A secure version of asymptotic numericalmethod via convergence acceleration
International audience
Multigrid Schemes for High Order Discretizations of Hyperbolic Problems
Published in Journal of Scientific Computing
Total variation diminishing multigrid methods have been developed for first order accurate discretizations of hyperbolic conservation laws. This technique is based on a so-called upwind biased residual interpolation and allows for algorithms devoid of spurious numerical oscillations in the transient phase. In this paper, we justify the introduction...
A non-intrusive global/local approach applied to phase-field modeling of brittle fracture
Published in Advanced Modeling and Simulation in Engineering Sciences
This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research c...
Matrix completion with ε-algorithm
Published in Numerical Algorithms
We show in this paper how the convergence of an algorithm for matrix completion can be significantly improved by applying Wynn’s ε-algorithm. Straightforward generalization of the scalar ε-algorithm to matrices fails. However, accelerating the convergence of only the missing matrix elements turns out to be very successful.
Convergence acceleration of alternating series
Published in Numerical Algorithms
We propose a new simple convergence acceleration method for a wide range class of convergent alternating series. It has some common features with Smith’s and Ford’s modification of Levin’s and Weniger’s sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Nu...
Comments on “Anderson Acceleration, Mixing and Extrapolation”
Published in Numerical Algorithms
The Extrapolation Algorithm is a technique devised in 1962 for accelerating the rate of convergence of slowly converging Picard iterations for fixed point problems. Versions to this technique are now called Anderson Acceleration in the applied mathematics community and Anderson Mixing in the physics and chemistry communities, and these are related ...
New properties of a certain method of summation of generalized hypergeometric series
Published in Numerical Algorithms
In a recent paper (Appl. Math. Comput. 215:1622–1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence acceleration theorem in the case of summation of generalized hypergeometric series. Some new theore...
The simplified topological ε-algorithms: software and applications
Published in Numerical Algorithms
In this paper, we describe the Matlab toolbox EPSfun for implementing and using the simplified topological ε-algorithms for accelerating the convergence of sequences of elements of a vector space. The functions for other similar algorithms are also provided. We give applications to the solution of linear and nonlinear systems of equations and to th...
Convergence acceleration for partitioned simulations of the fluid-structure interaction in arteries
Published in Computational Mechanics
We present a partitioned approach to fluid-structure interaction problems arising in analyses of blood flow in arteries. Several strategies to accelerate the convergence of the fixed-point iteration resulting from the coupling of the fluid and the structural sub-problem are investigated. The Aitken relaxation and variants of the interface quasi-New...
Monte Carlo criticality calculations accelerated by a growing neutron population
We propose a fission source convergence acceleration method for Monte Carlo criticality simulation. As the efficiency of Monte Carlo criticality simulations is sensitive to the selected neutron population size, the method attempts to achieve the acceleration via on-the-fly control of the neutron population size. The neutron population size is gradu...
