Articles de revista
http://hdl.handle.net/2117/6145
Tue, 24 Jan 2017 13:27:23 GMT2017-01-24T13:27:23ZA Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change
http://hdl.handle.net/2117/99876
A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change
Oliveira, Beñat; Afonso, Juan Carlos; Zlotnik, Sergio
This paper presents a particle-based Lagrangian–Eulerian algorithm for the solution of the unsteady advection–diffusion–reaction heat transfer equation with phase change. The algorithm combines a Lagrangian formulation for the advection + reaction problem with the Eulerian-based heat source method for the diffusion + phase change problem. The coupling between the Lagrangian and Eulerian subproblems is achieved with a phase change detector scheme based on a local latent heat balance and a consistent/conservative interpolation technique between Lagrangian particles and the Eulerian grid. This technique makes use of an auxiliary (finer) Eulerian grid that provides a simple and efficient method of tracking internal heterogeneities (e.g. phase boundaries), allows the use of higher order integration quadratures, and facilitates the implementation of multiscale techniques. The performance of the proposed algorithm is compared against one- and two-dimensional benchmark problems, i.e. pure rigid-body advection, isothermal and non-isothermal phase change, two-phase advective heat transfer and chemical reactions coupled with diffusion and advection. The numerical results confirm that the proposed solution method is accurate, oscillation-free and useful for and applicable to a wide range of fully coupled problems in science and engineering.
Mon, 23 Jan 2017 15:28:21 GMThttp://hdl.handle.net/2117/998762017-01-23T15:28:21ZOliveira, BeñatAfonso, Juan CarlosZlotnik, SergioThis paper presents a particle-based Lagrangian–Eulerian algorithm for the solution of the unsteady advection–diffusion–reaction heat transfer equation with phase change. The algorithm combines a Lagrangian formulation for the advection + reaction problem with the Eulerian-based heat source method for the diffusion + phase change problem. The coupling between the Lagrangian and Eulerian subproblems is achieved with a phase change detector scheme based on a local latent heat balance and a consistent/conservative interpolation technique between Lagrangian particles and the Eulerian grid. This technique makes use of an auxiliary (finer) Eulerian grid that provides a simple and efficient method of tracking internal heterogeneities (e.g. phase boundaries), allows the use of higher order integration quadratures, and facilitates the implementation of multiscale techniques. The performance of the proposed algorithm is compared against one- and two-dimensional benchmark problems, i.e. pure rigid-body advection, isothermal and non-isothermal phase change, two-phase advective heat transfer and chemical reactions coupled with diffusion and advection. The numerical results confirm that the proposed solution method is accurate, oscillation-free and useful for and applicable to a wide range of fully coupled problems in science and engineering.Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
http://hdl.handle.net/2117/99875
Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
Signorini, Marianna; Zlotnik, Sergio; Díez, Pedro
The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wave length. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. This optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced order models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model.
In particular, the proper generalized decomposition produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A proper generalized decomposition solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post-process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.
This is the peer reviewed version of the following article: [Signorini, M., Zlotnik, S., and Díez, P. (2017) Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems. Int. J. Numer. Meth. Engng, 109: 1085–1102. doi: 10.1002/nme.5313], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5313/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Mon, 23 Jan 2017 15:19:36 GMThttp://hdl.handle.net/2117/998752017-01-23T15:19:36ZSignorini, MariannaZlotnik, SergioDíez, PedroThe identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wave length. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. This optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced order models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model.
In particular, the proper generalized decomposition produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A proper generalized decomposition solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post-process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.Unified formulation of a family of iterative solvers for power systems analysis
http://hdl.handle.net/2117/99557
Unified formulation of a family of iterative solvers for power systems analysis
Borzacchiello, Domenico; Chinesta, Francisco; Malik, Muhammad H.; García Blanco, Raquel; Díez, Pedro
This paper illustrates the construction of a new class of iterative solvers for power flow calculations based on the method of Alternating Search Directions. This method is fit to the particular algebraic structure of the power flow problem resulting from the combination of a globally linear set of equations and nonlinear local relations imposed by power conversion devices, such as loads and generators. The choice of the search directions is shown to be crucial for improving the overall robustness of the solver. A noteworthy advantage is that constant search directions yield stationary methods that, in contrast with Newton or Quasi-Newton methods, do not require the evaluation of the Jacobian matrix. Such directions can be elected to enforce the convergence to the high voltage operative solution. The method is explained through an intuitive example illustrating how the proposed generalized formulation is able to include other nonlinear solvers that are classically used for power flow analysis, thus offering a unified view on the topic. Numerical experiments are performed on publicly available benchmarks for large distribution and transmission systems.
Tue, 17 Jan 2017 19:26:06 GMThttp://hdl.handle.net/2117/995572017-01-17T19:26:06ZBorzacchiello, DomenicoChinesta, FranciscoMalik, Muhammad H.García Blanco, RaquelDíez, PedroThis paper illustrates the construction of a new class of iterative solvers for power flow calculations based on the method of Alternating Search Directions. This method is fit to the particular algebraic structure of the power flow problem resulting from the combination of a globally linear set of equations and nonlinear local relations imposed by power conversion devices, such as loads and generators. The choice of the search directions is shown to be crucial for improving the overall robustness of the solver. A noteworthy advantage is that constant search directions yield stationary methods that, in contrast with Newton or Quasi-Newton methods, do not require the evaluation of the Jacobian matrix. Such directions can be elected to enforce the convergence to the high voltage operative solution. The method is explained through an intuitive example illustrating how the proposed generalized formulation is able to include other nonlinear solvers that are classically used for power flow analysis, thus offering a unified view on the topic. Numerical experiments are performed on publicly available benchmarks for large distribution and transmission systems.Sticking and sliding of lipid bilayers on deformable substrates
http://hdl.handle.net/2117/99478
Sticking and sliding of lipid bilayers on deformable substrates
Stubbington, L; Arroyo Balaguer, Marino; Staykova, M
We examine here the properties of lipid bilayers coupled to deformable substrates. We show that by changing the extent of the substrate hydrophilicity, we can control the membrane–substrate coupling and the response of the bilayer to strain deformation. Our results demonstrate that lipid bilayers coupled to flexible substrates can easily accommodate large strains, form stable protrusions and open reversibly pores. These properties, which differ significantly from those of free standing membranes, can extend the applications of the current lipid technologies. Moreover, such systems better capture the mechanical architecture of the cell interface and can provide insights into the capacity of cells to reshape and respond to mechanical perturbations.
Tue, 17 Jan 2017 13:23:54 GMThttp://hdl.handle.net/2117/994782017-01-17T13:23:54ZStubbington, LArroyo Balaguer, MarinoStaykova, MWe examine here the properties of lipid bilayers coupled to deformable substrates. We show that by changing the extent of the substrate hydrophilicity, we can control the membrane–substrate coupling and the response of the bilayer to strain deformation. Our results demonstrate that lipid bilayers coupled to flexible substrates can easily accommodate large strains, form stable protrusions and open reversibly pores. These properties, which differ significantly from those of free standing membranes, can extend the applications of the current lipid technologies. Moreover, such systems better capture the mechanical architecture of the cell interface and can provide insights into the capacity of cells to reshape and respond to mechanical perturbations.Non-regularised inverse finite element analysis for 3D traction force microscopy
http://hdl.handle.net/2117/99311
Non-regularised inverse finite element analysis for 3D traction force microscopy
Muñoz Romero, José
The tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.
Mon, 16 Jan 2017 12:38:07 GMThttp://hdl.handle.net/2117/993112017-01-16T12:38:07ZMuñoz Romero, JoséThe tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.Charting molecular free-energy landscapes with an atlas of collective variables
http://hdl.handle.net/2117/98674
Charting molecular free-energy landscapes with an atlas of collective variables
Hashemian, B.; Millán, Raúl Daniel; Arroyo Balaguer, Marino
Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and ß-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies.
Tue, 20 Dec 2016 19:26:33 GMThttp://hdl.handle.net/2117/986742016-12-20T19:26:33ZHashemian, B.Millán, Raúl DanielArroyo Balaguer, MarinoCollective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and ß-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies.Un estimador de error residual semiexplícito en cantidades de interés para un problema mecánico lineal
http://hdl.handle.net/2117/98648
Un estimador de error residual semiexplícito en cantidades de interés para un problema mecánico lineal
Rosales, R.; Díez, Pedro
We aim at defining a semi-explicit approach to estimate the error in quantities of interest associated with the Finite Element solution of a linear elasticity problem. The advocated procedure is split in two parts, an implicit error estimate for the adjoint problem and an explicit estimate assessing the error in the direct (primal) problem. The implicit part of the estimate (on the adjoint problem) embraces two phases, each consisting in projecting the error on
Tue, 20 Dec 2016 16:27:14 GMThttp://hdl.handle.net/2117/986482016-12-20T16:27:14ZRosales, R.Díez, PedroWe aim at defining a semi-explicit approach to estimate the error in quantities of interest associated with the Finite Element solution of a linear elasticity problem. The advocated procedure is split in two parts, an implicit error estimate for the adjoint problem and an explicit estimate assessing the error in the direct (primal) problem. The implicit part of the estimate (on the adjoint problem) embraces two phases, each consisting in projecting the error onVademecum-based GFEM (V-GFEM): optimal enrichment for transient problems
http://hdl.handle.net/2117/98640
Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems
Canales, Diego; Leygue, Adrien; Chinesta Soria, Francisco; González Ibáñez, David; Cueto Prendes, Elias; Feulvarch, Eric; Bergheau, Jean-Michel; Huerta, Antonio
This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum-generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.
This is the accepted version of the following article: [Canales, D., Leygue, A., Chinesta, F., González, D., Cueto, E., Feulvarch, E., Bergheau, J. -M., and Huerta, A. (2016) Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems. Int. J. Numer. Meth. Engng, 108: 971–989. doi: 10.1002/nme.5240.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5240/full
Tue, 20 Dec 2016 15:41:21 GMThttp://hdl.handle.net/2117/986402016-12-20T15:41:21ZCanales, DiegoLeygue, AdrienChinesta Soria, FranciscoGonzález Ibáñez, DavidCueto Prendes, EliasFeulvarch, EricBergheau, Jean-MichelHuerta, AntonioThis paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum-generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.Real-time simulation techniques for augmented learning in science and engineering
http://hdl.handle.net/2117/97463
Real-time simulation techniques for augmented learning in science and engineering
Quesada, C.; González, D.; Alfaro, Icíar; Cueto Prendes, Elias; Huerta, Antonio; Chinesta, Francisco
In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.
Tue, 29 Nov 2016 17:42:46 GMThttp://hdl.handle.net/2117/974632016-11-29T17:42:46ZQuesada, C.González, D.Alfaro, IcíarCueto Prendes, EliasHuerta, AntonioChinesta, FranciscoIn this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.Optimizing mesh distortion by hierarchical iteration relocation of the nodes on the CAD entities
http://hdl.handle.net/2117/90814
Optimizing mesh distortion by hierarchical iteration relocation of the nodes on the CAD entities
Ruiz Gironés, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Josep
Mesh untangling and smoothing is an important part of the meshing process to obtain high-quality discretizations. The usual approach consists on moving the position of the interior nodes while considering fixed the position of the boundary ones. However, the boundary nodes may constrain the quality of the whole mesh, and high-quality elements may not be generated. Specifically, thin regions in the geometry or special configurations of the boundary edges may induce low-quality elements. To overcome this drawback, we present a smoothing and untangling procedure that moves the interior nodes as well as the boundary ones, via an optimization process. The objective function is defined as a regularized distortion of the elements, and takes the nodal Cartesian coordinates as input arguments. When dealing with surface and edge nodes, the objective function uses the nodal parametric coordinates in order to avoid projecting them to the boundary. The novelty of the approach is that we consider a single target objective function (mesh distortion) where all the nodes, except the vertex nodes, are free to move on the corresponding CAD entity. Although the objective function is defined globally, for implementation purposes we propose to perform a node-by-node process. To minimize the objective function, we consider a block iterated non-linear Gauss-Seidel method using a hierarchical approach. That is, we first smooth the edge nodes, then the face nodes, and finally the inner nodes. This process is iterated using a node-by-node Gauss-Seidel approach until convergence is achieved.
Tue, 18 Oct 2016 07:55:09 GMThttp://hdl.handle.net/2117/908142016-10-18T07:55:09ZRuiz Gironés, EloiRoca Navarro, Francisco JavierSarrate Ramos, JosepMesh untangling and smoothing is an important part of the meshing process to obtain high-quality discretizations. The usual approach consists on moving the position of the interior nodes while considering fixed the position of the boundary ones. However, the boundary nodes may constrain the quality of the whole mesh, and high-quality elements may not be generated. Specifically, thin regions in the geometry or special configurations of the boundary edges may induce low-quality elements. To overcome this drawback, we present a smoothing and untangling procedure that moves the interior nodes as well as the boundary ones, via an optimization process. The objective function is defined as a regularized distortion of the elements, and takes the nodal Cartesian coordinates as input arguments. When dealing with surface and edge nodes, the objective function uses the nodal parametric coordinates in order to avoid projecting them to the boundary. The novelty of the approach is that we consider a single target objective function (mesh distortion) where all the nodes, except the vertex nodes, are free to move on the corresponding CAD entity. Although the objective function is defined globally, for implementation purposes we propose to perform a node-by-node process. To minimize the objective function, we consider a block iterated non-linear Gauss-Seidel method using a hierarchical approach. That is, we first smooth the edge nodes, then the face nodes, and finally the inner nodes. This process is iterated using a node-by-node Gauss-Seidel approach until convergence is achieved.