481 research outputs found
To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case
In parametric equations - stochastic equations are a special case - one may
want to approximate the solution such that it is easy to evaluate its
dependence of the parameters. Interpolation in the parameters is an obvious
possibility, in this context often labeled as a collocation method. In the
frequent situation where one has a "solver" for the equation for a given
parameter value - this may be a software component or a program - it is evident
that this can independently solve for the parameter values to be interpolated.
Such uncoupled methods which allow the use of the original solver are classed
as "non-intrusive". By extension, all other methods which produce some kind of
coupled system are often - in our view prematurely - classed as "intrusive". We
show for simple Galerkin formulations of the parametric problem - which
generally produce coupled systems - how one may compute the approximation in a
non-intusive way
An efficient technique based on polynomial chaos to model the uncertainty in the resonance frequency of textile antennas due to bending
The generalized polynomial chaos theory is combined with a dedicated cavity model for curved textile antennas to statistically quantify variations in the antenna's resonance frequency under randomly varying bending conditions. The nonintrusive stochastic method solves the dispersion relation for the resonance frequencies of a set of radius of curvature realizations corresponding to the Gauss quadrature points belonging to the orthogonal polynomials having the probability density function of the random variable as a weighting function. The formalism is applied to different distributions for the radius of curvature, either using a priori known or on-the-fly constructed sets of orthogonal polynomials. Numerical and experimental validation shows that the new approach is at least as accurate as Monte Carlo simulations while being at least 100 times faster. This makes the method especially suited as a design tool to account for performance variability when textile antennas are deployed on persons with varying body morphology
Level Set Methods for Stochastic Discontinuity Detection in Nonlinear Problems
Stochastic physical problems governed by nonlinear conservation laws are
challenging due to solution discontinuities in stochastic and physical space.
In this paper, we present a level set method to track discontinuities in
stochastic space by solving a Hamilton-Jacobi equation. By introducing a speed
function that vanishes at discontinuities, the iso-zero of the level set
problem coincide with the discontinuities of the conservation law. The level
set problem is solved on a sequence of successively finer grids in stochastic
space. The method is adaptive in the sense that costly evaluations of the
conservation law of interest are only performed in the vicinity of the
discontinuities during the refinement stage. In regions of stochastic space
where the solution is smooth, a surrogate method replaces expensive evaluations
of the conservation law. The proposed method is tested in conjunction with
different sets of localized orthogonal basis functions on simplex elements, as
well as frames based on piecewise polynomials conforming to the level set
function. The performance of the proposed method is compared to existing
adaptive multi-element generalized polynomial chaos methods
Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)
In this paper, we are interested in the acceleration of numerical
simulations. We focus on a hypersonic planetary reentry problem whose
simulation involves coupling fluid dynamics and chemical reactions. Simulating
chemical reactions takes most of the computational time but, on the other hand,
cannot be avoided to obtain accurate predictions. We face a trade-off between
cost-efficiency and accuracy: the simulation code has to be sufficiently
efficient to be used in an operational context but accurate enough to predict
the phenomenon faithfully. To tackle this trade-off, we design a hybrid
simulation code coupling a traditional fluid dynamic solver with a neural
network approximating the chemical reactions. We rely on their power in terms
of accuracy and dimension reduction when applied in a big data context and on
their efficiency stemming from their matrix-vector structure to achieve
important acceleration factors ( to ). This paper aims
to explain how we design such cost-effective hybrid simulation codes in
practice. Above all, we describe methodologies to ensure accuracy guarantees,
allowing us to go beyond traditional surrogate modeling and to use these codes
as references.Comment: Under revie
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New ”directional” cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
Hyperbolic Balance Laws: modeling, analysis, and numerics (hybrid meeting)
This workshop brought together
leading experts, as well as the most
promising young researchers, working on nonlinear
hyperbolic balance laws. The meeting focused on addressing new cutting-edge research in
modeling, analysis, and numerics. Particular topics included ill-/well-posedness,
randomness and multiscale modeling, flows in a moving domain, free boundary problems,
games and control
- …