Search results for "Numerical"

A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges

2015

In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…

A novel numerical meshless approach for electric potential estimation in transcranial stimulation

2015

In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.

On a step method and a propagation of discontinuity

2019

In this paper we analyze how to compute discontinuous solutions for functional differential equations, looking at an approach which allows to study simultaneously continuous and discontinuous solutions. We focus our attention on the integral representation of solutions and we justify the applicability of such an approach. In particular, we improve the step method in such a way to solve a problem of vanishing discontinuity points. Our solutions are considered as regulated functions.

Conceptual knowledge‐based strategy training in single‐digit calculation: a single case intervention study in a child with specific language impairme…

2009

The aim of this single‐case intervention study was to examine whether a conceptual knowledge‐based strategy training would improve the accuracy of single‐digit arithmetical calculation in a child with specific language impairment. The intervention concerned an11‐year‐old Finnish‐speaking child with specific language impairment. He was trained individually once a week for three months. On the basis of his baseline performance single‐digit arithmetical problems were divided into ‘well‐known arithmetical problems’ and ‘error‐prone arithmetical problems’. Error‐prone problems were taught in meaningful relation to well‐known problems, which he repeatedly solved correctly by using arithmetical fa…

The finite element implementation of 3D fractional viscoelastic constitutive models

2018

Abstract The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. …

Neemo: New electrical energy from marine oscillation

A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advective Fluxes

1989

Abstract A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes. Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion an…

Well-Balanced Adaptive Mesh Refinement for shallow water flows

2014

Well-balanced shock capturing (WBSC) schemes constitute nowadays the state of the art in the numerical simulation of shallow water flows. They allow to accurately represent discontinuous behavior, known to occur due to the non-linear hyperbolic nature of the shallow water system, and, at the same time, numerically maintain stationary solutions. In situations of practical interest, these schemes often need to be combined with some kind of adaptivity, in order to speed up computing times. In this paper we discuss what ingredients need to be modified in a block-structured AMR technique in order to ensure that, when combined with a WBSC scheme, the so-called 'water at rest' stationary solutions…

Riesz transform and vertical oscillation in the Heisenberg group

2023

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…

Tectono-stratigraphic modelling of the North Sicily continental margin (southern Tyrrhenian Sea).

2004

A two-dimensional numerical modelling that simulate the kinematic and thermal response of the lithosphere to thinning was used for the quantitative reconstruction of the late Neogene to Recent times tectonic and stratigraphic evolution of the North Sicily continental margin (southern Tyrrhenian Sea). The numerical study of the evolution of the North Sicily margin builds on the crustal image and kinematic interpretation of the margin obtained by Pepe et al. [Tectonics 19 (2000) 241] on the basis of seismic data and gravity modelling. Tectonic modeling indicate that different segments of the margin were undergoing different vertical movements, which are mainly expression of the rifting and th…