1,721,026 research outputs found
A Reduced Basis Method for a PDE-constrained optimization formulation in Discrete Fracture Network flow simulations
Full text linkIn classic Reduced Basis (RB) framework, we propose a new technique for the offline greedy error analysis which relies on a residual-based a posteriori error estimator. This approach is as an alternative to classical a posteriori RB estimators, avoiding a discrete inf-sup lower bound estimate. We try to use less common ingredients of the RB framework to retrieve a better approximation of the RB error, such as the estimation of the distance between the continuous solution and the reduced one. In particular we focus on the application of the reduction model for the flow simulations in underground fractured media, in which high accurate simulations suffer for the complexity of the domain geometry. Finally, some numerical tests are assessed to confirm the viability and the efficacy of the technique proposed
A new quality preserving polygonal mesh refinement algorithm for Polygonal Element Methods
No full textMesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first, adaptively refine a provided good quality polygonal mesh preserving quality, second, improve the quality of a coarse poor quality polygonal mesh during the refinement process. For finite element methods and triangular meshes, convergence of a posteriori mesh refinement algorithms and optimality properties have been widely investigated, whereas convergence and optimality are still open problems for polygonal adaptive methods. In this article, we propose a new refinement method for convex cells with the aim of introducing some properties useful to tackle convergence and optimality for adaptive methods. The key issues in refining convex general polygons are: a refinement dependent only on the marked cells for refinement at each refinement step; a partial quality improvement, or, at least, a non degenerate quality of the mesh during the refinement iterations; a bound on the number of unknowns of the discrete problem with respect to the number of the cells in the mesh. Although these properties are quite common for refinement algorithms of triangular meshes, these issues are still open problems for polygonal meshes
Efficient partitioning of conforming virtual element discretizations for large scale discrete fracture network flow parallel solvers
Full text linkDiscrete Fracture Network models are largely used for large scale geological flow simulations in fractured media. For these complex simulations, it is worth investigating suitable numerical methods and tools for efficient parallel solutions on High Performance Computing systems. In this paper we propose and compare different partitioning strategies, that result to be highly efficient and scalable, overperforming the classical mesh partitioning approach used to balance the workload of a conforming mesh among several processes. The proposed DFN-based partitioning strategies rely on the distribution of the fractures among parallel processes. The computational cost of the DFN-based partitionings is very small compared to the cost of classical mesh partitioning and the numerical results prove their effectiveness and good performances in solving linear systems for realistic DFN flow simulations
HEMSim: a new MATLAB software to simulate the behavior of highly energetic materials upon Chapman-Jouguet hypothesis
No full textIn this paper, we present a comprehensive simulation framework developed in MATLAB called HEMSim (Highly Energetic Materials Simulator) for modeling ideal detonations based on the fundamental principles of the Chapman-Jouguet (CJ) theory. The code efficiently computes the properties of an ideal detonation at the CJ point under the assumption of chemical, mechanical and thermal equilibrium, as well as the values of the isentropic expansion, while also enabling a fit of the parameters of the well-established JWL equation of state. Our code employs advanced equations of state (IMP EXPP 6 or BKWC for gaseous products and Birch-Murnaghan with thermal expansion for condensed products) to accurately model the behavior of a multiphase mixture of products coming from an ideal detonation. To our knowledge, there are no freely available codes capable of performing these complex calculations. Our implementation hence provides a robust framework for the accurate determination of ideal detonation parameters
Orthogonal polynomial bases in the mixed virtual element method
Full text linkThe use of orthonormal polynomial bases has been found to be efficient in preventing ill-conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of badly-shaped polygons. However, we show that using the natural extension of a orthogonal polynomial basis built for the primal formulation is not sufficient to cure ill-conditioning in the mixed case. Thus, in the present work, we introduce an orthogonal vector-polynomial basis which is built ad hoc for being used in the mixed formulation of VEM and which leads to very high-quality solution in each tested case. Furthermore, a numerical experiment related to simulations in Discrete Fracture Networks (DFN), which are often characterised by very badly-shaped elements, is proposed to validate our procedures
Fast and robust flow simulations in discrete fracture networks with GPGPUs
No full textA new approach for flow simulation in very complex discrete fracture networks based
on PDE-constrained optimization has been recently proposed in Berrone et al. (SIAM
J Sci Comput 35(2):B487–B510, 2013b; J Comput Phys 256:838–853, 2014) with
the aim of improving robustness with respect to geometrical complexities. This is
an essential issue, in particular for applications requiring simulations on geometries
automatically generated like the ones used for uncertainty quantification analyses and
hydro-mechanical simulations. In this paper, implementation of this approach in order
to exploit Nvidia Compute Unified Device Architecture is discussed with the main
focus to speed up the linear algebra operations required by the approach, being this task
the most computational demanding part of the approach. Furthermore, two different
approaches for linear algebra operations and two storage formats for sparse matrices
are compared in terms of computational efficiency and memory constraints
Comparison of standard and stabilization free Virtual Elements on anisotropic elliptic problems
Full text linkIn this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E2V EM) with the focus on some elliptic test problems whose solution and diffusivity tensor are characterized by anisotropies. Results show that the possibility to avoid an arbitrary stabilizing part, offered by E2V EM methods, can reduce the magnitude of the error on general polygonal meshes and help convergence
Trattamento delle fratture mandibolari complicate da pseudoartrosi ed osteomielite dopo fissazione rigida
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