We present a parallel implementation of a fully unstructured spectral element method for elastic ... more We present a parallel implementation of a fully unstructured spectral element method for elastic wave propagation problems. Our target is to merge the high accuracy of spectral methods with the flexibility of finite elements in dealing with complex geometries. The spectral algorithms we propose is based on a domain decomposition approach, implemented into a multiprocessor environment. Parallelism is exploited at the algebraic level: the global linear system is distributed among processors, and then solved by iterative techniques
Spectral Elements have been applied to various applications in computational engineering, and ena... more Spectral Elements have been applied to various applications in computational engineering, and enable reductions of computational resources respect to more traditional techniques like finite elements or finite differences. The main advantage is their high order approach, which equals the accuracy of low order methods while showing computational efficiency and suitability to parallel computation. This work illustrates how Spectral Elements can be used to solve various problems usually encountered in geophysics, such as the scalar acoustic equation and linear and non-linear elasticity
We present a domain decomposition method for the solution of acoustic and elastodynamic problems ... more We present a domain decomposition method for the solution of acoustic and elastodynamic problems in two-dimensional heterogeneous media. The problem is formulated in a variational form and the spatial discretization is based on the spectral Legendre collocation method. The matching conditions at subdomain interfaces are discussed. The numerical validation illustrates the accuracy, flexibility and robustness of our method.
We discuss the application of the spectral element method to the monodomain and bidomain equation... more We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key el...
A new numerical method is presented for propagating elastic waves in heterogeneous earth media, b... more A new numerical method is presented for propagating elastic waves in heterogeneous earth media, based on spectral approximations of the wavefield combined with domain decomposition techniques. The flexibility of finite element techniques in dealing with irregular geologic structures is preserved, together with the high accuracy of spectral methods. High computational efficiency can be achieved especially in 3D calculations, where the
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) ... more Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility...
Journal of Physics A: Mathematical and Theoretical, 2008
... structural and dynamical analysis of a human protein signalling network Alberto de la Fuente,... more ... structural and dynamical analysis of a human protein signalling network Alberto de la Fuente, Giorgio Fotia, Fabio Maggio, Gianmaria Mancosu and Enrico Pieroni CRS4 Bioinformatica, Parco Tecnologico POLARIS, Ed.1, Loc Piscinamanna, Pula, Italy E-mail: [email protected] ...
International Journal of Imaging Systems and Technology, 1995
The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that... more The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that the solution is affected by numeric instability. As a consequence, the solution provided by the so-called inverse filter is completely contaminated by noise and, in general, is deprived of any physical meaning. If one looks for approximate solutions, the ill-posedness of the problem implies
Strong ground motion observed at an instrumented hill site is first analysed through the standard... more Strong ground motion observed at an instrumented hill site is first analysed through the standard (SSR) and the horizontal-to-vertical (HVSR) spectral ratio techniques. A reasonable agreement is found between these approaches. The observations are then compared with 3D numerical simulations, performed with a highly efficient numerical code based on a spectral method, that allowed for reasonable computer times also on
A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propa... more A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2-D heterogeneous media. Starting from a variational formulation of the problem, two different approaches are proposed for the spatial discretization: a mixed Fourier‐Legendre and a full Legendre collocation. The matching conditions at subdomain interfaces are carefully analyzed, and the stability and efficiency of time‐advancing schemes are investigated. The numerical validation with some significant test cases illustrates the accuracy, flexibility, and robustness of our methods. These allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy.
Computer Methods in Applied Mechanics and Engineering, 2002
We present a hybrid spectral element/finite element domain decomposition method for solving elast... more We present a hybrid spectral element/finite element domain decomposition method for solving elastic wave propagation problems. Aim of the method is to exploit both the enhanced accuracy of spectral elements, allowing significant reductions of the computational load, and the flexibility of finite elements in treating irregular geometries and nonlinear media. Interfaces between finite and spectral elements are managed by the mortar method, which enjoys optimal accuracy and allows to discretize the different regions independently. Several test cases illustrate the robustness of this method and its tolerance to a significant range of geometrical models, characterized by different grid refinements.
We describe several algorithms with winning performance in the Dialogue for Reverse Engineering A... more We describe several algorithms with winning performance in the Dialogue for Reverse Engineering Assessments and Methods (DREAM2) Reverse Engineering Competition 2007. After the gold standards for the challenges were released, the performance of the algorithms could be thoroughly evaluated under different parameters or alternative ways of solving systems of equations. For the analysis of Challenge 4, the "In-silico" challenges, we employed methods to explicitly deal with perturbation data and timeseries data. We show that original methods used to produce winning submissions could easily be altered to substantially improve performance. For Challenge 5, the genomescale Escherichia coli network, we evaluated a variety of measures of association. These data are troublesome, and no good solutions could be produced, either by us or by any other teams. Our best results were obtained when analyzing subdatasets instead of considering the dataset as a whole.
The spectral element method (SEM) is a powerful numerical technique naturally suited for wave pro... more The spectral element method (SEM) is a powerful numerical technique naturally suited for wave propagation and dynamic soil-structure interaction (DSSI) analyses. A class of SEM has been widely used in the seismological field (local or global seismology) thanks to its capability of providing high accuracy and allowing the implementation of optimized parallel algorithms. We illustrate in this contribution how the SEM can be effectively used also for the numerical analysis of DSSI problems, with reference to the 3D seismic response of a railway viaduct in Italy. This numerical analysis includes the combined effect of: a) strong lateral variations of soil properties; b) topographic amplification; c) DSSI; d) spatial variation of earthquake ground motion in the structural response. Some hints on the work in progress to effectively handle nonlinear problems with SEM are also given.
We present a parallel implementation of a fully unstructured spectral element method for elastic ... more We present a parallel implementation of a fully unstructured spectral element method for elastic wave propagation problems. Our target is to merge the high accuracy of spectral methods with the flexibility of finite elements in dealing with complex geometries. The spectral algorithms we propose is based on a domain decomposition approach, implemented into a multiprocessor environment. Parallelism is exploited at the algebraic level: the global linear system is distributed among processors, and then solved by iterative techniques
Spectral Elements have been applied to various applications in computational engineering, and ena... more Spectral Elements have been applied to various applications in computational engineering, and enable reductions of computational resources respect to more traditional techniques like finite elements or finite differences. The main advantage is their high order approach, which equals the accuracy of low order methods while showing computational efficiency and suitability to parallel computation. This work illustrates how Spectral Elements can be used to solve various problems usually encountered in geophysics, such as the scalar acoustic equation and linear and non-linear elasticity
We present a domain decomposition method for the solution of acoustic and elastodynamic problems ... more We present a domain decomposition method for the solution of acoustic and elastodynamic problems in two-dimensional heterogeneous media. The problem is formulated in a variational form and the spatial discretization is based on the spectral Legendre collocation method. The matching conditions at subdomain interfaces are discussed. The numerical validation illustrates the accuracy, flexibility and robustness of our method.
We discuss the application of the spectral element method to the monodomain and bidomain equation... more We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key el...
A new numerical method is presented for propagating elastic waves in heterogeneous earth media, b... more A new numerical method is presented for propagating elastic waves in heterogeneous earth media, based on spectral approximations of the wavefield combined with domain decomposition techniques. The flexibility of finite element techniques in dealing with irregular geologic structures is preserved, together with the high accuracy of spectral methods. High computational efficiency can be achieved especially in 3D calculations, where the
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) ... more Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility...
Journal of Physics A: Mathematical and Theoretical, 2008
... structural and dynamical analysis of a human protein signalling network Alberto de la Fuente,... more ... structural and dynamical analysis of a human protein signalling network Alberto de la Fuente, Giorgio Fotia, Fabio Maggio, Gianmaria Mancosu and Enrico Pieroni CRS4 Bioinformatica, Parco Tecnologico POLARIS, Ed.1, Loc Piscinamanna, Pula, Italy E-mail: [email protected] ...
International Journal of Imaging Systems and Technology, 1995
The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that... more The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that the solution is affected by numeric instability. As a consequence, the solution provided by the so-called inverse filter is completely contaminated by noise and, in general, is deprived of any physical meaning. If one looks for approximate solutions, the ill-posedness of the problem implies
Strong ground motion observed at an instrumented hill site is first analysed through the standard... more Strong ground motion observed at an instrumented hill site is first analysed through the standard (SSR) and the horizontal-to-vertical (HVSR) spectral ratio techniques. A reasonable agreement is found between these approaches. The observations are then compared with 3D numerical simulations, performed with a highly efficient numerical code based on a spectral method, that allowed for reasonable computer times also on
A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propa... more A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2-D heterogeneous media. Starting from a variational formulation of the problem, two different approaches are proposed for the spatial discretization: a mixed Fourier‐Legendre and a full Legendre collocation. The matching conditions at subdomain interfaces are carefully analyzed, and the stability and efficiency of time‐advancing schemes are investigated. The numerical validation with some significant test cases illustrates the accuracy, flexibility, and robustness of our methods. These allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy.
Computer Methods in Applied Mechanics and Engineering, 2002
We present a hybrid spectral element/finite element domain decomposition method for solving elast... more We present a hybrid spectral element/finite element domain decomposition method for solving elastic wave propagation problems. Aim of the method is to exploit both the enhanced accuracy of spectral elements, allowing significant reductions of the computational load, and the flexibility of finite elements in treating irregular geometries and nonlinear media. Interfaces between finite and spectral elements are managed by the mortar method, which enjoys optimal accuracy and allows to discretize the different regions independently. Several test cases illustrate the robustness of this method and its tolerance to a significant range of geometrical models, characterized by different grid refinements.
We describe several algorithms with winning performance in the Dialogue for Reverse Engineering A... more We describe several algorithms with winning performance in the Dialogue for Reverse Engineering Assessments and Methods (DREAM2) Reverse Engineering Competition 2007. After the gold standards for the challenges were released, the performance of the algorithms could be thoroughly evaluated under different parameters or alternative ways of solving systems of equations. For the analysis of Challenge 4, the "In-silico" challenges, we employed methods to explicitly deal with perturbation data and timeseries data. We show that original methods used to produce winning submissions could easily be altered to substantially improve performance. For Challenge 5, the genomescale Escherichia coli network, we evaluated a variety of measures of association. These data are troublesome, and no good solutions could be produced, either by us or by any other teams. Our best results were obtained when analyzing subdatasets instead of considering the dataset as a whole.
The spectral element method (SEM) is a powerful numerical technique naturally suited for wave pro... more The spectral element method (SEM) is a powerful numerical technique naturally suited for wave propagation and dynamic soil-structure interaction (DSSI) analyses. A class of SEM has been widely used in the seismological field (local or global seismology) thanks to its capability of providing high accuracy and allowing the implementation of optimized parallel algorithms. We illustrate in this contribution how the SEM can be effectively used also for the numerical analysis of DSSI problems, with reference to the 3D seismic response of a railway viaduct in Italy. This numerical analysis includes the combined effect of: a) strong lateral variations of soil properties; b) topographic amplification; c) DSSI; d) spatial variation of earthquake ground motion in the structural response. Some hints on the work in progress to effectively handle nonlinear problems with SEM are also given.
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Papers by Fabio Maggio