Workshop on numerical methods in applied science and engineering
http://hdl.handle.net/2099/6549
2019-08-25T03:15:43ZStrict error bounds in linear solid mechanics using a subdomain-based flux-free approach
http://hdl.handle.net/2099/7821
Strict error bounds in linear solid mechanics using a subdomain-based flux-free approach
Cottereau, Regis; Díez, Pedro
In this paper, we derive, in the framework of the ux-free method, strict bounds for the energy norm of the error associated to a finite element computation. In that framework, and when using linear elements, the problems posed on the subdomains are solvable only when modified by the introduction of a projection operator in the residual.
We introduce a new such operator, and show that, in the context of a dual formulation,
it further allows to construct statically admissible fields over each subdomain. When
combined, these local stress fields provide the desired strict bound.
2009-06-08T11:56:46ZCottereau, RegisDíez, PedroIn this paper, we derive, in the framework of the ux-free method, strict bounds for the energy norm of the error associated to a finite element computation. In that framework, and when using linear elements, the problems posed on the subdomains are solvable only when modified by the introduction of a projection operator in the residual.
We introduce a new such operator, and show that, in the context of a dual formulation,
it further allows to construct statically admissible fields over each subdomain. When
combined, these local stress fields provide the desired strict bound.The block gauss-seidel method in sound transmission problems
http://hdl.handle.net/2099/7820
The block gauss-seidel method in sound transmission problems
Poblet-Puig, Jordi; Rodríguez Ferran, Antonio
Sound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in
order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This analysis highlights the negative influence on the convergence of a strong degree of coupling between the acoustic domains. A selective coupling strategy has been developed and successfully applied to problems with strong coupling (i.e. sound transmission through double walls).
2009-06-08T11:23:31ZPoblet-Puig, JordiRodríguez Ferran, AntonioSound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in
order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This analysis highlights the negative influence on the convergence of a strong degree of coupling between the acoustic domains. A selective coupling strategy has been developed and successfully applied to problems with strong coupling (i.e. sound transmission through double walls).Simple assessment of the numerical wave number in the fe solution of the helmholtz equation
http://hdl.handle.net/2099/7819
Simple assessment of the numerical wave number in the fe solution of the helmholtz equation
Steffens, Lindaura Maria; Díez, Pedro
When numerical methods are applied to the computation of stationary waves, it is observed that "numerical waves" are dispersive for high wave numbers. The numerical wave shows a phase velocity which depends on the wave number "k" of the Helmholtz equation. Recent works on goal-oriented error estimation techniques with respect to socalled quantities of interest or output functionals are developing. Thus, taken into account such aspects, the main purpose of this paper is a posteriori error estimation through of a assessment of the numerical wave number in finite element solution fot he simulation of acoustic wave propagation problems adressed by Helmholtz equation. A method to measure the dispersion on classical Galerkin FEM is presented. In this analysis, the phase difference between the exact and numerical solutions is researched. Fundamental results from a priori error estimation for one-dimensional are presented and issues dealing with pollution error at high wave numbers also are discussed.
2009-06-08T11:13:41ZSteffens, Lindaura MariaDíez, PedroWhen numerical methods are applied to the computation of stationary waves, it is observed that "numerical waves" are dispersive for high wave numbers. The numerical wave shows a phase velocity which depends on the wave number "k" of the Helmholtz equation. Recent works on goal-oriented error estimation techniques with respect to socalled quantities of interest or output functionals are developing. Thus, taken into account such aspects, the main purpose of this paper is a posteriori error estimation through of a assessment of the numerical wave number in finite element solution fot he simulation of acoustic wave propagation problems adressed by Helmholtz equation. A method to measure the dispersion on classical Galerkin FEM is presented. In this analysis, the phase difference between the exact and numerical solutions is researched. Fundamental results from a priori error estimation for one-dimensional are presented and issues dealing with pollution error at high wave numbers also are discussed.Numerical integration by using local-node gauss-hermite cubature
http://hdl.handle.net/2099/7818
Numerical integration by using local-node gauss-hermite cubature
Millán, Raúl Daniel; Rosolen, Adrián Martín; Arroyo Balaguer, Marino
A local–node numerical integration scheme for meshless methods is presented in this work. The distinguishing characteristic of the introduced scheme is that not support
mesh or grid to perform numerical integration is needed, besides the fact that gauss cubature points for each node are generated in a properly fashion and that the extension of the methodology to high dimensions is straightforward. The numerical integration is computed with the Gauss–Hermite cubature formulas, and the partition of unity is employed to introduce the Gaussian weight in a natural way. Selected numerical tests in two-dimensions are used to illustrate the validity of the proposed methodology. Although the obtained results are encouraging, the behavior of the integration error is not still well
understood when the dimensionless parameter which control the width of the Gaussian
kernel varies.
2009-06-08T10:53:59ZMillán, Raúl DanielRosolen, Adrián MartínArroyo Balaguer, MarinoA local–node numerical integration scheme for meshless methods is presented in this work. The distinguishing characteristic of the introduced scheme is that not support
mesh or grid to perform numerical integration is needed, besides the fact that gauss cubature points for each node are generated in a properly fashion and that the extension of the methodology to high dimensions is straightforward. The numerical integration is computed with the Gauss–Hermite cubature formulas, and the partition of unity is employed to introduce the Gaussian weight in a natural way. Selected numerical tests in two-dimensions are used to illustrate the validity of the proposed methodology. Although the obtained results are encouraging, the behavior of the integration error is not still well
understood when the dimensionless parameter which control the width of the Gaussian
kernel varies.Bounds and adaptivity for 3D limit analysis
http://hdl.handle.net/2099/7817
Bounds and adaptivity for 3D limit analysis
Muñoz, José J.; Bonet Carbonell, Javier; Huerta, Antonio; Peraire Guitart, Jaume
In the present paper we compute upper and lower bounds for limit analysis in two and three dimensions. From the solution of the discretised upper and lower bound problems, and from the optimum displacement rate and stress fields, we compute an error estimate defined at the body elements and at their boundaries, which are applied in an adaptive remeshing strategy. In order to reduce the computational cost in 3D limit analysis, the tightness of the upper bound is relaxed and its computation avoided. Instead, the results of the lower bound are used to estimate elemental and edge errors. The theory has been implemented for Von Mises materials, and applied to two- and three-dimensions
examples.
2009-06-08T10:28:14ZMuñoz, José J.Bonet Carbonell, JavierHuerta, AntonioPeraire Guitart, JaumeIn the present paper we compute upper and lower bounds for limit analysis in two and three dimensions. From the solution of the discretised upper and lower bound problems, and from the optimum displacement rate and stress fields, we compute an error estimate defined at the body elements and at their boundaries, which are applied in an adaptive remeshing strategy. In order to reduce the computational cost in 3D limit analysis, the tightness of the upper bound is relaxed and its computation avoided. Instead, the results of the lower bound are used to estimate elemental and edge errors. The theory has been implemented for Von Mises materials, and applied to two- and three-dimensions
examples.3D nurbs-enhanced finite element method
http://hdl.handle.net/2099/7816
3D nurbs-enhanced finite element method
Sevilla Cárdenas, Rubén; Fernández Méndez, Sonia; Huerta, Antonio
An improvement of the classical finite element method is proposed in [1], the NURBS-Enhanced Finite Element Method (NEFEM). It is able to exactly represent the geometry by means of the usual CAD description of the boundary with Non-Uniform
Rational B-Splines (NURBS). For elements not intersecting the boundary, a standard
finite element interpolation and numerical integration is used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. This document presents preliminary work on the 3D extension of NEFEM.
2009-06-08T10:12:04ZSevilla Cárdenas, RubénFernández Méndez, SoniaHuerta, AntonioAn improvement of the classical finite element method is proposed in [1], the NURBS-Enhanced Finite Element Method (NEFEM). It is able to exactly represent the geometry by means of the usual CAD description of the boundary with Non-Uniform
Rational B-Splines (NURBS). For elements not intersecting the boundary, a standard
finite element interpolation and numerical integration is used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. This document presents preliminary work on the 3D extension of NEFEM.Acoplamiento del modelo regional de calidad de aire (CMAQ) con el modelo de emisiones locales mediante elementos finitos
http://hdl.handle.net/2099/7815
Acoplamiento del modelo regional de calidad de aire (CMAQ) con el modelo de emisiones locales mediante elementos finitos
Pérez Foguet, Agustí; Oliver Serra, Albert
Existen modelos regionales de calidad del aire que son muy utilizados. Estos
modelos tienen modelos para estudiar el aporte de contaminantes provocados por fuentes importantes de contaminación, como pueden ser chimeneas, o poligonos industriales. El modelo regional que estudiamos en este trabajo es el CMAQ (Community Multiscale Air Quality), que usa el Plume-in-Grid (PinG) como modelo para estudiar el aporte de fuentes locales de contaminación. El PinG és un modelo lagrangiano de pluma gausiana, y en
este trabajo queremos cambiar esta estratégia de modelación de emisores puntuales por un modelo euleriano por elementos finitos. Para poder conseguir la integración, mallamos nuestro volumen de estudio, mediante una estratégia que nos permite la fácil integración de los tetrahedros de nuestro modelo de elementos finitos, con los elementos del modelo regional. Tambien necesitamos interpolar
el campo de viento que nos da el modelo regional para conocer el campo de viento los
nodos de nuestro dominio. Finalmente necesitamos usar los valores de contaminación del modelo regional en nuestro modelo local.
2009-06-08T09:47:57ZPérez Foguet, AgustíOliver Serra, AlbertExisten modelos regionales de calidad del aire que son muy utilizados. Estos
modelos tienen modelos para estudiar el aporte de contaminantes provocados por fuentes importantes de contaminación, como pueden ser chimeneas, o poligonos industriales. El modelo regional que estudiamos en este trabajo es el CMAQ (Community Multiscale Air Quality), que usa el Plume-in-Grid (PinG) como modelo para estudiar el aporte de fuentes locales de contaminación. El PinG és un modelo lagrangiano de pluma gausiana, y en
este trabajo queremos cambiar esta estratégia de modelación de emisores puntuales por un modelo euleriano por elementos finitos. Para poder conseguir la integración, mallamos nuestro volumen de estudio, mediante una estratégia que nos permite la fácil integración de los tetrahedros de nuestro modelo de elementos finitos, con los elementos del modelo regional. Tambien necesitamos interpolar
el campo de viento que nos da el modelo regional para conocer el campo de viento los
nodos de nuestro dominio. Finalmente necesitamos usar los valores de contaminación del modelo regional en nuestro modelo local.Shock-capturing with discontinuous garlekin methods
http://hdl.handle.net/2099/7814
Shock-capturing with discontinuous garlekin methods
Huerta, Antonio; Casoni Rero, Eva
A shock capturing strategy for high order Discontinuous Galerkin methods for
conservation laws is proposed. We present a method in the one-dimensional case based
on the introduction of artificial viscosity into the original equations. With this approach the shock is capture with sharp resolution maintaining high-order accuracy. The ideas for the extension to the two-dimensional case are also set.
2009-06-08T08:32:41ZHuerta, AntonioCasoni Rero, EvaA shock capturing strategy for high order Discontinuous Galerkin methods for
conservation laws is proposed. We present a method in the one-dimensional case based
on the introduction of artificial viscosity into the original equations. With this approach the shock is capture with sharp resolution maintaining high-order accuracy. The ideas for the extension to the two-dimensional case are also set.Management, design and developement of a mesh generation environment using open source software
http://hdl.handle.net/2099/7813
Management, design and developement of a mesh generation environment using open source software
Roca Navarro, Francisco Javier; Ruiz Gironès, Eloi; Sarrate Ramos, Josep
In this paper we present an object oriented implementation of a general-purpose mesh generation environment for geometry-based simulations. The aim of this application is to unify available legacy code and new research algorithms in only one mesh
generation suite. We focus in two aspects that can be of the general interest for managers, designers and developers of similar projects. On the one hand, we analyze the software engineering practices that we have followed in the management and development process. In addition, we detail and discuss the Open Source tools and libraries that we have used. On the other hand, we discuss the design and the data structure of the environment. In particular, we first summarize the topological and geometrical representation. Second, we
detail our implementation of the hierarchical mesh generation structure. Third we present our design to mediate collaboration between classes. Finally, we present some of the mesh generation features to show the capabilities of the environment.
2009-06-08T08:15:56ZRoca Navarro, Francisco JavierRuiz Gironès, EloiSarrate Ramos, JosepIn this paper we present an object oriented implementation of a general-purpose mesh generation environment for geometry-based simulations. The aim of this application is to unify available legacy code and new research algorithms in only one mesh
generation suite. We focus in two aspects that can be of the general interest for managers, designers and developers of similar projects. On the one hand, we analyze the software engineering practices that we have followed in the management and development process. In addition, we detail and discuss the Open Source tools and libraries that we have used. On the other hand, we discuss the design and the data structure of the environment. In particular, we first summarize the topological and geometrical representation. Second, we
detail our implementation of the hierarchical mesh generation structure. Third we present our design to mediate collaboration between classes. Finally, we present some of the mesh generation features to show the capabilities of the environment.A critical comparison of two discontinuous galerkin methods for the navier-stokes equations using solenoidal aproximations
http://hdl.handle.net/2099/7802
A critical comparison of two discontinuous galerkin methods for the navier-stokes equations using solenoidal aproximations
Villardi de Montlaur, Adeline de; Peraire Guitart, Jaume; Huerta, Antonio
This paper compares two methods to solve incompressible problems, in particular
the Navier-Stokes equations, using a discontinuous polynomial interpolation that is exactly divergence-free in each element. The first method is an Interior Penalty Method, whereas the second method follows the Compact Discontinuous Galerkin approach for the diffusive part of the problem. In both cases the Navier-Stokes equations are then solved using a fractional-step method, using an implicit method for the diffusion part and a semiimplicit method for the convection. Numerical examples compare the efficiency and the accuracy of the two proposed methods.
2009-06-08T07:49:26ZVillardi de Montlaur, Adeline dePeraire Guitart, JaumeHuerta, AntonioThis paper compares two methods to solve incompressible problems, in particular
the Navier-Stokes equations, using a discontinuous polynomial interpolation that is exactly divergence-free in each element. The first method is an Interior Penalty Method, whereas the second method follows the Compact Discontinuous Galerkin approach for the diffusive part of the problem. In both cases the Navier-Stokes equations are then solved using a fractional-step method, using an implicit method for the diffusion part and a semiimplicit method for the convection. Numerical examples compare the efficiency and the accuracy of the two proposed methods.