Search results for "numerical analysis"
showing 10 items of 883 documents
Monotone cubic spline interpolation for functions with a strong gradient
2021
Abstract Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can appear due to the Gibbs phenomenon. Also, preservation of data monotonicity is a requirement in some applications, and that property is not automatically verified by the interpolator. Hence, some additional techniques have to be incorporated so as to ensure monotonicity. The final interpolator is not actually a spline as C 2 regularity and monotonicity are not ensured at the same time. In this paper, we study sufficient conditions to obtain monot…
Crack detection using electrostatic measurements
2001
In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation of our algorithm more computationally demanding.
BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
2022
Abstract Magnetic fields generated by normal or superconducting electromagnets are used to guide and focus particle beams in storage rings, synchrotron light sources, mass spectrometers, and beamlines for radiotherapy. The accurate determination of the magnetic field by measurement is critical for the prediction of the particle beam trajectory and hence the design of the accelerator complex. In this context, state-of-the-art numerical field computation makes use of boundary-element methods (BEM) to express the magnetic field. This enables the accurate computation of higher-order partial derivatives and local expansions of magnetic potentials used in efficient numerical codes for particle tr…
Analysis of infilled frames using A coupled finite element and boundary element solution scheme
1988
The behaviour of infilled frames subjected to horizontal loads is analysed by an iterative numerical procedure. The stiffness of the structural system is determined with variations in geometrical and mechanical characteristics. The analysis is carried out utilizing the boundary element method (BEM) for the infill and opportunely dividing the frame into finite elements, so as to transform the mutual interactions of the two subsystems into stresses distributed along the boundary for the infill and into nodal actions for the frame. This makes it possible to take into account the separation arising between the two substructures when mutual tensile stresses are involved. At first, infills withou…
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…
Numerical Modelling for Assessing the Structural Efficiency of CAM® Reinforcement System for Masonry Walls
2022
A large portion of the Italian building heritage is made of masonry construc-tions, which were erected in the first decades of the last century and were conceived to support gravitational loads only. Many research activities have been carried out in order to propose retrofitting techniques aimed at improving seismic behaviour of existing ma-sonry buildings. The present paper focuses on the CAM® reinforcing system. Such a retrofitting technique, which is widely used in Italy, consists in the application of pre-tensioned stainless steel ribbons on existing masonry walls, conferring to them addi-tional strength, ductility and beneficial confinement effects. The preliminary outcomes of a common…
Nonlinear FE analysis of out-of-plane behaviour of masonry walls with and without CFRP reinforcement
2014
Abstract The out-of-plane behaviour of unreinforced and CFRP reinforced masonry wall is studied by means of experimental investigation and numerical FE modelling. The latter is based on a linear constitutive law both for ashlars and mortar joints constituting masonry and the lines of potential delamination are taken into account by means of an interface element with bi-linear law, reproducing the opening failure mode. When reinforcement is introduced, an interface element with bi-linear law is also used, reproducing sliding failure mode. Comparison between numerical and experimental results show the reliability of the modelling. Moreover, a parametric analysis is carried out in order to inv…
The energy minimization problem for two-level dissipative quantum systems
2010
In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.
A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model
2007
Abstract A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are…
General theory for cross-ply laminated beams
1997
We present a general formulation of the elasticity theory of the cross-ply composite laminated beam subjected to various loadings such as axial load, bending moment, shear/bending, and torsion. The formulation is based on the integral equation theory, and a direct approach is employed to obtain the boundary integral equations for the analysis of the laminated beam. The integral equations governing the elasticity problem are directly deduced from the reciprocity theorem, by using the singular solutions of the orthotropic elasticity explicitly derived. The numerical solution is achieved by the boundary element method, which gives, once the traction free boundary conditions and the interfacial…