http://hdl.handle.net/2099/6549 Tue, 21 May 2013 14:39:15 GMT 2013-05-21T14:39:15Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://eprints.upc.es:80/revistes/retrieve/35104/logo_LaCaN.gif http://hdl.handle.net/2099/6549 http://hdl.handle.net/2099/7821 Title: Strict error bounds in linear solid mechanics using a subdomain-based flux-free approach Authors: Cottereau, Regis; Díez, Pedro Abstract: 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. Mon, 08 Jun 2009 11:56:46 GMT http://hdl.handle.net/2099/7821 2009-06-08T11:56:46Z Cottereau, Regis; Díez, Pedro no Error estimation, Error bounds, Residual-based estimators, Functional outputs 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. http://hdl.handle.net/2099/7820 Title: The block gauss-seidel method in sound transmission problems Authors: Poblet Puig, Jordi; Rodríguez Ferran, Antonio Abstract: 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). Mon, 08 Jun 2009 11:23:31 GMT http://hdl.handle.net/2099/7820 2009-06-08T11:23:31Z Poblet Puig, Jordi; Rodríguez Ferran, Antonio no Sound transmission, Block iterative solver, Fluid-structure interaction, Double walls 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). http://hdl.handle.net/2099/7819 Title: Simple assessment of the numerical wave number in the fe solution of the helmholtz equation Authors: Steffens, Lindaura Maria; Díez, Pedro Abstract: 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. Mon, 08 Jun 2009 11:13:41 GMT http://hdl.handle.net/2099/7819 2009-06-08T11:13:41Z Steffens, Lindaura Maria; Díez, Pedro no Helmholtz equation, Wave number, Dispersion and pollution effect 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. http://hdl.handle.net/2099/7818 Title: Numerical integration by using local-node gauss-hermite cubature Authors: Millán, Raúl Daniel; Rosolen, Adrián Martín; Arroyo Balaguer, Marino Abstract: 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. Mon, 08 Jun 2009 10:53:59 GMT http://hdl.handle.net/2099/7818 2009-06-08T10:53:59Z Millán, Raúl Daniel; Rosolen, Adrián Martín; Arroyo Balaguer, Marino no Meshfree methods, Gauss–Hermite cubature, Numerical integration 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. http://hdl.handle.net/2099/7817 Title: Bounds and adaptivity for 3D limit analysis Authors: Muñoz, José J.; Bonet Carbonell, Javier; Huerta, Antonio; Peraire Guitart, Jaume Abstract: 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. Mon, 08 Jun 2009 10:28:14 GMT http://hdl.handle.net/2099/7817 2009-06-08T10:28:14Z Muñoz, José J.; Bonet Carbonell, Javier; Huerta, Antonio; Peraire Guitart, Jaume no Adaptivity, SOCP, Limit analysis, Bounds, Error estimates 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. http://hdl.handle.net/2099/7816 Title: 3D nurbs-enhanced finite element method Authors: Sevilla Cárdenas, Rubén; Fernandez Mendez, Sonia; Huerta, Antonio Abstract: 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. Mon, 08 Jun 2009 10:12:04 GMT http://hdl.handle.net/2099/7816 2009-06-08T10:12:04Z Sevilla Cárdenas, Rubén; Fernandez Mendez, Sonia; Huerta, Antonio no NURBS, Finite Elements, CAD, Exact geometry representation, High-order isoparametric finite elements 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. http://hdl.handle.net/2099/7815 Title: Acoplamiento del modelo regional de calidad de aire (CMAQ) con el modelo de emisiones locales mediante elementos finitos Authors: Pérez Foguet, Agustí; Oliver Serra, Albert Abstract: 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. Mon, 08 Jun 2009 09:47:57 GMT http://hdl.handle.net/2099/7815 2009-06-08T09:47:57Z Pérez Foguet, Agustí; Oliver Serra, Albert no CMAQ, Elementos Finitos, Dispersión, Contaminación atmosférica, Transporte, Malla, Interpolación, Campo de viento 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. http://hdl.handle.net/2099/7814 Title: Shock-capturing with discontinuous garlekin methods Authors: Huerta, Antonio; Casoni, Eva Abstract: 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. Mon, 08 Jun 2009 08:32:41 GMT http://hdl.handle.net/2099/7814 2009-06-08T08:32:41Z Huerta, Antonio; Casoni, Eva no Discontinuous Galerkin, Artificial Viscosity, Discontinuity Sensor 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. http://hdl.handle.net/2099/7813 Title: Management, design and developement of a mesh generation environment using open source software Authors: Roca Navarro, Francisco Javier; Ruiz Gironès, Eloi; Sarrate Ramos, Josep Abstract: 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. Mon, 08 Jun 2009 08:15:56 GMT http://hdl.handle.net/2099/7813 2009-06-08T08:15:56Z Roca Navarro, Francisco Javier; Ruiz Gironès, Eloi; Sarrate Ramos, Josep no Mesh generation, Software engineering, Agile methodologies, Design patterns, Data structure 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. http://hdl.handle.net/2099/7802 Title: A critical comparison of two discontinuous galerkin methods for the navier-stokes equations using solenoidal aproximations Authors: Villardi de Montlaur, Adeline de; Peraire Guitart, Jaume; Huerta, Antonio Abstract: 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. Mon, 08 Jun 2009 07:49:26 GMT http://hdl.handle.net/2099/7802 2009-06-08T07:49:26Z Villardi de Montlaur, Adeline de; Peraire Guitart, Jaume; Huerta, Antonio no Compact Discontinuous Galerkin, Solenoidal, Navier-Stokes, Incompressible flow, Interior Penalty Method, Fractional-step method 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. http://hdl.handle.net/2099/7765 Title: Galerkin discontinuo local aplicado a problemas de ondas acústicas: condiciones de frontera absorbente locales de bajo orden Authors: Cadenas, Carlos; Fernandez Mendez, Sonia; Huerta, Antonio Abstract: En este trabajo se presenta una comparación de la solución numérica de la ecuación de Helmholtz utilizando el método de elementos finitos Galerkin Discontinuo Local (LDG) con varias condiciones de contorno absorbentes locales de bajo orden. Se describe brevemente el proceso de discretización y se realizan pruebas con ejemplos clásicos presentes en la literatura. Tue, 02 Jun 2009 10:26:49 GMT http://hdl.handle.net/2099/7765 2009-06-02T10:26:49Z Cadenas, Carlos; Fernandez Mendez, Sonia; Huerta, Antonio no Discontinuous Galerkin, Helmholtz, Absorbing Boundary Condition En este trabajo se presenta una comparación de la solución numérica de la ecuación de Helmholtz utilizando el método de elementos finitos Galerkin Discontinuo Local (LDG) con varias condiciones de contorno absorbentes locales de bajo orden. Se describe brevemente el proceso de discretización y se realizan pruebas con ejemplos clásicos presentes en la literatura. http://hdl.handle.net/2099/7764 Title: Hierarchical x-fem applied to n-phase flow Authors: Zlotnik, Sergio; Díez, Pedro Abstract: In this work we proposed an extencion of the level set technique to track any number of free surfaces. This extension is based in a hierarchical ordering of several level set functions. To complete the X–FEM approach, the enrichment via partition of the unity method is also extended. The ridge function, base of the enriched interpolation, is restated to include several level sets and the hierarchy between them. Tue, 02 Jun 2009 09:26:48 GMT http://hdl.handle.net/2099/7764 2009-06-02T09:26:48Z Zlotnik, Sergio; Díez, Pedro no Multiphase flow, Level set methods, Enrichment, Extended finite element method (X-FEM) In this work we proposed an extencion of the level set technique to track any number of free surfaces. This extension is based in a hierarchical ordering of several level set functions. To complete the X–FEM approach, the enrichment via partition of the unity method is also extended. The ridge function, base of the enriched interpolation, is restated to include several level sets and the hierarchy between them. http://hdl.handle.net/2099/7763 Title: Solmec: an efficient c++ library to solve linear and nonlinear elasticity problems Authors: Rosolen, Adrián Martín; Millán, Raúl Daniel; Arroyo Balaguer, Marino Abstract: A C++ library based on local maximum-entropy approximation schemes to solve linear and nonlinear elasticity problem is presented. The available tools are briefly described, and several implementation details are also mentioned. Selected numerical examples are shown in order to illustrate the capabilities of the library. The current and future developments are indicated. Tue, 02 Jun 2009 09:11:26 GMT http://hdl.handle.net/2099/7763 2009-06-02T09:11:26Z Rosolen, Adrián Martín; Millán, Raúl Daniel; Arroyo Balaguer, Marino no Linear and nonlinear elasticity, Meshfree schemes, Direct and iterative solvers, Quasi-Newton methods, Constrained optimization, C++ library A C++ library based on local maximum-entropy approximation schemes to solve linear and nonlinear elasticity problem is presented. The available tools are briefly described, and several implementation details are also mentioned. Selected numerical examples are shown in order to illustrate the capabilities of the library. The current and future developments are indicated. http://hdl.handle.net/2099/7653 Title: Generación de mallas de hexaedros en geometrías múltiplemente conexas mediante submapping Authors: Ruiz Gironès, Eloi; Sarrate Ramos, Josep Abstract: En este trabajo se presenta una mejora del método de submapping para ampliar su aplicabilidad. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que los ángulos entre las aristas y las caras de la geometría tienen que ser, aproximadamente, múltiplos enteros de π/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. En este trabajo se presenta una extensión del algoritmo de submapping para mallar geometrías con agujeros totalmente interiores. Tue, 26 May 2009 11:36:11 GMT http://hdl.handle.net/2099/7653 2009-05-26T11:36:11Z Ruiz Gironès, Eloi; Sarrate Ramos, Josep no Método de elementos finitos, Generación de mallas, Submapping, Hexaedros estructurados, Programación lineal, Interpolación transfinita, Geometría múltiplemente conexa En este trabajo se presenta una mejora del método de submapping para ampliar su aplicabilidad. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que los ángulos entre las aristas y las caras de la geometría tienen que ser, aproximadamente, múltiplos enteros de π/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. En este trabajo se presenta una extensión del algoritmo de submapping para mallar geometrías con agujeros totalmente interiores. http://hdl.handle.net/2099/7583 Title: Automatic generation of quadrilateral structured meshes using linear programming and transfinite interpolation Authors: Ruiz Gironès, Eloi; Sarrate Ramos, Josep Abstract: This paper presents an implementation of a structured quadrilateral algorithm called submapping. The meshing procedure splits the geometry into patches and then meshes each patch separately preserving the mesh compatibility between patches via an linear integer problem. The submapping algorithm can only be applied to geometries such that each angle between consecutive edges is, approximately, an integer multiple of ¼=2. Thu, 30 Apr 2009 11:25:15 GMT http://hdl.handle.net/2099/7583 2009-04-30T11:25:15Z Ruiz Gironès, Eloi; Sarrate Ramos, Josep no Finite element method; mesh generation; submapping; structured quadrilaterals; linear programming; transfinite interpolation This paper presents an implementation of a structured quadrilateral algorithm called submapping. The meshing procedure splits the geometry into patches and then meshes each patch separately preserving the mesh compatibility between patches via an linear integer problem. The submapping algorithm can only be applied to geometries such that each angle between consecutive edges is, approximately, an integer multiple of ¼=2.