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http://hdl.handle.net/10985/9957
Natural Element Method for the Simulation of Structures and Processes
CHINESTA, Francisco; CESCOTTO, Serge; CUETO, Elias; LORONG, Philippe
The Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/99572011-01-01T00:00:00ZCHINESTA, FranciscoCESCOTTO, SergeCUETO, EliasLORONG, PhilippeThe Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.Separated representation of incremental elastoplastic simulations
http://hdl.handle.net/10985/9514
Separated representation of incremental elastoplastic simulations
NASRI, Mohamed Aziz; AGUADO, Jose Vicente; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco; MOREL, Franck; ROBERT, Camille; EL AREM, Saber
Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/95142015-01-01T00:00:00ZNASRI, Mohamed AzizAGUADO, Jose VicenteAMMAR, AmineCUETO, EliasCHINESTA, FranciscoMOREL, FranckROBERT, CamilleEL AREM, SaberForming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.PGD-Based Computational Vademecum for Efficient Design, Optimization and Control
http://hdl.handle.net/10985/10241
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control
CHINESTA, Francisco; LEYGUE, Adrien; BORDEU, Felipe; AGUADO, Jose Vicente; CUETO, Elias; GONZALEZ, David; ALFARO, Iciar; AMMAR, Amine; HUERTA, Antonio
In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102412013-01-01T00:00:00ZCHINESTA, FranciscoLEYGUE, AdrienBORDEU, FelipeAGUADO, Jose VicenteCUETO, EliasGONZALEZ, DavidALFARO, IciarAMMAR, AmineHUERTA, AntonioIn this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.Nonincremental proper generalized decomposition solution of parametric uncoupled models defined in evolving domains
http://hdl.handle.net/10985/10287
Nonincremental proper generalized decomposition solution of parametric uncoupled models defined in evolving domains
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
This work addresses the recurrent issue related to the existence of reduced bases related to the solution of parametric models defined in evolving domains. In this first part of the work, we address the case of decoupled kinematics, that is, models whose solution does not affect the domain in which they are defined. The chosen framework considers an updated Lagrangian description of the kinematics, solved by using natural neighbor Galerkin methods within a nonincremental space–time framework that can be generalized for addressing parametric models. Examples showing the performance and potentialities of the proposed methodology are included.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/102872012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThis work addresses the recurrent issue related to the existence of reduced bases related to the solution of parametric models defined in evolving domains. In this first part of the work, we address the case of decoupled kinematics, that is, models whose solution does not affect the domain in which they are defined. The chosen framework considers an updated Lagrangian description of the kinematics, solved by using natural neighbor Galerkin methods within a nonincremental space–time framework that can be generalized for addressing parametric models. Examples showing the performance and potentialities of the proposed methodology are included.Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
http://hdl.handle.net/10985/10254
Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
ALFARO, Iciar; GONZALEZ, David; BORDEU, Felipe; LEYGUE, Adrien; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
Simulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102542014-01-01T00:00:00ZALFARO, IciarGONZALEZ, DavidBORDEU, FelipeLEYGUE, AdrienAMMAR, AmineCUETO, EliasCHINESTA, FranciscoSimulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.Wavelet-based multiscale proper generalized decomposition
http://hdl.handle.net/10985/13282
Wavelet-based multiscale proper generalized decomposition
ANGEL, Leon; BARASINSKI, Anais; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco
Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132822018-01-01T00:00:00ZANGEL, LeonBARASINSKI, AnaisABISSET-CHAVANNE, EmmanuelleCUETO, EliasCHINESTA, FranciscoSeparated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.Parametric solutions involving geometry: A step towards efficient shape optimization
http://hdl.handle.net/10985/10244
Parametric solutions involving geometry: A step towards efficient shape optimization
AMMAR, Amine; HUERTA, Antonio; CHINESTA, Francisco; CUETO, Elias; LEYGUE, Adrien
Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102442014-01-01T00:00:00ZAMMAR, AmineHUERTA, AntonioCHINESTA, FranciscoCUETO, EliasLEYGUE, AdrienOptimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.Towards a high-resolution numerical strategy based on separated representations
http://hdl.handle.net/10985/6522
Towards a high-resolution numerical strategy based on separated representations
AMMAR, Amine; CUETO, Elias; GONZALEZ, David; CHINESTA, Francisco
Many models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/65222008-01-01T00:00:00ZAMMAR, AmineCUETO, EliasGONZALEZ, DavidCHINESTA, FranciscoMany models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
http://hdl.handle.net/10985/8467
Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
The numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84672012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThe numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.Proper generalized decomposition of time-multiscale models
http://hdl.handle.net/10985/8499
Proper generalized decomposition of time-multiscale models
AMMAR, Amine; CHINESTA, Francisco; CUETO, Elias; DOBLARÉ, Manuel
Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one-dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84992012-01-01T00:00:00ZAMMAR, AmineCHINESTA, FranciscoCUETO, EliasDOBLARÉ, ManuelModels encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one-dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration.