Articles de revista
http://hdl.handle.net/2117/184749
20210419T05:08:56Z

A combined reduced orderfull order methodology for the solution of 3D magnetomechanical problems with application to magnetic resonance imaging scanners
http://hdl.handle.net/2117/341099
A combined reduced orderfull order methodology for the solution of 3D magnetomechanical problems with application to magnetic resonance imaging scanners
Seoane Chouciño, Marcos; Ledger, Paul D.; Gil, Antonio; Zlotnik, Sergio; Mallett, Mike
The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magnetomechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to highdimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magnetomechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the fullorder solution.
This is the peer reviewed version of the following article: Seoane, M. [et al.]. A combined reduced orderfull order methodology for the solution of 3D magnetomechanical problems with application to magnetic resonance imaging scanners. "International journal for numerical methods in engineering", 1 Gener 2020, vol. 121, núm. 16, p. 35293559. , which has been published in final form athttps://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6369. This article may be used for noncommercial purposes in accordance with Wiley Terms and Conditions for SelfArchiving.
20210308T11:11:22Z
Seoane Chouciño, Marcos
Ledger, Paul D.
Gil, Antonio
Zlotnik, Sergio
Mallett, Mike
The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magnetomechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to highdimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magnetomechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the fullorder solution.

A staggered highdimensional Proper Generalised Decomposition for coupled magnetomechanical problems with application to MRI scanners
http://hdl.handle.net/2117/335927
A staggered highdimensional Proper Generalised Decomposition for coupled magnetomechanical problems with application to MRI scanners
Barroso Gassiot, Guillem; Seoane Chouciño, Marcos; Gil Ruiz, Antonio Javier; Ledger, Paul D.; Mallett, Mike; Huerta, Antonio
Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a computational challenge to industry, due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of userfriendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where highdimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time. This paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electromagnetomechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a fivedimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailormade ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.
© 2020 Elsevier. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20210125T13:09:43Z
Barroso Gassiot, Guillem
Seoane Chouciño, Marcos
Gil Ruiz, Antonio Javier
Ledger, Paul D.
Mallett, Mike
Huerta, Antonio
Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a computational challenge to industry, due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of userfriendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where highdimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time. This paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electromagnetomechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a fivedimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailormade ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.

Reshaping diagrams for bending straightening of forged aeronautical components
http://hdl.handle.net/2117/334169
Reshaping diagrams for bending straightening of forged aeronautical components
Mena Andrade, Ramiro; Aguado, José Vicente; Guinard, S.; Huerta, Antonio
Large and thickwalled aluminium forgings exhibit shape distortions induced by residual stresses. To restore the nominal geometry, a series of highly manual and timeconsuming reshaping operations need to be carried out. In this paper, we are concerned with the development of efficient computer simulation tools to assist operators in bending straightening, which is one of the most common reshaping operations. Our approach is based on the computation of reshaping diagrams, a tool that allows selecting a nearly optimal bending load to be applied in order to minimize distortion. Most importantly, we show that the reshaping diagram needs not to account for the residual stress field, as its only effect is to shift of the reshaping diagram by some offset. That is, the overall behaviour including a realistic 3D residual stress field in a forged part can be retrieved by shifting the residual stress free reshaping diagram by the appropriate offset. Finally, we propose a strategy in order to identify the offset onthefly during the reshaping operation using simple forcedisplacement measures.
The final publication is available at Springer via http://dx.doi.org/10.1007/s0017002005856z
20201210T07:24:00Z
Mena Andrade, Ramiro
Aguado, José Vicente
Guinard, S.
Huerta, Antonio
Large and thickwalled aluminium forgings exhibit shape distortions induced by residual stresses. To restore the nominal geometry, a series of highly manual and timeconsuming reshaping operations need to be carried out. In this paper, we are concerned with the development of efficient computer simulation tools to assist operators in bending straightening, which is one of the most common reshaping operations. Our approach is based on the computation of reshaping diagrams, a tool that allows selecting a nearly optimal bending load to be applied in order to minimize distortion. Most importantly, we show that the reshaping diagram needs not to account for the residual stress field, as its only effect is to shift of the reshaping diagram by some offset. That is, the overall behaviour including a realistic 3D residual stress field in a forged part can be retrieved by shifting the residual stress free reshaping diagram by the appropriate offset. Finally, we propose a strategy in order to identify the offset onthefly during the reshaping operation using simple forcedisplacement measures.

Building a certified reduced basis for coupled thermohydromechanical systems with goaloriented error estimation
http://hdl.handle.net/2117/328986
Building a certified reduced basis for coupled thermohydromechanical systems with goaloriented error estimation
Larion, Ygee; Zlotnik, Sergio; Massart, Thierry J.; Díez, Pedro
A goaloriented aposteriori error estimator is developed for transient coupled thermohydromechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goaloriented error estimate is derived based on explicitlycomputed weak residual of the primal problem and implicitlycomputed adjoint solution associated with the QoI. The timedependence of the coupled THM system poses an additional complexity as the auxiliary adjoint problem evolves backwards in time. The error estimator guides a greedy adaptive procedure that constructs progressively an optimal reduced basis by smartly selecting snapshot points over a given parametric training sample. The reduced basis obtained is used to drastically reduce the coupled system spatial degrees of freedom by several orders of magnitude. The computational gain obtained from the developed methodology is demonstrated through applications in 2D and 3D parametrized problems simulating the evolution of coupled THM processes in rock masses.
This is a postpeerreview, precopyedit version of an article published in Computational mechanics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00466020018657
20200921T12:33:07Z
Larion, Ygee
Zlotnik, Sergio
Massart, Thierry J.
Díez, Pedro
A goaloriented aposteriori error estimator is developed for transient coupled thermohydromechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goaloriented error estimate is derived based on explicitlycomputed weak residual of the primal problem and implicitlycomputed adjoint solution associated with the QoI. The timedependence of the coupled THM system poses an additional complexity as the auxiliary adjoint problem evolves backwards in time. The error estimator guides a greedy adaptive procedure that constructs progressively an optimal reduced basis by smartly selecting snapshot points over a given parametric training sample. The reduced basis obtained is used to drastically reduce the coupled system spatial degrees of freedom by several orders of magnitude. The computational gain obtained from the developed methodology is demonstrated through applications in 2D and 3D parametrized problems simulating the evolution of coupled THM processes in rock masses.

A weakly compressible hybridizable discontinuous Galerkin formulation for fluidstructure interaction problems
http://hdl.handle.net/2117/328760
A weakly compressible hybridizable discontinuous Galerkin formulation for fluidstructure interaction problems
Spina, Andrea la; Kronbichler, Martin; Giacomini, Matteo; Wall, Wolfgang A.; Huerta, Antonio
A scheme for the solution of fluidstructure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advectiondominated flows with higher order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet–Neumann scheme in the context of hybrid HDGCG discretizations and a monolithic approach based on Nitsche’s method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.
© 2020. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20200915T12:09:36Z
Spina, Andrea la
Kronbichler, Martin
Giacomini, Matteo
Wall, Wolfgang A.
Huerta, Antonio
A scheme for the solution of fluidstructure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advectiondominated flows with higher order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet–Neumann scheme in the context of hybrid HDGCG discretizations and a monolithic approach based on Nitsche’s method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.

Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows
http://hdl.handle.net/2117/328743
Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows
Sevilla Cárdenas, Rubén; Borchini, Luca; Giacomini, Matteo; Huerta, Antonio
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a highorder hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an offline solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a userdefined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal mesh convergence properties of the proposed method and demonstrate its applicability in two and three dimensions, with particular emphasis on parametrised flows in microfluidics.
© 2020. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20200915T09:39:23Z
Sevilla Cárdenas, Rubén
Borchini, Luca
Giacomini, Matteo
Huerta, Antonio
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a highorder hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an offline solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a userdefined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal mesh convergence properties of the proposed method and demonstrate its applicability in two and three dimensions, with particular emphasis on parametrised flows in microfluidics.

Fast solution of elliptic harbor agitation problems under frequencydirection input spectra by model order reduction and NURBSenhanced FEM
http://hdl.handle.net/2117/188011
Fast solution of elliptic harbor agitation problems under frequencydirection input spectra by model order reduction and NURBSenhanced FEM
Modesto Galende, David; Ye, Boyi; Zlotnik, Sergio; Huerta, Antonio
Many harbor applications are based on the solution of linear elliptic agitation problems for many spectral conditions. One of the main goals consists in computing the linear combination of numerous simulations of the harbor agitation problem, using monochromatic waves of different spectral components (i.e. frequency and incoming wave direction). In practice, the standard strategy selects the number of wave components according to a prescribed discretization of the 2D input spectra. The main issue relies on some quantities of interest that are very sensitive to the level of refinement of the spectra, such as the significant wave height at every mesh point or the identification of resonance modes induced by long wave scattering. In many cases, achieving enough quality in these quantities may impose numerous simulations and, consequently, nonpractical computer costs. This can drastically limit the final accuracy of results. To overcome this situation, here a new strategy is proposed to efficiently solve a large number of harbor agitation problems derived from dense discretizations of the 2D input spectra. The strategy is based on the combination of two different numerical approaches. Firstly, each required monochromatic simulation is solved via high order NURBS (nonuniform rational Bsplines) enhanced finite elements (NEFEM). More precisely, NEFEM captures the exact harbor geometry using large mesh elements that produce accurate solutions and significant savings on the system size, particularly in long wave cases. Secondly, a model order reduction technique is used to approximate the original elliptic harbor model by a socalled surrogate model. The main advantage is that, once the surrogate model is constructed, it can be rapidly evaluated to provide simulations for any value of the spectral components within a range of interest, and without the need of solving any new harbor agitation problem (as the standard strategy does). Thus, this enables the possibility of using any desired discretization of the 2D input spectra with no additional computer cost. The construction of the surrogate model is performed using the proper generalized decomposition method with a novel incremental computation along the frequency dimension. The proposed strategy is discussed, and its superior performance with respect to standard strategies is demonstrated, on two harbor agitation examples with several applications.
© 2020. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20200519T06:35:40Z
Modesto Galende, David
Ye, Boyi
Zlotnik, Sergio
Huerta, Antonio
Many harbor applications are based on the solution of linear elliptic agitation problems for many spectral conditions. One of the main goals consists in computing the linear combination of numerous simulations of the harbor agitation problem, using monochromatic waves of different spectral components (i.e. frequency and incoming wave direction). In practice, the standard strategy selects the number of wave components according to a prescribed discretization of the 2D input spectra. The main issue relies on some quantities of interest that are very sensitive to the level of refinement of the spectra, such as the significant wave height at every mesh point or the identification of resonance modes induced by long wave scattering. In many cases, achieving enough quality in these quantities may impose numerous simulations and, consequently, nonpractical computer costs. This can drastically limit the final accuracy of results. To overcome this situation, here a new strategy is proposed to efficiently solve a large number of harbor agitation problems derived from dense discretizations of the 2D input spectra. The strategy is based on the combination of two different numerical approaches. Firstly, each required monochromatic simulation is solved via high order NURBS (nonuniform rational Bsplines) enhanced finite elements (NEFEM). More precisely, NEFEM captures the exact harbor geometry using large mesh elements that produce accurate solutions and significant savings on the system size, particularly in long wave cases. Secondly, a model order reduction technique is used to approximate the original elliptic harbor model by a socalled surrogate model. The main advantage is that, once the surrogate model is constructed, it can be rapidly evaluated to provide simulations for any value of the spectral components within a range of interest, and without the need of solving any new harbor agitation problem (as the standard strategy does). Thus, this enables the possibility of using any desired discretization of the 2D input spectra with no additional computer cost. The construction of the surrogate model is performed using the proper generalized decomposition method with a novel incremental computation along the frequency dimension. The proposed strategy is discussed, and its superior performance with respect to standard strategies is demonstrated, on two harbor agitation examples with several applications.

A local multiple proper generalized decomposition based on the partition of unity
http://hdl.handle.net/2117/178345
A local multiple proper generalized decomposition based on the partition of unity
Ibáñez Pinillo, Rubén; Abisset Chavanne, Emmanuelle; Chinesta Soria, Francisco; Huerta, Antonio; Cueto Prendes, Elias
It is well known that model order reduction techniques that project the solution of the problem at hand onto alowdimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of nonlinear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employingProper Generalized Decompositions at each local patch.
This is the peer reviewed version of the following article: Ibáñez, R. [et al.]. A local multiple proper generalized decomposition based on the partition of unity. "International journal for numerical methods in engineering", 12 Octubre 2019, vol. 120, núm. 2, p. 139152, which has been published in final form at DOI:10.1002/nme.6128. This article may be used for noncommercial purposes in accordance with Wiley Terms and Conditions for SelfArchiving.
20200224T07:52:18Z
Ibáñez Pinillo, Rubén
Abisset Chavanne, Emmanuelle
Chinesta Soria, Francisco
Huerta, Antonio
Cueto Prendes, Elias
It is well known that model order reduction techniques that project the solution of the problem at hand onto alowdimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of nonlinear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employingProper Generalized Decompositions at each local patch.

A regularisedadaptive Proper Generalised Decomposition implementation for coupled magnetomechanical problems with application to MRI scanners
http://hdl.handle.net/2117/178343
A regularisedadaptive Proper Generalised Decomposition implementation for coupled magnetomechanical problems with application to MRI scanners
Barroso Gassiot, Guillem; Gil Ruiz, Antonio Javier; Ledger, Paul D.; Mallett, Mike; Huerta, Antonio
Latest developments in highstrength Magnetic Resonance Imaging (MRI) scanners with inbuilt high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their highstrength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to supercool the magnets. Optimum MRI scanner design requires the capturing of complex electromagnetomechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new costeffective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for realtime simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electromagnetomechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the illconditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.
© 2020. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20200224T06:45:14Z
Barroso Gassiot, Guillem
Gil Ruiz, Antonio Javier
Ledger, Paul D.
Mallett, Mike
Huerta, Antonio
Latest developments in highstrength Magnetic Resonance Imaging (MRI) scanners with inbuilt high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their highstrength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to supercool the magnets. Optimum MRI scanner design requires the capturing of complex electromagnetomechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new costeffective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for realtime simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electromagnetomechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the illconditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.

Hybrid coupling of CG and HDG discretizations based on Nitsche’s method
http://hdl.handle.net/2117/178282
Hybrid coupling of CG and HDG discretizations based on Nitsche’s method
Spina, Andrea la; Giacomini, Matteo; Huerta, Antonio
A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CGHDG coupling exploits the definition of the numerical flux and the trace of the solution on the mesh faces to impose the transmission conditions between the CG and HDG subdomains. The con tinuity of the solution is imposed in the CG problem via Nitsche’s method, whereas the equilibrium of the flux at the interface is naturally enforced as a Neumann con dition in the HDG global problem. The proposed strategy does not affect the core structure of CG and HDG discretizations. In fact, the resulting formulation leads to a minimallyintrusive coupling, suitable to be integrated in existing CG and HDG libraries. Numerical experiments in two and three dimensions show optimal global convergence of the stress and superconvergence of the displacement field, lockingfree approximation, as well as the potential to treat structural problems of engineering interest featuring multiple materials with compressible and nearly incompressible behaviors.
This is a postpeerreview, precopyedit version of an article published in Computational mechanics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00466019017708
20200221T11:39:39Z
Spina, Andrea la
Giacomini, Matteo
Huerta, Antonio
A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CGHDG coupling exploits the definition of the numerical flux and the trace of the solution on the mesh faces to impose the transmission conditions between the CG and HDG subdomains. The con tinuity of the solution is imposed in the CG problem via Nitsche’s method, whereas the equilibrium of the flux at the interface is naturally enforced as a Neumann con dition in the HDG global problem. The proposed strategy does not affect the core structure of CG and HDG discretizations. In fact, the resulting formulation leads to a minimallyintrusive coupling, suitable to be integrated in existing CG and HDG libraries. Numerical experiments in two and three dimensions show optimal global convergence of the stress and superconvergence of the displacement field, lockingfree approximation, as well as the potential to treat structural problems of engineering interest featuring multiple materials with compressible and nearly incompressible behaviors.