-based [...]

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• On the scalability of inexact balancing domain decomposition by constraints with overlapped coarse/fine corrections

  S. Badia, A. Martín, J. Principe

  Parallel Computing (2015). (Preprint) Vol. 50, pp. 1-24

  
  

  Abstract

  In this work, we analyze the scalability of inexact two-level balancing domain decomposition by constraints (BDDC) preconditioners for Krylov subspace iterative solvers, when using a highly scalable asynchronous parallel implementation where fine and coarse correction computations are overlapped in time. This way, the coarse-grid problem can be fully overlapped by fine-grid computations (which are embarrassingly parallel) in a wide range of cases. Further, we consider inexact solvers to reduce the computational cost/complexity and memory consumption of coarse and local problems and boost the scalability of the solver. Out of our numerical experimentation, we conclude that the BDDC preconditioner is quite insensitive to inexact solvers. In particular, one cycle of algebraic multigrid (AMG) is enough to attain algorithmic scalability. Further, the clear reduction of computing time and memory requirements of inexact solvers compared to sparse direct ones makes possible to scale far beyond state-of-the-art BDDC implementations. Excellent weak scalability results have been obtained with the proposed inexact/overlapped implementation of the two-level BDDC preconditioner, up to 93,312 cores and 20 billion unknowns on JUQUEEN. Further, we have also applied the proposed setting to unstructured meshes and partitions for the pressure Poisson solver in the backward-facing step benchmark domain.

  Abstract
  In this work, we analyze the scalability of inexact two-level balancing domain decomposition by constraints (BDDC) preconditioners for Krylov subspace iterative solvers, when [...]

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• A highly scalable parallel implementation of balancing domain decomposition by constraints

  S. Badia, A. Martín, J. Principe

  SIAM J. Numer. Anal. (2014). (preprint) Vol. 36 (2), pp, C190-C218

  
  

  Abstract

  In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then re-scheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments, that includes weak scalability analyses, with structured and unstructured meshes, and exact and inexact solvers for the 3D Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-memory machines. This experimental study reveals remarkable weak scalability in the solution of problems with thousands of millions of unknowns on several tens of thousands of computational cores.

  Abstract
  In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid [...]

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