Search results for "convergence"
showing 10 items of 655 documents
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
2015
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…
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…
Solution of time-independent Schrödinger equation by the imaginary time propagation method
2007
Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrodinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demons…
Recurrence relations for rational cubic methods I: The Halley method
1990
In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the initial point to ensure the convergence of Halley iterates, by means of a system of “recurrence relations”, analogous to those given for the Newton method by Kantorovich, improving previous results by Doring [4]. The error bounds presented are optimal for second degree polynomials. Other rational cubic methods, as the Chebyshev method, will be treated in a subsequent paper.
Upstream Product Market Regulations, ICT, R&D and Productivity
2017
Our study aims to assess the actual importance of the two main channels via which upstream anti-competitive sector regulations are usually considered to impact productivity growth, i.e. by acting as a disincentive to business investments in R&D and in ICT. We estimate the specific impacts of these two channels and their shares in the total impact as opposed to alternative channels of investments in other forms of intangible capital that we cannot explicitly consider for lack of appropriate data such as improvements in skills, management and organization. To achieve this, we specify an extended production function explicitly relating productivity to R&D and ICT capital as well as to upstream…
Zobārstu pilnā vainaga preparātu konverģences pārbaude Latvijā, laboratorijas pētījums
2020
Ievads: Vienas vienības kroņa vai fiksētas daļējas protēzes saglabāšana un pretestība ir divi mehāniski faktori, kas ir saistīti ar veiktās atjaunošanas prognozi. Publicētajā literatūrā tiek atbalstīti īpaši zoba sagatavošanas parametri kroņa uzlikšanai. Preparācijas vertikālajām sienām jābūt ar konverģences leņķi no 10-14 grādiem, lai nodrošinātu kroņa saglabāšanu. Šo parametru neievērošana rada lielāku risku zaudēt kroņa saglabāšanu. Tomēr pētījumi liecina, ka šie kritēriji parasti netiek ievēroti. Nespēja ierobežot vertikālās sienas konverģenci (kopējo okluzālo konverģenci) izraisa protēzes struktūras zudumu, kariesu, palielina zobu struktūras zūdumu preparēšanas laikā un samazinā zoba p…
Approximation properties of q-Kantorovich-Stancu operator
2015
In this paper we study some properties of Kantorovich-type generalizations of the q-Stancu operators. We obtain some approximation properties for these operators, estimating the rate of convergence by using the first and second modulus of continuity. Also, we investigate the statistical approximation properties of the q-Kantorovich-Stancu operators using the Korovkin-type statistical approximation theorem.
Existence for shape optimization problems in arbitrary dimension
2002
We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.
3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization
2012
A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.
Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem
2016
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we prove some estimates on the rate of convergence to the exact solution.