LaCàN - Laboratori de Càlcul Numèric
http://hdl.handle.net/2117/2072
2016-07-26T06:37:11ZTutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems
http://hdl.handle.net/2117/88137
Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems
Sevilla Càrdenas, Ruben; Huerta, Antonio
The HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.
2016-06-17T14:10:02ZSevilla Càrdenas, RubenHuerta, AntonioThe HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms
http://hdl.handle.net/2117/87479
Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms
Muñoz Romero, José; Jelenic, Gordan; Crisfield, M. A.
The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack-and-pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy-momentum conserving time-stepping algorithm
2016-05-30T08:41:00ZMuñoz Romero, JoséJelenic, GordanCrisfield, M. A.The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack-and-pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy-momentum conserving time-stepping algorithmSpectral analysis of the Beznar dam accelerogram. Comparison with results in the northeastern of Spain
http://hdl.handle.net/2117/87083
Spectral analysis of the Beznar dam accelerogram. Comparison with results in the northeastern of Spain
Canas Torres, José Antonio; Barbat Barbat, Horia Alejandro; Pujades Beneit, Lluís; Egozcue Rubí, Juan José; Sarrate Ramos, Josep
Numerical analysis applied to the Beznar dam accelerograms (longitudinal and transversal components) shows that the Fourier amplitude spectrum is a good approximation to the pseudo-velocity spectra. Thís fact makes possible to use displacement ar velocíty seismograrns to generate acceleration of the ground in places
where acceleration data are not available.
Maximae accelerations determined near and at the Beznar dam are compared wíth the predicted acceleration values far the regían compressed by the Pyrenees Mountains, the lberic System and the Catalonia Coastal Mountains usíng a established theoretical formula
far this region. Theoretical and observad values are consistent among them.
2016-05-17T07:55:41ZCanas Torres, José AntonioBarbat Barbat, Horia AlejandroPujades Beneit, LluísEgozcue Rubí, Juan JoséSarrate Ramos, JosepNumerical analysis applied to the Beznar dam accelerograms (longitudinal and transversal components) shows that the Fourier amplitude spectrum is a good approximation to the pseudo-velocity spectra. Thís fact makes possible to use displacement ar velocíty seismograrns to generate acceleration of the ground in places
where acceleration data are not available.
Maximae accelerations determined near and at the Beznar dam are compared wíth the predicted acceleration values far the regían compressed by the Pyrenees Mountains, the lberic System and the Catalonia Coastal Mountains usíng a established theoretical formula
far this region. Theoretical and observad values are consistent among them.Boundary element method based on preliminary discretization
http://hdl.handle.net/2117/87019
Boundary element method based on preliminary discretization
Poblet-Puig, Jordi; Valyaev, Valery; Shanin, Andrey
A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.
The final publication is available at Springer via http://dx.doi.org/10.1134/S2070048214020082
2016-05-12T13:41:06ZPoblet-Puig, JordiValyaev, ValeryShanin, AndreyA new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.An error estimator for separated representations of highly multidimensional models
http://hdl.handle.net/2117/87000
An error estimator for separated representations of highly multidimensional models
Asaad Ammaar, Mouafk; Chinesta, F.; Díez, F.; Huerta, Antonio
2016-05-12T10:49:40ZAsaad Ammaar, MouafkChinesta, F.Díez, F.Huerta, AntonioNumerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment
http://hdl.handle.net/2117/86965
Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment
Hospital Bravo, Raúl; Sarrate Ramos, Josep; Díez, Pedro
A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-015-1257-8
2016-05-11T17:52:15ZHospital Bravo, RaúlSarrate Ramos, JosepDíez, PedroA new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.Sliding contact conditions using the master-slave approach with application on geometrically non-linear beams
http://hdl.handle.net/2117/86751
Sliding contact conditions using the master-slave approach with application on geometrically non-linear beams
Muñoz Romero, José; Jelenic, Gordan
Frictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.
2016-05-09T09:26:06ZMuñoz Romero, JoséJelenic, GordanFrictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields
http://hdl.handle.net/2117/86637
Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields
Cottereau, Régis; Díez, Pedro
We present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.
2016-05-05T12:08:08ZCottereau, RégisDíez, PedroWe present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.AAR-based decomposition method for lower-bound limit analysis
http://hdl.handle.net/2117/86620
AAR-based decomposition method for lower-bound limit analysis
Muñoz Romero, José; Rabiei, Syednima
Despite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.
2016-05-05T08:50:31ZMuñoz Romero, JoséRabiei, SyednimaDespite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators
http://hdl.handle.net/2117/86474
Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators
Abdollahi Hosnijeh, Amir; Arias Vicente, Irene
Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.
2016-05-02T12:12:55ZAbdollahi Hosnijeh, AmirArias Vicente, IreneFlexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.