Search results for " Mesh"
showing 10 items of 304 documents
A semi-Lagrangian AMR scheme for 2D transport problems in conservation form
2013
In this paper, we construct a semi-Lagrangian (SL) Adaptive-Mesh-Refinement (AMR) solver for 1D and 2D transport problems in conservation form. First, we describe the a-la-Harten AMR framework: the adaptation process selects a hierarchical set of grids with different resolutions depending on the features of the integrand function, using as criteria the point value prediction via interpolation from coarser meshes, and the appearance of large gradients. We integrate in time by reconstructing at the feet of the characteristics through the Point-Value Weighted Essentially Non-Oscillatory (PV-WENO) interpolator. We propose, then, an extension to the 2D setting by making the time integration dime…
Mesoscopic aspects of the computational homogenization with meshless modeling for masonry material
2020
The multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed-form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also i…
Monotonic solution of heterogeneous anisotropic diffusion problems
2013
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…
The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media
2012
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…
Numerical Investigations of an Implicit Leapfrog Time-Domain Meshless Method
2014
Numerical solution of partial differential equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes in time. A predefined grid in the problem domain and a stability step size restriction need. Recently, the authors have reformulated the meshless framework based on smoothed particle hydrodynamics, in order to be applied for time domain electromagnetic simulation. Despite the good spatial properties, the numerical explicit time integration introduces, also in a meshless context, a severe constraint. In this paper, at first, the stability condition is addressed in a general way by allowing the time step inc…
Exponential convergence andH-c multiquadric collocation method for partial differential equations
2003
The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size
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…
A numerical meshless particle method in solving the magnetoencephalography forward problem
2012
In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…
Anisotropic potential of velocity fields in real fluids: Application to the MAST solution of shallow water equations
2013
In the present paper it is first shown that, due to their structure, the general governing equations of uncompressible real fluids can be regarded as an "anisotropic" potential flow problem and closed streamlines cannot occur at any time. For a discretized velocity field, a fast iterative procedure is proposed to order the computational elements at the beginning of each time level, allowing a sequential solution element by element of the advection problem. Some closed circuits could appear due to the discretization error and the elements involved in these circuits could not be ordered. We prove in the paper that the total flux of these not ordered elements goes to zero by refining the compu…
Validity of needle core biopsy in the histological characterisation of mammary lesions
2006
Summary Over the last few years, there has been an enormous increase in the use of needle core biopsy (CB) for the histopathological characterisation of suspect lesions of the breast. The aim of this study was to verify the diagnostic reliability of CB by comparing the histological results obtained with the use of this technique with those obtained from the whole of the surgically resected specimen. We studied 198 out of 426 patients with clinically and/or radiologically suspect breast lesions. We found correspondence between the histological examination of the whole of the excised specimen and that of the CB in 94.9% of the cases of infiltrating carcinoma and in 71.4% of those involving du…