845 research outputs found
Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems
We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations.
We can compute branches of solutions with limit points, bifurcation points, etc.
Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations
Four-field finite element solver and sensitivities for quasi-Newtonian flows
International audienceA computationally efficient finite element algorithm for power law fluid is elaborated in view of extensive direct and inverse simulations. We adopt a splitting technique to simplify the nonlinear structure of the fluids equations and derive a four-field saddle point formulation for which we prove the existence of a solution. The resolution of the corresponding variational inequalities is based on an augmented Lagrangian method and a mixed finite element discretization. The resulting iterative solver reveals to be fast and robust with low memory consumption. The time-saving provided by the algorithm compared to the standard algorithms of fixed point and Newton increases with the number of degrees of freedom and the nonlinearity of the problem. It is therefore well-suited for the solution of large problems with a great number of elements and for corresponding adjoint-based computations. Bidimensional numerical experiments are performed on two realistic situations of gravity flows: an experimental viscoplastic steady wave and a continental glacier. In the present study, results emphasize that for both cases, the modeling at bottom plays a strongly dominant role. Using surface velocitiy observations, the sensitivity analysis with respect to a spatially varying power-law exponent highlights the importance of an accurate knowledge of the rheology at high shear rate. The one on the basal sliding allows to detect the presence of a short wavelength (two times the thickness) free-slip area indetectable from surface velocities
Migration of a sphere in tube flow
The cross-stream migration of a single neutrally buoyant rigid sphere in tube flow is simulated by two packages, one (ALE) based on a moving and adaptive grid and another (DLM) using distributed Lagrange multipliers on a fixed grid. The two packages give results in good agreement with each other and with experiments. A lift law L=CUs (Ωs— Ωse) analogous to L=ρUΓ which was proposed and validated in two dimensions is validated in three dimensions here; C is a constant depending on material and geometric parameters, Us is the slip velocity and it is positive, Ωs is the slip angular velocity and Ωse is the slip angular velocity when the sphere is in equilibrium at the Segré–Silberberg radius. The slip angular velocity discrepancy Ωs— Ωse is the circulation for the free particle and it changes sign with the lift. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulae predict the change of sign of the lift force which is necessary in the Segré–Silberberg effect. Our correlation formula is compared with analytical lift formulae in the literature and with the results of two-dimensional simulations. Our work establishes a general procedure for obtaining correlation formulae from numerical experiments. This procedure forms a link between numerical simulation and engineering practice
Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method
Previously, we have proposed a direct simulation scheme for colloidal
dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved
formulation called the ``Smoothed Profile (SP) method'' is presented here in
which simultaneous time-marching is used for the host fluid and colloids. The
SP method is a direct numerical simulation of particulate flows and provides a
coupling scheme between the continuum fluid dynamics and rigid-body dynamics
through utilization of a smoothed profile for the colloidal particles.
Moreover, the improved formulation includes an extension to incorporate
multi-component fluids, allowing systems such as charged colloids in
electrolyte solutions to be studied. The dynamics of the colloidal dispersions
are solved with the same computational cost as required for solving
non-particulate flows. Numerical results which assess the hydrodynamic
interactions of colloidal dispersions are presented to validate the SP method.
The SP method is not restricted to particular constitutive models of the host
fluids and can hence be applied to colloidal dispersions in complex fluids
Finite element approximation of some degenerate monotone quasilinear elliptic systems
Published versio
Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings
We propose a method for effectively upscaling incompressible viscous flow in
large random polydispersed sphere packings: the emphasis of this method is on
the determination of the forces applied on the solid particles by the fluid.
Pore bodies and their connections are defined locally through a regular
Delaunay triangulation of the packings. Viscous flow equations are upscaled at
the pore level, and approximated with a finite volume numerical scheme. We
compare numerical simulations of the proposed method to detailed finite element
(FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A
good agreement is found both in terms of forces exerted on the solid particles
and effective permeability coefficients
High-temperature magnetodielectric Bi(Fe0.5Mn0.5)O3 thin films with checkerboard-ordered oxygen vacancies and low magnetic damping
The possibility of affecting the magnetic properties of a material by dielectric means, and vice versa, remains an attractive perspective for modern electronics and spintronics. Here, we report on epitaxial Bi(Fe0.5Mn0.5)O3 thin films with exceptionally low Gilbert damping and magnetoelectric coupling above room temperature (<400 K). The ferromagnetic order, not observed in bulk, has been detected with a total magnetization of 0.44 μB/formula units with low Gilbert damping parameter (0.0034), both at room temperature. Additionally, a previously overlooked check-board ordering of oxygen vacancies is observed, providing insights on the magnetic and dielectric origin of the multifunctional properties of the films. Finally, intrinsic magnetodielectric behavior is observed as revealed by the variation of dielectric permittivity well above room temperature. These findings show the possibility of electric-field-controlled magnetic properties, in low Gilbert-damping-based spintronic devices, using single-phase multiferroic material
Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
The augmented Lagrangiam method (ALM), widely used in quantum chemistry
constrained optimization problems, is applied in the context of the nuclear
Density Functional Theory (DFT) in the self-consistent constrained Skyrme
Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of
multidimensional energy surfaces in the space of collective coordinates that
are needed to, e.g., determine fission pathways and saddle points; it improves
accuracy of computed derivatives with respect to collective variables that are
used to determine collective inertia; and is well adapted to supercomputer
applications.Comment: 6 pages, 3 figures; to appear in Eur. Phys. J.
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
- …