Search results for "Numerical Analysis"
showing 10 items of 883 documents
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.
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}{…
Optimization of depth increment distribution in the ring-core method
1996
The integral equation method is the most suitable calculation procedure for the determination of non-uniform residual stresses by semi-destructive mechanical methods such as hole and ring-core drilling. However, the high sensitivity to strain measurement errors due to the ill-conditioning of the equation sets has prevented its practical use. Examination of the influence of the strain measurement error on the calculated stresses and its propagation has shown that, for given maximum groove depth and total steps number, the error sensitivity depends on the particular depth increment distribution used. By means of an alternative matrix formulation of the equation sets the depth increment distr…
Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws
2007
We review a conservative finite difference shock capturing scheme that has been used by our research team over the last years for the numerical simulations of complex flows [3, 6]. This scheme is based on Shu and Osher’s technique [9] for the design of highly accurate finite difference schemes obtained by flux reconstruction procedures (ENO, WENO) on Cartesian meshes and Donat-Marquina’s flux splitting [4]. We then motivate the need for mesh adaptivity to tackle realistic hydrodynamic simulations on two and three dimensions and describe some details of our Adaptive Mesh Refinement (AMR) ([2, 7]) implementation of the former finite difference scheme [1]. We finish the work with some numerica…
A Simple Method for the Consecutive Determination of Protonation Constants through Evaluation of Formation Curves
2013
A simple method is presented for the consecutive determination of protonation constants of polyprotic acids based on their formation curves. The procedure is based on generally known equations that describe dissociation equilibria. It has been demonstrated through simulation that the values obtained through the proposed method are sufficiently consistent with the actual values. In contrast with the universally known and applied Bjerrum’s method, no differences in the accuracy of determination of subsequent protonation constant values are observed. The proposed method requires the value of one of the protonation constants (e.g., of the first one, K1) of the polyprotic acid. An iterative meth…
Self-organization of active particles by quorum sensing rules
2018
Many microorganisms regulate their behaviour according to the density of neighbours. Such quorum sensing is important for the communication and organisation within bacterial populations. In contrast to living systems, where quorum sensing is determined by biochemical processes, the behaviour of synthetic active particles can be controlled by external fields. Accordingly they allow to investigate how variations of a density-dependent particle response affect their self-organisation. Here we experimentally and numerically demonstrate this concept using a suspension of light-activated active particles whose motility is individually controlled by an external feedback-loop, realised by a particl…
Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws
2012
Adaptive mesh refinement is nowadays a widely used tool in the numerical solution of hyperbolic partial differential equations. The algorithm is based on the numerical approximation of the solution of the equations on a hierarchical set of meshes with different resolutions. Among the different parts that compose an adaptive mesh refinement algorithm, the decision of which level of resolution is adequate for each part of the domain, i.e., the design of a refinement criterion, is crucial for the performance of the algorithm. In this work we analyze a refinement strategy based on interpolation errors, as a building block of a high order adaptive mesh refinement algorithm. We show that this tec…
A primal-dual algorithm for the fermat-weber problem involving mixed gauges
1987
We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior an…
An order-adaptive compact approximation Taylor method for systems of conservation laws
2021
Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…