@article{Garcia-Blanco2018,

title = {A polyconvex computational formulation for electro-activation in cardiac mechanics},

author = {Emilio Garcia-Blanco and Rogelio Ortigosa and Antonio J. Gil and C. H. Lee and Javier Bonet},

year  = {2018},

date = {2018-07-01},

urldate = {2018-07-01},

journal = {Biomechanics and Modeling in Mechanobiology},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2018,

title = {On a family of numerical models for couple stress based exoelectricity for continua and beams},

author = {Roman Poya and Antonio J. Gil and Rogelio Ortigosa and Roberto Palma},

year  = {2018},

date = {2018-07-01},

urldate = {2018-07-01},

journal = {Journal of the Mechanics and Physics of Solids},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Morales2017,

title = {Robust Optimal Design of Quantum Electronic Devices},

author = {Ociel Morales and Francisco Periago and José A. Vallejo},

url = {https://www.hindawi.com/journals/mpe/2018/3095257/abs/},

issn = {2331-8422},

year  = {2018},

date = {2018-04-05},

urldate = {2018-04-05},

journal = {Mathematical Problems in Engineering},

volume = {2018},

pages = {10},

abstract = {We consider the optimal design of a sequence of quantum barriers in order to manufacture an electronic device at the nanoscale such that the dependence of its transmission coefficient on the bias voltage is linear. The technique presented here is easily adaptable to other response characteristics. The transmission coefficient is computed using the Wentzel-Kramers-Brillouin (WKB) method, so we can explicitly compute the gradient of the objective function. In contrast with earlier treatments, manufacturing uncertainties are incorporated in the model through random variables and the optimal design problem is formulated in a probabilistic setting. As a measure of robustness, a weighted sum of the expectation and the variance of a least-squares performance metric is considered. Several simulations illustrate the proposed approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{JMF_CMAME_2017,

title = {Risk-averse structural topology optimization under random fields using stochastic expansion methods},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306990 

http://www.upct.es/mc3/files/JMF/riskaverse_cmame.pdf},

issn = {0045-7825},

year  = {2018},

date = {2018-03-01},

urldate = {2018-03-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {330},

pages = {180-206},

abstract = {This work proposes a level-set based approach for solving risk-averse structural topology optimization problems considering random field loading and material uncertainty. The use of random fields increases the dimensionality of the stochastic domain, which poses several computational challenges related to the minimization of the Excess Probability as a measure of risk awareness. This problem is addressed both from the theoretical and numerical viewpoints. First, an existence result under a typical geometrical constraint on the set of admissible shapes is proved. Second, a level-set continuous approach to find the numerical solution of the problem is proposed. Since the considered cost functional has a discontinuous integrand, the numerical approximation of the functional and its sensitivity combine an adaptive anisotropic Polynomial Chaos (PC) approach with a Monte-Carlo (MC) sampling method for uncertainty propagation. Furthermore, to address the increment of dimensionality induced by the random field, an anisotropic sparse grid stochastic collocation method is used for the efficient computation of the PC coefficients. A key point is that the non-intrusive nature of such an approach facilitates the use of High Performance Computing (HPC) to alleviate the computational burden of the problem. Several numerical experiments including random field loading and material uncertainty are presented to show the feasibility of the proposal.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2018b,

title = {A curvilinear high order finite element framework for electro-mechanics: From linearised electro-elasticity to massively deformable dielectric elastomers},

author = {Roman Poya and Antonio J. Gil and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306503},

doi = {https://doi.org/10.1016/j.cma.2017.09.020},

year  = {2018},

date = {2018-02-01},

urldate = {2018-02-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {329},

pages = {75-117},

abstract = {This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2017,

title = {Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://doi.org/10.1007/s10957-017-1128-x 

http://localhost/mc3/files/FPE/marin_17.pdf},

doi = {10.1007/s10957-017-1128-x},

issn = {1573-2878},

year  = {2017},

date = {2017-08-01},

urldate = {2017-08-01},

journal = {Journal of Optimization Theory and Applications},

volume = {174},

number = {2},

pages = {428–454},

abstract = {This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Poya2017,

title = {A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics},

author = {Roman Poya and Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0010465517300681},

doi = {https://doi.org/10.1016/j.cpc.2017.02.016},

issn = {0010-4655},

year  = {2017},

date = {2017-07-01},

urldate = {2017-07-01},

journal = {Computer Physics Communications},

volume = {216},

pages = {35-52},

abstract = {The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{andAntonioGil2017,

title = {A framework for polyconvex large strain phase-field methods to fracture},

author = {C. Hesch and Antonio J. Gil and Rogelio Ortigosa and M. Dittmann and C. Bilgen and P. Betsch and M. Franke and A. Janz and K.Weinberg},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516309677},

doi = {https://doi.org/10.1016/j.cma.2016.12.035},

issn = {0045-7825},

year  = {2017},

date = {2017-04-15},

urldate = {2017-04-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {317},

pages = {649-683},

abstract = {Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy–Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn–Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu–Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS201747,

title = {Efficient topology optimization using GPU computing with multilevel granularity},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S0965997816302332},

doi = {https://doi.org/10.1016/j.advengsoft.2017.01.009},

issn = {0965-9978},

year  = {2017},

date = {2017-04-01},

urldate = {2017-04-01},

journal = {Advances in Engineering Software},

volume = {106},

number = {Supplement C},

pages = {47 - 62},

abstract = {Abstract This paper proposes a well-suited strategy for High Performance Computing (HPC) of density-based topology optimization using Graphics Processing Units (GPUs). Such a strategy takes advantage of Massively Parallel Processing (MPP) architectures to overcome the computationally demanding procedures of density-based topology design, both in terms of memory consumption and processing time. This is done exploiting data locality and minimizing both memory consumption and data transfers. The proposed GPU instance makes use of different granularities for the topology optimization pipeline, which are selected to properly balance the workload between the threads exploiting the parallelization potential of massively parallel architectures. The performance of the fine-grained GPU instance of the solving stage is evaluated using two preconditioning techniques. The proposal is also compared with the classical CPU implementation for diverse topology optimization problems, including stiffness maximization, heat sink design and compliant mechanism design.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2017119,

title = {GPU acceleration for evolutionary topology optimization of continuum structures using isosurfaces},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S004579491630459X},

doi = {https://doi.org/10.1016/j.compstruc.2016.10.018},

issn = {0045-7949},

year  = {2017},

date = {2017-04-01},

urldate = {2017-04-01},

journal = {Computers & Structures},

volume = {182},

number = {Supplement C},

pages = {119 - 136},

abstract = {Abstract Evolutionary topology optimization of three-dimensional continuum structures is a computationally demanding task in terms of memory consumption and processing time. This work aims to alleviate these constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal adopts a fine-grained GPU instance of matrix-free iterative solver for structural analysis and an efficient GPU implementation for isosurface extraction and volume fraction calculation. The performance of the solving stage is evaluated using two preconditioning techniques, including the comparison with the sparse-matrix CPU implementation. The proposal is evaluated using topology optimization problems for real-world applications.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016393,

title = {Large-scale robust topology optimization using multi-GPU systems},

author = {Jesús Martínez-Frutos},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516309574},

doi = {https://doi.org/10.1016/j.cma.2016.08.016},

issn = {0045-7825},

year  = {2016},

date = {2016-11-01},

urldate = {2016-11-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {311},

number = {Supplement C},

pages = {393 - 414},

abstract = {Abstract Robust topology optimization of continuum structures is an intensive computational task due to the use of uncertainty propagation methods to estimate the statistical metrics within the topology optimization process. Such a computational problem is exacerbated for large finite element (FE) models in terms of memory consumption and processing time. For these reasons, the efficient resolution of robust topology optimization with large models remains an important computational challenge. This work aims to alleviate these computational constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal exploits the multilevel parallelism provided by multi-GPU systems for the parallel execution both within FE models and through uncertainty propagation methods. Task-level parallelism is used to concurrently evaluate the independent simulation models arising from a sparse grid stochastic collocation method. Data-level parallelism with different granularities is then exploited for the efficient resolution of each simulation model and the computation required by the topology optimization process. The resolution of the different calculations of robust topology optimization pipeline using multi-GPU systems are compared to the classically used multi-CPU implementation achieving significant speedups.},

note = {Listed among CMAME’s most downloaded articles from December 2016- February 2017},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016b,

title = {A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies},

author = {Rogelio Ortigosa and Antonio J. Gil and C. H. Lee},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516302286},

doi = {https://doi.org/10.1016/j.cma.2016.06.025},

issn = {0045-7825},

year  = {2016},

date = {2016-10-01},

urldate = {2016-10-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {310},

pages = {297-334},

abstract = {The series of papers published by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 0000) introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Gil and Ortigosa (2016) in the context of compressible electro-elasticity, a novel extended Hu–Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-variable energy functionals. Ultimately, this leads to the definition of new tangent operators for the Helmholtz’s energy functional in the specific context of incompressible electro-elasticity. Fifth, a Petrov–Galerkin stabilisation technique is applied on the three-field formulation for the circumvention of the Ladyz˘enskaja–Babus˘ka–Brezzi (LBB) condition, enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem. Finally, a series of challenging numerical examples is presented in order to provide an exhaustive comparison of the different variational formulations presented in this paper.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016c,

title = {A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto- mechanics},

author = {Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516303991},

doi = {https://doi.org/10.1016/j.cma.2016.05.019},

issn = {0045-7825},

year  = {2016},

date = {2016-09-01},

urldate = {2016-09-01},

journal = {Computer Methods in Applied Mechanics and Engineering,},

volume = {309},

pages = {202-242},

abstract = {This work is the third on a series of papers by Gil and Ortigosa (Gil and Ortigosa 2016; Ortigosa and Gil 2016) on the development of a new computational framework for the analysis of Electro Active Polymers, where the concept of polyconvexity (Ball 1976) is extended to the case of electro-magneto-mechanical energy functionals. Specifically, four key novelties are incorporated in this paper. Firstly, a new set of first order hyperbolic equations is presented in the context of nonlinear electro-magneto-elasticity, including conservation laws for all the fields of the extended set of arguments which determine the convex multi-variable nature of the internal energy. Secondly, the one-to-one and invertible relationship between this extended set and its associated entropy conjugate set enables the definition of a generalised convex entropy function, resulting in the symmetrisation of the system when expressed in terms of the entropy variables. Thirdly, this paper shows that, after careful analysis of the eigenvalue structure of the system, the definition of multi-variable convexity in Gil and Ortigosa (2016) leads to positive definiteness of the electro-magneto-acoustic tensor. Therefore, multi-variable convexity ensures the satisfaction of the Legendre–Hadamard condition, hence showing that the speeds of propagation of acoustic and electro-magnetic waves in the neighbourhood of a stationary point are real. Finally, under a characteristic experimental set-up for electrostrictive dielectric elastomers, a study of the material stability of convex and non-convex multi-variable constitutive models is carried out.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Bonet2016,

title = {On a tensor cross product based formulation of large strain solid mechanics},

author = {Javier Bonet and Antonio J. Gil and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045782516303991},

doi = {https://doi.org/10.1016/j.ijsolstr.2015.12.030},

issn = {0020-7683},

year  = {2016},

date = {2016-05-01},

urldate = {2016-05-01},

journal = {International Journal of Solids and Structures},

volume = {84},

pages = {49-63},

abstract = {This paper describes in detail the formulation of large strain solid mechanics based on the tensor cross product, originally presented by R. de Boer (1982) and recently re-introduced by Bonet et al. (2015a) and Bonet et al. (2015b). The paper shows how the tensor cross product facilitates the algebra associated with the area and volume maps between reference and final configurations. These maps, together with the fibre map, make up the fundamental kinematic variables in polyconvex elasticity. The algebra proposed leads to novel expressions for the tangent elastic operator which neatly separates material from geometrical dependencies. The paper derives new formulas for the spatial and material stress and their corresponding elasticity tensors. These are applied to the simple case of a Mooney–Rivlin material model. The extension to transversely isotropic material models is also considered.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016d,

title = {A new framework for large strain electromechanics based on convex multi- variable strain energies: variational formulation and material characterisation},

author = {Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782515004168},

doi = {https://doi.org/10.1016/j.cma.2015.11.036},

year  = {2016},

date = {2016-04-15},

urldate = {2016-04-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {302},

pages = {293-328},

abstract = {Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain energies which depend on non-strain based variables introducing other physical measures such as the electric displacement. Six key novelties are incorporated in this work. First, a new definition of the electro-mechanical internal energy is introduced expressed as a convex multi-variable function of a new extended set of electromechanical arguments. Crucially, this new definition of the internal energy enables the most accepted constitutive inequality, namely ellipticity, to be extended to the entire range of deformations and electric fields and, in addition, to incorporate the electro-mechanical energy of the vacuum, and hence that for ideal dielectric elastomers, as a degenerate case. Second, a new extended set of variables, work conjugate to those characterising the new definition of multi-variable convexity, is introduced in this paper. Third, both new sets of variables enable the definition of novel extended Hu–Washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro-elasticity. Fourth, some simple strategies to create appropriate convex multi-variable energy functionals (in terms of convex multi-variable invariants) by incorporating minor modifications to a priori non-convex multi-variable functionals are also presented. Fifth, a tensor cross product operation (de Boer, 1982) used in Bonet et al. (2015) to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro-mechanical framework, leading to insightful representations of otherwise complex algebraic expressions. Finally, under a characteristic experimental setup in dielectric elastomers, the behaviour of a convex multi-variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction, is numerically studied.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016e,

title = {A new framework for large strain electromechanics based on convex multi- variable strain energies: Finite Element discretisation and computational implementation},

author = {Rogelio Ortigosa and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782515004090},

doi = {https://doi.org/10.1016/j.cma.2015.12.007},

issn = {0045-7825},

year  = {2016},

date = {2016-04-15},

urldate = {2016-04-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {302},

pages = {329-360},

abstract = {In Gil and Ortigosa (2016), Gil and Ortigosa introduced a new convex multi-variable framework for the numerical simulation of Electro Active Polymers (EAPs) in the presence of extreme deformations and electric fields. This extends the concept of polyconvexity to strain energies which depend on non-strain based variables. The consideration of the new concept of multi-variable convexity guarantees the well posedness of generalised Gibbs’ energy density functionals and, hence, opens up the possibility of a new family of mixed variational principles. The aim of this paper is to present, as an example, the Finite Element implementation of two of these mixed variational principles. These types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement-potential based formulation yields non-physical results, such as volumetric locking, bending and shear locking, pressure oscillations and electro-mechanical locking, to name but a few. Crucially, the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out. This results in mixed formulations with a computational cost comparable to that of the displacement-potential based approach, yet far more accurate. Finally, a series of very challenging numerical examples are presented in order to demonstrate the accuracy, robustness and efficiency of the proposed methodology.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NME:NME5210,

title = {Robust optimal Robin boundary control for the transient heat equation with random input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Arnaud Münch and Francisco Periago},

url = {http://dx.doi.org/10.1002/nme.5210 

http://localhost/mc3/files/FPE/ijnme_16.pdf},

doi = {10.1002/nme.5210},

issn = {1097-0207},

year  = {2016},

date = {2016-03-02},

urldate = {2016-03-02},

journal = {International Journal for Numerical Methods in Engineering},

volume = {108},

number = {2},

pages = {116–135},

abstract = {The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient-based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Gil2016,

title = {A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity},

author = {Antonio J. Gil and C. H. Lee and Javier Bonet and Rogelio Ortigosa},

url = {https://www.sciencedirect.com/science/article/pii/S0045782515003631},

doi = {https://doi.org/10.1016/j.cma.2015.11.010},

issn = {0045-7825},

year  = {2016},

date = {2016-03-01},

urldate = {2016-03-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {300},

pages = {146-181},

abstract = {In Part I of this series, Bonet et al. (2015) introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics, where a mixed set of Total Lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures, namely the deformation gradient, its co-factor and its Jacobian. The main aim of this paper is to expand this formulation to the case of nearly incompressible and truly incompressible materials. The paper is further enhanced with three key novelties. First, the use of polyconvex nearly incompressible strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes. Two variants of the same formulation can then be obtained, namely, conservation-based and entropy-based, depending on the unknowns of the system. Crucially, the study of the eigenvalue structure of the system is carried out in order to demonstrate its hyperbolicity and, thus, obtain the correct time step bounds for explicit time integrators. Second, the development of a stabilised Petrov–Galerkin framework is presented for both systems of hyperbolic equations, that is, when expressed in terms of either conservation or entropy variables. Third, an adapted fractional step method, built upon the work presented in Gil et al. (2014), is presented to extend the range of applications towards the incompressibility limit. Finally, a series of numerical examples are presented in order to assess the applicability and robustness of the proposed formulation. The overall scheme shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding equal order of convergence for velocities and stresses.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2016f,

title = {A computational framework for polyconvex large strain elasticity for geometrically exact beam theory},

author = {Rogelio Ortigosa and Antonio J. Gil and Javier Bonet and Christian Hesch},

url = {https://link.springer.com/article/10.1007/s00466-015-1231-5},

doi = {https://doi.org/10.1007/s00466-015-1231-5},

issn = {0178-7675},

year  = {2016},

date = {2016-02-01},

urldate = {2016-02-01},

journal = {Computational Mechanics},

volume = {57},

pages = {277–303},

abstract = {In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016271,

title = {Robust shape optimization of continuous structures via the level set method},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516300834 

http://localhost/mc3/files/FPE/cmame16.pdf},

doi = {https://doi.org/10.1016/j.cma.2016.03.003},

issn = {0045-7825},

year  = {2016},

date = {2016-01-15},

urldate = {2016-01-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {305},

number = {Supplement C},

pages = {271 - 291},

abstract = {Abstract This work proposes a stochastic shape optimization method for continuous structures using the level-set method. Such a method aims to minimize the expected compliance and its variance as measures of the structural robustness. The behavior of continuous structures is modeled by linear elasticity equations with uncertain loading and material. This uncertainty can be modeled using random variables with different probability distributions as well as random fields. The proper problem formulation is ensured by the proof of the existence colorrev of solution under certain geometrical constraints on the set of admissible shapes. The proposed method addresses the stochastic linear elasticity problem in its weak form obtaining the explicit expressions for the continuous shape derivatives. Some numerical examples are presented to show the effectiveness of the proposed approach.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2016,

title = {Kriging-based infill sampling criterion for constraint handling in multi-objective optimization},

author = {Jesús Martínez-Frutos},

url = {https://doi.org/10.1007/s10898-015-0370-8},

doi = {10.1007/s10898-015-0370-8},

issn = {1573-2916},

year  = {2016},

date = {2016-01-01},

urldate = {2016-01-01},

journal = {Journal of Global Optimization},

volume = {64},

number = {1},

pages = {97–115},

abstract = {This paper proposes a novel infill sampling criterion for constraint handling in multi-objective optimization of computationally expensive black-box functions. To reduce the computational burden, Kriging models are used to emulate the objective and constraint functions. The challenge of this multi-objective optimization problem arises from the fact that the epistemic uncertainty of the Kriging models should be taken into account to find Pareto-optimal solutions in the feasible domain. This is done by the proposed sampling criterion combining the Expected HyperVolume Improvement of the front of nondominated solutions and the Probability of Feasibility of new candidates. The proposed criterion is non-intrusive and derivative-free, and it is oriented to: (1) problems in which the computational cost is mainly from the function evaluation rather than optimization, and (2) problems that use complex in-house or commercial software that cannot be modified. The results using the proposed sampling criterion are compared with the results using Multi-Objective Evolutionary Algorithms. These results show that the proposed sampling criterion permits to identify both the feasible domain and an approximation of the Pareto front using a reduced number of computationally expensive simulations.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2015,

title = {Robust optimal shape design for an elliptic PDE with uncertainty in its input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

doi = {10.1051/cocv/2014049},

issn = {1262-3377},

year  = {2015},

date = {2015-05-20},

urldate = {2015-05-20},

journal = {ESAIM: COCV},

volume = {21},

number = {4},

pages = {901--923},

publisher = {EDP Sciences},

keywords = {19274/PI/14, Computational Mathematics, Control and Optimization, Control and Systems Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2013,

title = {Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation},

author = {Francisco Periago},

doi = {10.1007/s10957-013-0447-9},

issn = {1573-2878},

year  = {2014},

date = {2014-06-00},

urldate = {2014-06-00},

journal = {J Optim Theory Appl},

volume = {161},

number = {3},

pages = {951--968},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2013,

title = {Numerical approximation of bang–bang controls for the heat equation: An optimal design approach},

author = {Arnaud Münch and Francisco Periago},

doi = {10.1016/j.sysconle.2013.04.009},

issn = {0167-6911},

year  = {2013},

date = {2013-08-00},

urldate = {2013-08-00},

journal = {Systems & Control Letters},

volume = {62},

number = {8},

pages = {643--655},

publisher = {Elsevier BV},

keywords = {Control and Systems Engineering, Electrical and Electronic Engineering, General Computer Science, Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Font2012,

title = {A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines},

author = {Roberto Font and Pablo Pedregal and Francisco Periago},

doi = {10.1002/oca.2024},

issn = {1099-1514},

year  = {2013},

date = {2013-03-00},

urldate = {2013-03-00},

journal = {Optim Control Appl Methods},

volume = {34},

number = {2},

pages = {236--252},

publisher = {Wiley},

abstract = {<jats:title>SUMMARY</jats:title><jats:p>On the basis of the classical variational reformulation of optimal control problems, we introduce a numerical scheme for solving those problems where the goal is the computation of optimal controls in feedback and digital forms defined on a discrete time mesh. The algorithm reduces the computation of such controls to solving a suitable nonlinear mathematical programming problem where the unknowns are the controls and slope of the state variable of the original problem. The motivation for this study comes from the real‐world engineering problem which consists of maneuvering a manned submarine by using the blowing‐venting control system of the ballast tanks of the vehicle. After checking the proposed algorithm in an academic example, we apply it to the maneuvering problem of submarines whose mathematical model includes a state law which is composed of a system of twenty‐four nonlinear ordinary differential equations. Numerical results illustrate the performance of the numerical scheme. Copyright © 2012 John Wiley & Sons, Ltd.</jats:p>},

keywords = {Applied Mathematics, Control and Optimization, Control and Systems Engineering, Software},

pubstate = {published},

tppubtype = {article}

}

@article{Ovalle2011,

title = {Analysis and numerical simulation of a nonlinear mathematical model for testing the manoeuvrability capabilities of a submarine},

author = {Diana M. Ovalle and Javier García and Francisco Periago},

doi = {10.1016/j.nonrwa.2010.11.001},

issn = {1468-1218},

year  = {2011},

date = {2011-06-00},

urldate = {2011-06-00},

journal = {Nonlinear Analysis: Real World Applications},

volume = {12},

number = {3},

pages = {1654--1669},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2011,

title = {Optimal distribution of the internal null control for the one-dimensional heat equation},

author = {Arnaud Münch and Francisco Periago},

doi = {10.1016/j.jde.2010.10.020},

issn = {0022-0396},

year  = {2011},

date = {2011-01-00},

urldate = {2011-01-00},

journal = {Journal of Differential Equations},

volume = {250},

number = {1},

pages = {95--111},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Font2010,

title = {Numerical simulation of the boundary exact control for the system of linear elasticity},

author = {Roberto Font and Francisco Periago},

doi = {10.1016/j.aml.2010.04.030},

issn = {0893-9659},

year  = {2010},

date = {2010-09-00},

urldate = {2010-09-00},

journal = {Applied Mathematics Letters},

volume = {23},

number = {9},

pages = {1021--1026},

publisher = {Elsevier BV},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2010,

title = {A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle},

author = {Francisco Periago and Jorge Tiago},

doi = {10.1016/j.nonrwa.2009.09.002},

issn = {1468-1218},

year  = {2010},

date = {2010-08-00},

urldate = {2010-08-00},

journal = {Nonlinear Analysis: Real World Applications},

volume = {11},

number = {4},

pages = {2573--2583},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},

pubstate = {published},

tppubtype = {article}

}

@article{Allaire2010,

title = {Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation},

author = {Grégoire Allaire and Arnaud Münch and Francisco Periago},

doi = {10.1137/090780481},

issn = {1095-7138},

year  = {2010},

date = {2010-01-00},

urldate = {2010-01-00},

journal = {SIAM J. Control Optim.},

volume = {48},

number = {8},

pages = {5333--5356},

publisher = {Society for Industrial & Applied Mathematics (SIAM)},

keywords = {Applied Mathematics, Control and Optimization},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2008,

title = {Optimal Internal Stabilization of the Linear System of Elasticity},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1007/s00205-008-0187-4},

issn = {1432-0673},

year  = {2009},

date = {2009-07-00},

urldate = {2009-07-00},

journal = {Arch Rational Mech Anal},

volume = {193},

number = {1},

pages = {171--193},

publisher = {Springer Science and Business Media LLC},

keywords = {Analysis, Mathematics (miscellaneous), Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2009,

title = {Optimal shape and position of the support for the internal exact control of a string},

author = {Francisco Periago},

doi = {10.1016/j.sysconle.2008.08.007},

issn = {0167-6911},

year  = {2009},

date = {2009-02-00},

urldate = {2009-02-00},

journal = {Systems & Control Letters},

volume = {58},

number = {2},

pages = {136--140},

publisher = {Elsevier BV},

keywords = {Control and Systems Engineering, Electrical and Electronic Engineering, General Computer Science, Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Pedregal2008,

title = {A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems},

author = {Pablo Pedregal and Francisco Periago and Jorge Villena},

doi = {10.1111/j.1467-9590.2008.00406.x},

issn = {1467-9590},

year  = {2008},

date = {2008-07-00},

urldate = {2008-07-00},

journal = {Stud Appl Math},

volume = {121},

number = {1},

pages = {27--47},

publisher = {Wiley},

abstract = {<jats:p>This paper deals with the numerical computation of the boundary controls of linear, time‐reversible, second‐order evolution systems. Based on a method introduced by Russell (<jats:italic>Stud. Appl. Math.</jats:italic> LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.</jats:p>},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2008b,

title = {Relaxation of an optimal design problem for the heat equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.matpur.2007.12.009},

issn = {0021-7824},

year  = {2008},

date = {2008-03-00},

urldate = {2008-03-00},

journal = {Journal de Mathématiques Pures et Appliquées},

volume = {89},

number = {3},

pages = {225--247},

publisher = {Elsevier BV},

keywords = {Applied Mathematics, General Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2006b,

title = {Optimal design of the damping set for the stabilization of the wave equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.jde.2006.06.009},

issn = {0022-0396},

year  = {2006},

date = {2006-12-00},

urldate = {2006-12-00},

journal = {Journal of Differential Equations},

volume = {231},

number = {1},

pages = {331--358},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Pedregal2006,

title = {Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation},

author = {Pablo Pedregal and Francisco Periago},

doi = {10.1090/s0033-569x-06-01022-4},

issn = {1552-4485},

year  = {2006},

date = {2006-09-00},

urldate = {2006-09-00},

journal = {Quart. Appl. Math.},

volume = {64},

number = {3},

pages = {529--546},

publisher = {American Mathematical Society (AMS)},

abstract = {<p>This paper contains three results concerning the homogenization and exact controllability for the one-dimensional wave equation. First, we give sufficient conditions on the initial data to ensure the convergence of the conormal derivatives associated with the wave equation with a rapidly oscillating coefficient and zero Dirichlet boundary conditions. Secondly, we apply this result to prove the existence of a class of initial data whose associated boundary controls are uniformly bounded and obtain some information (in particular, its limit behavior) on this class of data. Finally, we prove that all initial data in <inline-formula content-type="math/mathml">

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared times upper H Superscript negative 1">

  <mml:semantics>

    <mml:mrow>

      <mml:msup>

        <mml:mi>L</mml:mi>

        <mml:mn>2</mml:mn>

      </mml:msup>

      <mml:mo>×<!-- × --></mml:mo>

      <mml:msup>

        <mml:mi>H</mml:mi>

        <mml:mrow class="MJX-TeXAtom-ORD">

          <mml:mo>−<!-- − --></mml:mo>

          <mml:mn>1</mml:mn>

        </mml:mrow>

      </mml:msup>

    </mml:mrow>

    <mml:annotation encoding="application/x-tex">L^2times H^{-1}</mml:annotation>

  </mml:semantics>

</mml:math>

</inline-formula> may be uniformly controlled but at the price of adding an internal feedback control in our system. The main advantage of this last procedure is that we have explicit formulae for both states and controls.</p>},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2006,

title = {A variational approach to a shape design problem for the wave equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.crma.2006.07.013},

issn = {1631-073X},

year  = {2006},

date = {2006-09-00},

urldate = {2006-09-00},

journal = {Comptes Rendus Mathematique},

volume = {343},

number = {5},

pages = {371--376},

publisher = {Cellule MathDoc/CEDRAM},

keywords = {General Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2003,

title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},

author = {Francisco Periago},

doi = {10.1016/s0022-247x(03)00126-4},

issn = {0022-247X},

year  = {2003},

date = {2003-04-00},

urldate = {2003-04-00},

journal = {Journal of Mathematical Analysis and Applications},

volume = {280},

number = {2},

pages = {413--423},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2003c,

title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},

author = {Francisco Periago},

doi = {10.1016/s0022-247x(03)00126-4},

issn = {0022-247X},

year  = {2003},

date = {2003-04-00},

journal = {Journal of Mathematical Analysis and Applications},

volume = {280},

number = {2},

pages = {413--423},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2003b,

title = {On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem},

author = {Francisco Periago and B. Straub},

doi = {10.4064/sm155-2-7},

issn = {1730-6337},

year  = {2003},

date = {2003-00-00},

urldate = {2003-00-00},

journal = {Studia Math.},

volume = {155},

number = {2},

pages = {183--193},

publisher = {Institute of Mathematics, Polish Academy of Sciences},

keywords = {General Mathematics},

pubstate = {published},

tppubtype = {article}

}