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2025
Journal article
Open Access
Regularized methods via cubic model subspace minimization for nonconvex optimization
Bellavia S., Palitta D., Porcelli M., Simoncini V.
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low dimensional subspace that, in contrast to classic approaches, is reused for a number of iterations. Whenever the trial step produced by the low-dimensional minimization process is unsatisfactory, we employ a regularized Newton step whose regularization parameter is a by-product of the model minimization over the low-dimensional subspace. We show that the worst-case complexity of classic cubic regularized methods is preserved, despite the possible regularized Newton steps. We focus on the large class of problems for which (sparse) direct linear system solvers are available and provide several experimental results showing the very large gains of our new approach when compared to standard implementations of adaptive cubic regularization methods based on direct linear solvers. Our first choice as projection space for the low-dimensional model minimization is the polynomial Krylov subspace; nonetheless, we also explore the use of rational Krylov subspaces in case where the polynomial ones lead to less competitive numerical results.Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
DOI: 10.1007/s10589-025-00655-2
DOI: 10.48550/arxiv.2306.14290
Metrics:
Bellavia S., Palitta D., Porcelli M., Simoncini V.
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low dimensional subspace that, in contrast to classic approaches, is reused for a number of iterations. Whenever the trial step produced by the low-dimensional minimization process is unsatisfactory, we employ a regularized Newton step whose regularization parameter is a by-product of the model minimization over the low-dimensional subspace. We show that the worst-case complexity of classic cubic regularized methods is preserved, despite the possible regularized Newton steps. We focus on the large class of problems for which (sparse) direct linear system solvers are available and provide several experimental results showing the very large gains of our new approach when compared to standard implementations of adaptive cubic regularization methods based on direct linear solvers. Our first choice as projection space for the low-dimensional model minimization is the polynomial Krylov subspace; nonetheless, we also explore the use of rational Krylov subspaces in case where the polynomial ones lead to less competitive numerical results.Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
DOI: 10.1007/s10589-025-00655-2
DOI: 10.48550/arxiv.2306.14290
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arXiv.org e-Print Archive 
| Computational Optimization and Applications | CNR IRIS | link.springer.com | doi.org 
| CNR IRIS | CNR IRIS
2024
Conference article
Open Access
Dictionary Learning for data compression within a Digital Twin Framework
Cavalli L., Brandoni D., Porcelli M., Pascolo E.
Digital Twin system plays a crucial role in several contexts, from smart agriculture to predictive maintenance, from healthcare to weather modelling. To be effective, it involves a continuous exchange of massive data between IoT sensors on real world and digital system hosted on HPC and vice versa. Nevertheless, the transmitted signals often exhibit high similarity, resulting in a redundant dataset very suitable for compression. This paper shows how Dictionary Learning can be used as a preprocessing technique for AI algorithms due to its ability to compress large data volumes up to 80% with a potential enhancement of the performances acting both as a denoising and compression technique. This algorithm operates efficiently on various types of datasets, from images to timeseries, and is well-suited for deployment on devices with limited computational resources, like IoT sensors.Source: CEUR WORKSHOP PROCEEDINGS, vol. 3762, pp. 182-187. Naples, Italy, 29-30/05/2024
Cavalli L., Brandoni D., Porcelli M., Pascolo E.
Digital Twin system plays a crucial role in several contexts, from smart agriculture to predictive maintenance, from healthcare to weather modelling. To be effective, it involves a continuous exchange of massive data between IoT sensors on real world and digital system hosted on HPC and vice versa. Nevertheless, the transmitted signals often exhibit high similarity, resulting in a redundant dataset very suitable for compression. This paper shows how Dictionary Learning can be used as a preprocessing technique for AI algorithms due to its ability to compress large data volumes up to 80% with a potential enhancement of the performances acting both as a denoising and compression technique. This algorithm operates efficiently on various types of datasets, from images to timeseries, and is well-suited for deployment on devices with limited computational resources, like IoT sensors.Source: CEUR WORKSHOP PROCEEDINGS, vol. 3762, pp. 182-187. Naples, Italy, 29-30/05/2024
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ceur-ws.org | CNR IRIS | CNR IRIS
2023
Journal article
Open Access
Numerical solution of a class of quasi-linear matrix equations
Porcelli M, Simoncini V
Given the matrix equation AX + XB + f (X)C = D in the unknown n * m matrix X, we analyze existence and uniqueness conditions, together with computational solution strategies for [...] being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions f. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.Source: LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 664, pp. 349-368
DOI: 10.1016/j.laa.2023.01.024
Metrics:
Porcelli M, Simoncini V
Given the matrix equation AX + XB + f (X)C = D in the unknown n * m matrix X, we analyze existence and uniqueness conditions, together with computational solution strategies for [...] being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions f. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.Source: LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 664, pp. 349-368
DOI: 10.1016/j.laa.2023.01.024
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CNR IRIS | ISTI Repository | www.sciencedirect.com | CNR IRIS | CNR IRIS
2023
Contribution to book
Open Access
Numerical modelling of historical masonry structures with the finite element code NOSA-ITACA
Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.
This chapter presents the finite element code NOSA-ITACA for static and modal analyses of masonry structures of architectural interest. NOSA-ITACA adopts the constitutive equation of masonrylike materials, which considers masonry a non-linear elastic material with zero tensile strength. The capability of modelling restoration and consolidation operations makes the code a helpful tool for maintaining historical buildings. In recent years, long-term vibration monitoring turned out to be an effective non-destructive technique to investigate the dynamic behaviour and check the health status of historical buildings. Changes in their dynamic properties, such as natural frequencies, can represent effective damage indicators. The latest NOSA-ITACA developments are oriented towards structural health monitoring. The availability of the experimental modal properties of a structure makes it possible to calibrate its finite element model via model updating procedures. In particular, the unknown structure's characteristics, such as materials' properties and boundary conditions, can be determined by solving a minimum problem whose objective function is expressed as the discrepancy between experimental frequencies and mode shapes and their numerical counterparts. Several case studies are presented to show the main features of NOSA-ITACA and its effectiveness in the conservation of architectural heritage.Source: SPRINGER INDAM SERIES (ONLINE), vol. 55, pp. 133-152
DOI: 10.1007/978-981-99-3679-3_9
Metrics:
Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.
This chapter presents the finite element code NOSA-ITACA for static and modal analyses of masonry structures of architectural interest. NOSA-ITACA adopts the constitutive equation of masonrylike materials, which considers masonry a non-linear elastic material with zero tensile strength. The capability of modelling restoration and consolidation operations makes the code a helpful tool for maintaining historical buildings. In recent years, long-term vibration monitoring turned out to be an effective non-destructive technique to investigate the dynamic behaviour and check the health status of historical buildings. Changes in their dynamic properties, such as natural frequencies, can represent effective damage indicators. The latest NOSA-ITACA developments are oriented towards structural health monitoring. The availability of the experimental modal properties of a structure makes it possible to calibrate its finite element model via model updating procedures. In particular, the unknown structure's characteristics, such as materials' properties and boundary conditions, can be determined by solving a minimum problem whose objective function is expressed as the discrepancy between experimental frequencies and mode shapes and their numerical counterparts. Several case studies are presented to show the main features of NOSA-ITACA and its effectiveness in the conservation of architectural heritage.Source: SPRINGER INDAM SERIES (ONLINE), vol. 55, pp. 133-152
DOI: 10.1007/978-981-99-3679-3_9
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CNR IRIS | link.springer.com | ISTI Repository | CNR IRIS | CNR IRIS | CNR IRIS
2022
Journal article
Open Access
A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
Padovani C, Porcelli M
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following interior point method coupled with a Mehrotra's predictor-corrector approach is proposed. Implementations based on well-known symmetrization schemes and on direct methods are theoretically and numerically investigated taking into account tensors C arising in the modelling of masonry-like materials. For these special cases, indications on the preferable symmetrization scheme that take into account the conditioning of the arising linear systems are given.Source: CALCOLO (ONLINE), vol. 59 (issue 33)
DOI: 10.1007/s10092-022-00478-1
Metrics:
Padovani C, Porcelli M
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following interior point method coupled with a Mehrotra's predictor-corrector approach is proposed. Implementations based on well-known symmetrization schemes and on direct methods are theoretically and numerically investigated taking into account tensors C arising in the modelling of masonry-like materials. For these special cases, indications on the preferable symmetrization scheme that take into account the conditioning of the arising linear systems are given.Source: CALCOLO (ONLINE), vol. 59 (issue 33)
DOI: 10.1007/s10092-022-00478-1
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CNR IRIS | link.springer.com | ISTI Repository | CNR IRIS
2022
Journal article
Open Access
Exploiting problem structure in derivative free optimization
Porcelli M., Toint P. L.
A structured version of derivative-free random pattern search optimization algorithms is introduced, which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems. This technique improves performance by orders of magnitude and makes it possible to solve large problems that otherwise are totally intractable by other derivative-free methods. A library of interpolation-based modelling tools is also described, which can be associated with the structured or unstructured versions of the initial pattern search algorithm. The use of the library further enhances performance, especially when associated with structure. The significant gains in performance associated with these two techniques are illustrated using a new freely-available release of the Brute Force Optimizer (BFO) package firstly introduced in [Porcelli and Toint 2017], which incorporates them. An interesting conclusion of the numerical results presented is that providing global structural information on a problem can result in significantly less evaluations of the objective function than attempting to building local Taylor-like models.Source: ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (ONLINE), vol. 48 (issue 1)
DOI: 10.1145/3474054
DOI: 10.48550/arxiv.2001.04801
Metrics:
Porcelli M., Toint P. L.
A structured version of derivative-free random pattern search optimization algorithms is introduced, which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems. This technique improves performance by orders of magnitude and makes it possible to solve large problems that otherwise are totally intractable by other derivative-free methods. A library of interpolation-based modelling tools is also described, which can be associated with the structured or unstructured versions of the initial pattern search algorithm. The use of the library further enhances performance, especially when associated with structure. The significant gains in performance associated with these two techniques are illustrated using a new freely-available release of the Brute Force Optimizer (BFO) package firstly introduced in [Porcelli and Toint 2017], which incorporates them. An interesting conclusion of the numerical results presented is that providing global structural information on a problem can result in significantly less evaluations of the objective function than attempting to building local Taylor-like models.Source: ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (ONLINE), vol. 48 (issue 1)
DOI: 10.1145/3474054
DOI: 10.48550/arxiv.2001.04801
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arXiv.org e-Print Archive | ACM Transactions on Mathematical Software | dl.acm.org | CNR IRIS | ISTI Repository | ACM Transactions on Mathematical Software | doi.org | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | CNR IRIS | CNR IRIS
2022
Journal article
Open Access
An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations
Garmatter D, Porcelli M, Rinaldi F, Stoll M
This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra issues, arising from the PDE discretization. Since classical solution approaches such as the branch-and-bound framework are typically overwhelmed by such large-scale problems, this work extends an improved penalty algorithm proposed by the authors, to the time-dependent setting. The main contribution is a novel combination of an interior point method, preconditioning, and model order reduction yielding a tailored local optimization solver at the heart of the overall solution procedure. A thorough numerical investigation is carried out both for the heat equation as well as a convection-diffusion problem demonstrating the versatility of the approach.Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (DORDR., ONLINE)
DOI: 10.1007/s10589-022-00386-8
Metrics:
Garmatter D, Porcelli M, Rinaldi F, Stoll M
This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra issues, arising from the PDE discretization. Since classical solution approaches such as the branch-and-bound framework are typically overwhelmed by such large-scale problems, this work extends an improved penalty algorithm proposed by the authors, to the time-dependent setting. The main contribution is a novel combination of an interior point method, preconditioning, and model order reduction yielding a tailored local optimization solver at the heart of the overall solution procedure. A thorough numerical investigation is carried out both for the heat equation as well as a convection-diffusion problem demonstrating the versatility of the approach.Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (DORDR., ONLINE)
DOI: 10.1007/s10589-022-00386-8
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CNR IRIS | ISTI Repository | rdcu.be | CNR IRIS
2021
Journal article
Open Access
Improved penalty algorithm for mixed integer PDE constrained optimization problems
Garmatter D., Porcelli M., Rinaldi F., Stoll M.
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the branch-and-bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially in a large-scale context, this article investigates penalization techniques. Taking inspiration from a well-known family of existing exact penalty algorithms, a novel improved penalty algorithm is derived, whose key ingredients are a basin hopping strategy and an interior point method, both of which are specialized for the problem class. A thorough numerical investigation is carried out for a standard stationary test problem. Extensions to a convection-diffusion as well as a nonlinear test problem finally demonstrate the versatility of the approach.Source: COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987), vol. 116, pp. 2-14
DOI: 10.1016/j.camwa.2021.11.004
DOI: 10.48550/arxiv.1907.06462
Metrics:
Garmatter D., Porcelli M., Rinaldi F., Stoll M.
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the branch-and-bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially in a large-scale context, this article investigates penalization techniques. Taking inspiration from a well-known family of existing exact penalty algorithms, a novel improved penalty algorithm is derived, whose key ingredients are a basin hopping strategy and an interior point method, both of which are specialized for the problem class. A thorough numerical investigation is carried out for a standard stationary test problem. Extensions to a convection-diffusion as well as a nonlinear test problem finally demonstrate the versatility of the approach.Source: COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987), vol. 116, pp. 2-14
DOI: 10.1016/j.camwa.2021.11.004
DOI: 10.48550/arxiv.1907.06462
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arXiv.org e-Print Archive | Computers & Mathematics with Applications | CNR IRIS | ISTI Repository | www.sciencedirect.com | Computers & Mathematics with Applications | doi.org | CNR IRIS | CNR IRIS
2021
Journal article
Open Access
Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications
Meli E., Morini B., Porcelli M., Sgattoni C.
Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.Source: JOURNAL OF SCIENTIFIC COMPUTING, vol. 90 (issue 1), p. 30
DOI: 10.1007/s10915-021-01690-x
DOI: 10.48550/arxiv.2005.05851
Metrics:
Meli E., Morini B., Porcelli M., Sgattoni C.
Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.Source: JOURNAL OF SCIENTIFIC COMPUTING, vol. 90 (issue 1), p. 30
DOI: 10.1007/s10915-021-01690-x
DOI: 10.48550/arxiv.2005.05851
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arXiv.org e-Print Archive | Journal of Scientific Computing | CNR IRIS | link.springer.com | ISTI Repository | Journal of Scientific Computing | doi.org | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | CNR IRIS | CNR IRIS
2019
Journal article
Open Access
Finite element model updating for structural applications
Girardi M, Padovani C, Pellegrini D, Porcelli M, Robol L
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown material parameters (such as mass density and Young's modulus) of the materials and/or the boundary conditions, which are often known only approximately. In particular, this is the case when considering historical buildings. The straightforward application of a general-purpose optimizer can be impractical, given the large size of the model involved. In the paper, we show that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, form the basis for a reliable and efficient specialized algorithm. We describe an optimization strategy based on this approach, and we provide numerical experiments that confirm its effectiveness and accuracy.Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 370
DOI: 10.1016/j.cam.2019.112675
DOI: 10.48550/arxiv.1801.09122
Metrics:
Girardi M, Padovani C, Pellegrini D, Porcelli M, Robol L
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown material parameters (such as mass density and Young's modulus) of the materials and/or the boundary conditions, which are often known only approximately. In particular, this is the case when considering historical buildings. The straightforward application of a general-purpose optimizer can be impractical, given the large size of the model involved. In the paper, we show that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, form the basis for a reliable and efficient specialized algorithm. We describe an optimization strategy based on this approach, and we provide numerical experiments that confirm its effectiveness and accuracy.Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 370
DOI: 10.1016/j.cam.2019.112675
DOI: 10.48550/arxiv.1801.09122
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arXiv.org e-Print Archive | Journal of Computational and Applied Mathematics | CNR IRIS | ISTI Repository | www.sciencedirect.com | Journal of Computational and Applied Mathematics | doi.org | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | CNR IRIS | CNR IRIS | CNR IRIS
2018
Conference article
Open Access
Fea for masonry structures and vibration-based model updating using NOSA-ITACA
Girardi M, Padovani C, Pellegrini D, Porcelli M, Robol L
NOSA-ITACA is a finite-element code developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR for the structural analysis of masonry constructions of historical interest via the constitutive equation of masonry-like materials. The latest improvements in the software allow applying model updating techniques to match experimentally measured frequencies in order to fine-tune calculation of the free parameters in the model. The numerical method is briefly presented and applied to two historical buildings in Lucca, the Church of San Francesco and the Clock Tower.
Girardi M, Padovani C, Pellegrini D, Porcelli M, Robol L
NOSA-ITACA is a finite-element code developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR for the structural analysis of masonry constructions of historical interest via the constitutive equation of masonry-like materials. The latest improvements in the software allow applying model updating techniques to match experimentally measured frequencies in order to fine-tune calculation of the free parameters in the model. The numerical method is briefly presented and applied to two historical buildings in Lucca, the Church of San Francesco and the Clock Tower.
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CNR IRIS | ISTI Repository | CNR IRIS | CNR IRIS
2017
Software
Open Access
NOSA-ITACA 1.1
Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D, Porcelli M, Robol L
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.
Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D, Porcelli M, Robol L
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.
See at:
CNR IRIS | ISTI Repository | www.nosaitaca.it | CNR IRIS
2016
Conference article
Open Access
Safety assessment of masonry constructions via numerical tools: the NOSA-ITACA code
Binante V, Girardi M, Lucchesi M, Padovani C, Pellegrini D, Margherita P
This paper describes the main features of the NOSA-ITACA code, software for the structural analysis of masonry buildings of historical interest resulting from integration of the finite element code NOSA and the open-source platform SALOME. After a short description of the constitutive equation used to model the mechanical behaviour of masonry constructions, some details are given concerning the code's implementation. Then, the result of a static analysis of the "Voltone" in Livorno, performed via the NOSAITACA code, is presented with the aim of highlighting the important role of mathematical models and numerical tools in assessing the safety of historical masonry buildings.
Binante V, Girardi M, Lucchesi M, Padovani C, Pellegrini D, Margherita P
This paper describes the main features of the NOSA-ITACA code, software for the structural analysis of masonry buildings of historical interest resulting from integration of the finite element code NOSA and the open-source platform SALOME. After a short description of the constitutive equation used to model the mechanical behaviour of masonry constructions, some details are given concerning the code's implementation. Then, the result of a static analysis of the "Voltone" in Livorno, performed via the NOSAITACA code, is presented with the aim of highlighting the important role of mathematical models and numerical tools in assessing the safety of historical masonry buildings.
See at:
CNR IRIS | ISTI Repository | CNR IRIS
2014
Software
Open Access
NOSA-ITACA
Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D, Porcelli M
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.
Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D, Porcelli M
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.
See at:
CNR IRIS | ISTI Repository | www.nosaitaca.it | CNR IRIS
2014
Journal article
Restricted
New updates of incomplete LU factorizations and applications to large nonlinear systems
Bellavia S, Morini B, Porcelli M
In this paper, we address the problem of preconditioning sequences of large sparse indefinite systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal update. For a general treatment, an incomplete LU (ILU) factorization is considered, but the proposed approaches apply to incomplete factorizations of symmetric matrices as well. The first strategy is an approximate diagonal update of the ILU factorization; the second strategy relies on banded approximations of the factors in the ideal update. The efficiency and reliability of the proposed preconditioners are shown in the solution of nonlinear systems of equations by preconditioned Newton-Krylov methods. Nearly matrix-free implementations of the updating strategy are provided, and numerical experiments are carried out on application problems.Source: OPTIMIZATION METHODS & SOFTWARE, vol. 29 (issue 2), pp. 321-340
DOI: 10.1080/10556788.2012.762517
Metrics:
Bellavia S, Morini B, Porcelli M
In this paper, we address the problem of preconditioning sequences of large sparse indefinite systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal update. For a general treatment, an incomplete LU (ILU) factorization is considered, but the proposed approaches apply to incomplete factorizations of symmetric matrices as well. The first strategy is an approximate diagonal update of the ILU factorization; the second strategy relies on banded approximations of the factors in the ideal update. The efficiency and reliability of the proposed preconditioners are shown in the solution of nonlinear systems of equations by preconditioned Newton-Krylov methods. Nearly matrix-free implementations of the updating strategy are provided, and numerical experiments are carried out on application problems.Source: OPTIMIZATION METHODS & SOFTWARE, vol. 29 (issue 2), pp. 321-340
DOI: 10.1080/10556788.2012.762517
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Optimization Methods and Software | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | CNR IRIS | CNR IRIS | www.tandfonline.com
2013
Other
Restricted
A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for l1-regularized least-squares
Porcelli M, Rinaldi F
The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields like e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss- Seidel algorithm for solving l1-regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple rule. We prove the global convergence of the method and we report numerical results on some test problems showing the efficiency of the implemented algorithm.
Porcelli M, Rinaldi F
The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields like e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss- Seidel algorithm for solving l1-regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple rule. We prove the global convergence of the method and we report numerical results on some test problems showing the efficiency of the implemented algorithm.
2013
Other
Open Access
Aircraft fuselage sizing with multilevel optimization
Colson B, Porcelli M, Toint P
In this technical report we describe the activity research carried out in the years 2010-2012 at Department of Mathematics, University of Namur, Namur (Belgium) in collaboration with LMS Samtech, Angleur (Belgium), in the framework of the project "Méthodes de résolution de problèmes d'optimisation de grande taille pour les structures en matériaux composites" (Acronym LARGO "LARge-scale Optimization problems"). LARGO was granted by the Walloon Region and LMS Samtech in the context of the First Program (convention number 916981).
Colson B, Porcelli M, Toint P
In this technical report we describe the activity research carried out in the years 2010-2012 at Department of Mathematics, University of Namur, Namur (Belgium) in collaboration with LMS Samtech, Angleur (Belgium), in the framework of the project "Méthodes de résolution de problèmes d'optimisation de grande taille pour les structures en matériaux composites" (Acronym LARGO "LARge-scale Optimization problems"). LARGO was granted by the Walloon Region and LMS Samtech in the context of the First Program (convention number 916981).
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CNR IRIS | ISTI Repository | CNR IRIS
2013
Contribution to conference
Open Access
On the numerical solution of constrained eigenvalue problems in structural engineering
Porcelli M, Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D
The poster is devoted to the analysis of the numerical linear algebra issues arising in the modal analysis of structures with application to masonry construction of historical interest. Although the constitutive equation adopted for masonry is nonlinear, modal analysis gives important qualitative information on the dynamic behavior of masonry structures and allows for assessing their seismic vulnerability, while taking Italian regulations into account. Modal analysis consists in the solution of a constrained eigenvalue problem arising from the solution of the free vibration equilibrium equations in a finite-element setting and involves the mass and stiffness matrices and a set of constraints which enforce relationships between degrees of freedom. A simple example of a constraint, is the imposition of the Dirichlet boundary conditions which usually consists in setting certain degrees of freedom to zero (single-point or fixed constraints). A further example is given by the so called master-slave constraints which impose that the displacement of a node (called the slave) depends linearly on the displacements of other nodes (called the masters). These constraints are crucial, e.g., in modeling the contact interaction between masonry and reinforcement. We propose an efficient implementation of numerical methods for constrained eigenvalue problems, specialized for the modal analysis of structures taking into account both the sparsity of the matrices and the features of master-slave constraints. The implementation will be based on open-source packages embedded in the finite-element code NOSA-ITACA developed in the framework of a research project funded by the Region of Tuscany (www.nosaitaca.it/en/). Numerical examples will be shown on the Project case study "Voltone" - a large vaulted masonry structure located beneath Piazza della Repubblica in Livorno, Italy.
Porcelli M, Binante V, Girardi M, Padovani C, Pasquinelli G, Pellegrini D
The poster is devoted to the analysis of the numerical linear algebra issues arising in the modal analysis of structures with application to masonry construction of historical interest. Although the constitutive equation adopted for masonry is nonlinear, modal analysis gives important qualitative information on the dynamic behavior of masonry structures and allows for assessing their seismic vulnerability, while taking Italian regulations into account. Modal analysis consists in the solution of a constrained eigenvalue problem arising from the solution of the free vibration equilibrium equations in a finite-element setting and involves the mass and stiffness matrices and a set of constraints which enforce relationships between degrees of freedom. A simple example of a constraint, is the imposition of the Dirichlet boundary conditions which usually consists in setting certain degrees of freedom to zero (single-point or fixed constraints). A further example is given by the so called master-slave constraints which impose that the displacement of a node (called the slave) depends linearly on the displacements of other nodes (called the masters). These constraints are crucial, e.g., in modeling the contact interaction between masonry and reinforcement. We propose an efficient implementation of numerical methods for constrained eigenvalue problems, specialized for the modal analysis of structures taking into account both the sparsity of the matrices and the features of master-slave constraints. The implementation will be based on open-source packages embedded in the finite-element code NOSA-ITACA developed in the framework of a research project funded by the Region of Tuscany (www.nosaitaca.it/en/). Numerical examples will be shown on the Project case study "Voltone" - a large vaulted masonry structure located beneath Piazza della Repubblica in Livorno, Italy.
See at:
CNR IRIS | ISTI Repository | CNR IRIS
2013
Other
Open Access
New preconditioner updates in Newton-Krylov methods for nonlinear systems
Porcelli M, Bellavia S, Morini B
We address the problem of preconditioning sequences of large sparse indefinite systems of linear equations arising in the solution of large nonlinear systems via Newton-Krylov methods. We present two new strategies to construct approximate updates of a factorized preconditioner for a reference matrix of the sequence. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal updates. Furthermore, nearly matrix-free implementations are discussed.
Porcelli M, Bellavia S, Morini B
We address the problem of preconditioning sequences of large sparse indefinite systems of linear equations arising in the solution of large nonlinear systems via Newton-Krylov methods. We present two new strategies to construct approximate updates of a factorized preconditioner for a reference matrix of the sequence. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal updates. Furthermore, nearly matrix-free implementations are discussed.
See at:
CNR IRIS | ISTI Repository | CNR IRIS
2013
Other
Restricted
A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA
Porcelli M, Binante V, Girardi M, Padovani C, Pasquinelli G
The paper presents an efficient and reliable implementation of numerical methods for constrained generalized eigenvalue problems, specialized for the modal analysis of linear elastic structures in a finite-element setting. The implementation, which takes into account the sparsity of the stiffness and mass matrices and the features of master-slave constraints, is based on open-source packages embedded in the finite-element code NOSA-ITACA. Numerical tests on historical building are performed, with the aims of calculating their vibration frequencies and mode shape vectors, comparing them to the results of a general purpose commercial code and assessing the accuracy of the tool developed.
Porcelli M, Binante V, Girardi M, Padovani C, Pasquinelli G
The paper presents an efficient and reliable implementation of numerical methods for constrained generalized eigenvalue problems, specialized for the modal analysis of linear elastic structures in a finite-element setting. The implementation, which takes into account the sparsity of the stiffness and mass matrices and the features of master-slave constraints, is based on open-source packages embedded in the finite-element code NOSA-ITACA. Numerical tests on historical building are performed, with the aims of calculating their vibration frequencies and mode shape vectors, comparing them to the results of a general purpose commercial code and assessing the accuracy of the tool developed.