LaCàN - Laboratori de Càlcul Numèric
http://hdl.handle.net/2117/2072
2016-10-24T07:06:50ZHybrid cell centred/vertex model for large tissue deformations
http://hdl.handle.net/2117/90839
Hybrid cell centred/vertex model for large tissue deformations
Muñoz Romero, José; Mosafa, Payman; Mao, Yanlan; Tetley, Rob; Asadipour, Nina; Rodríguez Ferran, Antonio
Macroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling
and cell intercalation. We here present a computational approach that can handle the
two types of deformations, and also take into account the active cell response. The model resorts
to cell-centred techniques, where particles represent cell nuclei, and to vertex models, where the
vertices represent cell boundaries. This hybrid approach allows to consider separately intracellular
and inter-cellular forces, and at the same time impose cell incompressibility.
In the proposed model, the cell boundaries (defined by vertices) and cell nuclei (or cellcentres)
networks are coupled through an interpolation scheme, which is eventually relaxed in
order to smooth the cell boundaries. We show that this coupling between the two networks
modifies the equilibrium equations and stabilises the vertex network. Incompressibility is implemented
through a penalty method. The resulting model can be implemented in two- and
three-dimensions, and is complemented with active rheological models.
We apply the model to simulate the stretching and relaxation of cell monolayers, and to
simulate wound healing process in the wing disc of Drosophila fly embryo. We show that the
numerical results agree with the experimental measurements.
2016-10-18T10:43:30ZMuñoz Romero, JoséMosafa, PaymanMao, YanlanTetley, RobAsadipour, NinaRodríguez Ferran, AntonioMacroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling
and cell intercalation. We here present a computational approach that can handle the
two types of deformations, and also take into account the active cell response. The model resorts
to cell-centred techniques, where particles represent cell nuclei, and to vertex models, where the
vertices represent cell boundaries. This hybrid approach allows to consider separately intracellular
and inter-cellular forces, and at the same time impose cell incompressibility.
In the proposed model, the cell boundaries (defined by vertices) and cell nuclei (or cellcentres)
networks are coupled through an interpolation scheme, which is eventually relaxed in
order to smooth the cell boundaries. We show that this coupling between the two networks
modifies the equilibrium equations and stabilises the vertex network. Incompressibility is implemented
through a penalty method. The resulting model can be implemented in two- and
three-dimensions, and is complemented with active rheological models.
We apply the model to simulate the stretching and relaxation of cell monolayers, and to
simulate wound healing process in the wing disc of Drosophila fly embryo. We show that the
numerical results agree with the experimental measurements.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, Xevi; 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.
2016-10-18T07:55:09ZRuiz Gironés, EloiRoca Navarro, XeviSarrate 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.Adaptividade e estimativas de erro orientadas por metas aplicadas a um benchmark test de propagação de onda
http://hdl.handle.net/2117/90741
Adaptividade e estimativas de erro orientadas por metas aplicadas a um benchmark test de propagação de onda
Steffens, Lindaura; Díez, Pedro; Parés Mariné, Núria; Alves, Marcelo Krajnc
O objetivo deste artigo é estudar a eficiência e a robustez de técnicas adaptativas e estimativas de erro orientadas por metas para um benchmark test. As técnicas utilizadas aqui são baseadas em um simples pós-processo das aproximacções de elementos finitos. As estimativas de erro orientadas por metas são obtidas por analisar o problema direto e um problema auxiliar, o qual está relacionado com a quantidade de interesse específico. O procedimento proposto é válido para quantidades lineares e não-lineares. Além disso, são discutidas diferentes representacções para o erro e é analisada a influência do erro de dispersão. Os resultados numéricos mostram que as estimativas de erro fornecem boas aproximações ao erro real e que a técnica de refino adaptativo proposta conduz a uma redução mais rápida do erro.
2016-10-13T12:42:25ZSteffens, LindauraDíez, PedroParés Mariné, NúriaAlves, Marcelo KrajncO objetivo deste artigo é estudar a eficiência e a robustez de técnicas adaptativas e estimativas de erro orientadas por metas para um benchmark test. As técnicas utilizadas aqui são baseadas em um simples pós-processo das aproximacções de elementos finitos. As estimativas de erro orientadas por metas são obtidas por analisar o problema direto e um problema auxiliar, o qual está relacionado com a quantidade de interesse específico. O procedimento proposto é válido para quantidades lineares e não-lineares. Além disso, são discutidas diferentes representacções para o erro e é analisada a influência do erro de dispersão. Os resultados numéricos mostram que as estimativas de erro fornecem boas aproximações ao erro real e que a técnica de refino adaptativo proposta conduz a uma redução mais rápida do erro.Un método de captura de choques basado en las funciones de forma para Galerkin discontinuo de alto orden
http://hdl.handle.net/2117/90730
Un método de captura de choques basado en las funciones de forma para Galerkin discontinuo de alto orden
Casoni Rero, Eva; Peraire Guitart, Jaume; Huerta, Antonio
En este artículo se presenta un método de alto orden de Galerkin discontinuo para problemas de flujo com- presible, en los cuales es muy frecuente la aparición de choques. La estabilización se introduce mediante una nueva base de funciones. Esta base tiene la flexibilidad de variar localmente (en cada elemento) entre un espacio de funciones polinómicas continuas o un espacio de funciones polinómicas a trozos. Así, el método propuesto proporciona un puente entre los métodos estándar de alto orden de Galerkin disconti- nuo y los clásicos métodos de volúmenes finitos, manteniendo la localidad y compacidad del esquema. La variación de las funciones de la base se define automáticamente en función de la regularidad de la solución y la estabilización se introduce mediante el operador salto, estándar en los métodos Galerkin disconti- nuo. A diferencia de los clásicos métodos de limitadores de pendiente, la estrategia que se presenta es muy local y robusta, y es aplicable a cualquier orden de aproximación. Además, el método propuesto no requiere refinamiento adaptativo de la malla ni restricción del esquema de integración temporal. Se consideran varias aplicaciones de las ecuaciones de Euler que demuestran la validez y efectividad del método, especialmente para altos órdenes de aproximación.
2016-10-13T11:33:45ZCasoni Rero, EvaPeraire Guitart, JaumeHuerta, AntonioEn este artículo se presenta un método de alto orden de Galerkin discontinuo para problemas de flujo com- presible, en los cuales es muy frecuente la aparición de choques. La estabilización se introduce mediante una nueva base de funciones. Esta base tiene la flexibilidad de variar localmente (en cada elemento) entre un espacio de funciones polinómicas continuas o un espacio de funciones polinómicas a trozos. Así, el método propuesto proporciona un puente entre los métodos estándar de alto orden de Galerkin disconti- nuo y los clásicos métodos de volúmenes finitos, manteniendo la localidad y compacidad del esquema. La variación de las funciones de la base se define automáticamente en función de la regularidad de la solución y la estabilización se introduce mediante el operador salto, estándar en los métodos Galerkin disconti- nuo. A diferencia de los clásicos métodos de limitadores de pendiente, la estrategia que se presenta es muy local y robusta, y es aplicable a cualquier orden de aproximación. Además, el método propuesto no requiere refinamiento adaptativo de la malla ni restricción del esquema de integración temporal. Se consideran varias aplicaciones de las ecuaciones de Euler que demuestran la validez y efectividad del método, especialmente para altos órdenes de aproximación.Melt fracturing and healing: a mechanism for rhyolite magma degassing and origin of obsidian
http://hdl.handle.net/2117/90728
Melt fracturing and healing: a mechanism for rhyolite magma degassing and origin of obsidian
Cabrera, Agustín; Weinberg, Roberto F.; Wright, Heather M. N.; Zlotnik, Sergio; Cas, Ray A.F.
We present water content transects across a healed fault in pyroclastic obsidian from Lami pumice cone, Lipari, Italy, using synchrotron Fourier transform infrared spectroscopy. Results indicate that rhyolite melt degassed through the fault surface. Transects define a trough of low water content coincident with the fault trace, surrounded on either side by high-water-content plateaus. Plateaus indicate that obsidian on either side of the fault equilibrated at different pressure-temperature (P-T) conditions before being juxtaposed. The curves into the troughs indicate disequilibrium and water loss through diffusion. If we assume constant T, melt equilibrated at pressures differing by 0.74 MPa before juxtaposition, and the fault acted as a low-P permeable path for H2O that diffused from the glass within time scales of 10 and 30 min. Assuming constant P instead, melt on either side could have equilibrated at temperatures differing by as much as 100 °C, before being brought together. Water content on the fault trace is particularly sensitive to post-healing diffusion. Its preserved value indicates either higher temperature or lower pressure than the surroundings, indicative of shear heating and dynamic decompression. Our results reveal that water contents of obsidian on either side of the faults equilibrated under different P-T conditions and were out of equilibrium with each other when they were juxtaposed due to faulting immediately before the system was quenched. Degassing due to faulting could be linked to cyclical seismic activity and general degassing during silicic volcanic activity, and could be an efficient mechanism of producing low-water-content obsidian.
2016-10-13T11:13:13ZCabrera, AgustínWeinberg, Roberto F.Wright, Heather M. N.Zlotnik, SergioCas, Ray A.F.We present water content transects across a healed fault in pyroclastic obsidian from Lami pumice cone, Lipari, Italy, using synchrotron Fourier transform infrared spectroscopy. Results indicate that rhyolite melt degassed through the fault surface. Transects define a trough of low water content coincident with the fault trace, surrounded on either side by high-water-content plateaus. Plateaus indicate that obsidian on either side of the fault equilibrated at different pressure-temperature (P-T) conditions before being juxtaposed. The curves into the troughs indicate disequilibrium and water loss through diffusion. If we assume constant T, melt equilibrated at pressures differing by 0.74 MPa before juxtaposition, and the fault acted as a low-P permeable path for H2O that diffused from the glass within time scales of 10 and 30 min. Assuming constant P instead, melt on either side could have equilibrated at temperatures differing by as much as 100 °C, before being brought together. Water content on the fault trace is particularly sensitive to post-healing diffusion. Its preserved value indicates either higher temperature or lower pressure than the surroundings, indicative of shear heating and dynamic decompression. Our results reveal that water contents of obsidian on either side of the faults equilibrated under different P-T conditions and were out of equilibrium with each other when they were juxtaposed due to faulting immediately before the system was quenched. Degassing due to faulting could be linked to cyclical seismic activity and general degassing during silicic volcanic activity, and could be an efficient mechanism of producing low-water-content obsidian.Defining an2-disparity measure to check and improve the geometric accuracy of noninterpolating curved high-order meshes
http://hdl.handle.net/2117/90725
Defining an2-disparity measure to check and improve the geometric accuracy of noninterpolating curved high-order meshes
Ruiz Gironés, Eloi; Sarrate Ramos, Josep; Roca Navarro, Xevi
We define an2-disparity measure between curved high-order meshes and parameterized manifolds in terms of an2norm. The main application of the proposed definition is to measure and improve the distance between a curved
high-order mesh and a target parameterized curve or surface. The approach allows considering meshes with the nodes on top of the curve or surface (interpolative), or floating freely in the physical space (non-interpolative). To compute the
disparity measure, the average of the squared point-wise differences is minimized in terms of the nodal coordinates of an auxiliary parametric high-order mesh. To improve the accuracy of approximating the target manifold with a noninterpolating
curved high-order mesh, we minimize the square of the disparity measure expressed both in terms of the nodal coordinates of the physical and parametric curved high-order meshes. The proposed objective functions are
continuously differentiable and thus, we are able to use minimization algorithms that require the first or the second derivatives of the objective function. Finally, we present several examples that show that the proposed methodology
generates high-order approximations of the target manifold with optimal convergence rates for the geometric accuracy even when non-uniform parameterizations of the manifolds are prescribed. Accordingly, we can generate coarse curved high-order meshes significantly more accurate than finer low-order meshes that feature the same resolution.
2016-10-13T10:46:15ZRuiz Gironés, EloiSarrate Ramos, JosepRoca Navarro, XeviWe define an2-disparity measure between curved high-order meshes and parameterized manifolds in terms of an2norm. The main application of the proposed definition is to measure and improve the distance between a curved
high-order mesh and a target parameterized curve or surface. The approach allows considering meshes with the nodes on top of the curve or surface (interpolative), or floating freely in the physical space (non-interpolative). To compute the
disparity measure, the average of the squared point-wise differences is minimized in terms of the nodal coordinates of an auxiliary parametric high-order mesh. To improve the accuracy of approximating the target manifold with a noninterpolating
curved high-order mesh, we minimize the square of the disparity measure expressed both in terms of the nodal coordinates of the physical and parametric curved high-order meshes. The proposed objective functions are
continuously differentiable and thus, we are able to use minimization algorithms that require the first or the second derivatives of the objective function. Finally, we present several examples that show that the proposed methodology
generates high-order approximations of the target manifold with optimal convergence rates for the geometric accuracy even when non-uniform parameterizations of the manifolds are prescribed. Accordingly, we can generate coarse curved high-order meshes significantly more accurate than finer low-order meshes that feature the same resolution.A Reduced Order Modeling approach for optimal allocation of Distributed Generation in power distribution systems
http://hdl.handle.net/2117/89506
A Reduced Order Modeling approach for optimal allocation of Distributed Generation in power distribution systems
García Blanco, Raquel; Díez, Pedro; Borzacchiello, Domenico; Chinesta, Francisco
This paper presents an “offline-online” strategy for optimal allocation and sizing of Distributed Generation. In traditional optimization approaches, each function evaluation requires the solution of a power flow problem, which makes global optimality a computationally challenging goal. In the proposed strategy the power flow solver is invoked only once and a parametric solution is constructed with a monolithic solver. Despite the fact that the parametrized power flow equations result in a high-dimensional problem, the proposed algorithm is specifically designed to circumvent the curse of dimensionality. This is achieved through the application of Model Reduction, in particular the Proper Generalized Decomposition combined with a nonlinear solver. Numerical examples are carried out for showing the validity of the proposed method.
2016-09-02T14:17:08ZGarcía Blanco, RaquelDíez, PedroBorzacchiello, DomenicoChinesta, FranciscoThis paper presents an “offline-online” strategy for optimal allocation and sizing of Distributed Generation. In traditional optimization approaches, each function evaluation requires the solution of a power flow problem, which makes global optimality a computationally challenging goal. In the proposed strategy the power flow solver is invoked only once and a parametric solution is constructed with a monolithic solver. Despite the fact that the parametrized power flow equations result in a high-dimensional problem, the proposed algorithm is specifically designed to circumvent the curse of dimensionality. This is achieved through the application of Model Reduction, in particular the Proper Generalized Decomposition combined with a nonlinear solver. Numerical examples are carried out for showing the validity of the proposed method.Building performance at low frequency range including flanking transmissions
http://hdl.handle.net/2117/89418
Building performance at low frequency range including flanking transmissions
Guigou-Carter, Catherine; Poblet-Puig, Jordi
Recent researches have proposed alternative formulas for the estimation of the vibration reduction index (Kij) at junctions. Among other aspects, the new approaches propose different expressions for the low, mid and high frequency ranges; the current recommendation in the Annex E of EN 12354 standard provides a single value for the whole frequency range. Vibration reduction index can also be evaluated for specific junctions (dimensions, characteristics) representative of those in a particular building. This work analyses the potential effect that the use of the new vibration reduction index expressions can have in the prediction of global sound insulation outputs at low frequencies for different French traditional concrete based buildings. Measured acoustic performance is compared to predicted performance obtained following the EN 12354 approach.
2016-08-30T11:52:11ZGuigou-Carter, CatherinePoblet-Puig, JordiRecent researches have proposed alternative formulas for the estimation of the vibration reduction index (Kij) at junctions. Among other aspects, the new approaches propose different expressions for the low, mid and high frequency ranges; the current recommendation in the Annex E of EN 12354 standard provides a single value for the whole frequency range. Vibration reduction index can also be evaluated for specific junctions (dimensions, characteristics) representative of those in a particular building. This work analyses the potential effect that the use of the new vibration reduction index expressions can have in the prediction of global sound insulation outputs at low frequencies for different French traditional concrete based buildings. Measured acoustic performance is compared to predicted performance obtained following the EN 12354 approach.Amplified catalogue of vibration reduction index formulas for junctions based on numerical simulations
http://hdl.handle.net/2117/89415
Amplified catalogue of vibration reduction index formulas for junctions based on numerical simulations
Poblet-Puig, Jordi; Guigou-Carter, Catherine
The vibration reduction index (Kij) is a key parameter in the prediction of flanking transmissions according to the EN-12354 standard. Formulas for the evaluation of Kij in L, T and X junctions that depend on the mass ratio are available in the Annex E. Junctions of straight elements with different thickness or thin elastic layers are also included. However, other junction types that are important for building industry are not considered: H-shaped junctions, L or T junctions not forming a right angle, asymmetrical T-junctions , X-junctions where only one of the parts is different (thickness or material) from the other three. In the current research, expressions for these non-covered junctions are provided. They are obtained by means of numerical simulations based on the spectral and/or the standard finite element method. Kij is predicted for a large population of junctions, considering usual thicknesses and material combinations. Afterwards, an statistical treatment of the data is done in order to obtain simple but representative formulas that can easily be used in the daily acoustic projects or included in design software without the need of large computations.
2016-08-30T11:34:55ZPoblet-Puig, JordiGuigou-Carter, CatherineThe vibration reduction index (Kij) is a key parameter in the prediction of flanking transmissions according to the EN-12354 standard. Formulas for the evaluation of Kij in L, T and X junctions that depend on the mass ratio are available in the Annex E. Junctions of straight elements with different thickness or thin elastic layers are also included. However, other junction types that are important for building industry are not considered: H-shaped junctions, L or T junctions not forming a right angle, asymmetrical T-junctions , X-junctions where only one of the parts is different (thickness or material) from the other three. In the current research, expressions for these non-covered junctions are provided. They are obtained by means of numerical simulations based on the spectral and/or the standard finite element method. Kij is predicted for a large population of junctions, considering usual thicknesses and material combinations. Afterwards, an statistical treatment of the data is done in order to obtain simple but representative formulas that can easily be used in the daily acoustic projects or included in design software without the need of large computations.Sub-structuring of mechanical systems based on the path concept
http://hdl.handle.net/2117/89414
Sub-structuring of mechanical systems based on the path concept
Magrans Fontrodona, Francesc Xavier; Poblet-Puig, Jordi; Rodríguez Ferran, Antonio
Real mechanical systems are usually complex. Their modelling with discretisation techniques involve a large number of degrees of freedom/unknowns. This leads to high computational costs especially at high frequencies. An alternative, the statistical methods, are sometimes limited by strong behavioural requirements. So, sub-structuring can be considered very often as a good alternative. The present research studies the coupling between subsystems from the point of view of transmission path analysis. The interest is focused on the signal transmission rather than the energy distribution. A subsystem identification method is proposed. It is based on the expression of the solution in terms of the powers of the transfer matrix. This is related with the description of high-order paths which are more affected by damping and system properties. Consequently, the identification of subsystems can be more easily done. The method provides a quantification of the degree of coupling between subsystems and of the error caused by the detachment of a system part from the global system in the modelling phase. The output of the presented technique can be a sub-system definition valid for the SEA method or relevant information to be used in the design of measurement procedures.
2016-08-30T11:32:15ZMagrans Fontrodona, Francesc XavierPoblet-Puig, JordiRodríguez Ferran, AntonioReal mechanical systems are usually complex. Their modelling with discretisation techniques involve a large number of degrees of freedom/unknowns. This leads to high computational costs especially at high frequencies. An alternative, the statistical methods, are sometimes limited by strong behavioural requirements. So, sub-structuring can be considered very often as a good alternative. The present research studies the coupling between subsystems from the point of view of transmission path analysis. The interest is focused on the signal transmission rather than the energy distribution. A subsystem identification method is proposed. It is based on the expression of the solution in terms of the powers of the transfer matrix. This is related with the description of high-order paths which are more affected by damping and system properties. Consequently, the identification of subsystems can be more easily done. The method provides a quantification of the degree of coupling between subsystems and of the error caused by the detachment of a system part from the global system in the modelling phase. The output of the presented technique can be a sub-system definition valid for the SEA method or relevant information to be used in the design of measurement procedures.