Search results for "Numerical approximation"
showing 10 items of 16 documents
Stochastic homogenization: Theory and numerics
2015
In this chapter, we pursue two related goals. First, we derive a theoretical stochastic homogenization result for the stochastic forward problem introduced in the first chapter. The key ingredient to obtain this result is the use of the Feynman-Kac formula for the complete electrode model. The proof is constructive in the sense that it yields a strategy to achieve our second goal, the numerical approximation of the effective conductivity. In contrast to periodic homogenization, which is well understood, numerical homogenization of random media still poses major practical challenges. In order to cope with these challenges, we propose a new numerical method inspired by a highly efficient stoc…
Preattentive and attentive responses to changes in small numerosities of tones in adult humans
2016
The brain hosts a primitive number sense to non-symbolically represent numerosities of objects or events. Small exact numerosities (~4 or less) can be individuated in parallel. In contrast, large numerosities (more than ~4) can only be approximated. However, whether small numerosities can be approximated without their parallel individuation remains unclear. Parallel individuation is suggested to be an attentive process and numerical approximation an automatic process. We, therefore, tested whether small numerosities can be represented preattentively. We recorded adult humans׳ event-related potentials (ERPs) and behavioral responses to 300-ms sequences of six tones (each of either 440 Hz or …
Better numerical approximation by Durrmeyer type operators
2018
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
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.
Improved fast Gauss transform for meshfree electromagnetic transients simulations
2019
Abstract In this paper improved fast summations are introduced to enhance a meshfree solver for the evolution of the electromagnetic fields over time. The original method discretizes the time-domain Maxwell’s curl equations via Smoothed Particle Hydrodynamics requiring many summations on the first derivatives of the kernel function and field vectors at each time step. The improved fast Gauss transform is properly adopted picking up the computational cost and the memory requirement at an acceptable level preserving the accuracy of the computation. Numerical simulations in two-dimensional domains are discussed giving evidence of improvements in the computation compared to the standard formula…
Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson
2011
We present a discontinuous Galerkin scheme for the numerical approximation of the one-dimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases. Une méthode de Galerkin discontinu est proposée pour l’approximation numérique de l’équation de Vlasov-Poisson 1D. L’approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, …
Accretion shock on CTTSs and its X-ray emission
2009
High spectral resolution X-ray observations of classical T Tauri stars (CTTSs) demonstrate the presence of plasma at T~2-3×10^6 K and ne~10^11-10^13 cm-3. Stationary models suggest that this emission is due to shock-heated accreting material. We address this issue by a 1-D hydrodynamic model of the impact of the accretion flow onto a chromosphere of a CTTS with the aim of investigating the stability of accretion shock and the role of the chromosphere. Our simulations include the effects of gravity, radiative losses from optically thin plasma, the thermal conduction and a detailed modeling of the stellar chromosphere. Here we present the results of a simulation based on the parameters of the…
Some considerations on the transmissivity of trirefringent metamaterials
2016
Nonlocal effects in metal–dielectric (MD) periodic nanostructures may typically be observed when the plasmonic particles and gaps are on the scale of a few tens of nanometers, enabling under certain conditions (succinctly for epsilon near zero) a collimated beam to split into three refracted signals. We developed a method for precisely evaluating the categorized transmissivity in an air/trirefringent metamaterial interface, which uses a fast one-dimensional Fourier transform and finite element solvers of Maxwell’s equations. In periodic arrays of MD nanofilms, it is proved a tunable transmissivity switch of the multirefracted beams under varying angle of incidence and wavelength, while keep…