Augmented Lagrangian and operator-splitting methods in by Roland Glowinski, Patrick Le Tallec

Posted by

By Roland Glowinski, Patrick Le Tallec

A necessity for a deeper figuring out of the convergence houses of augmented Lagrangian algorithms and in their courting to operator-splitting tools corresponding to alternating-methods path and the advance of extra effective algorithms brought on the authors to write down this ebook. the amount is orientated to purposes in continuum mechanics. This quantity bargains with the numerical simulation of the habit of constant media by way of augmented Lagrangian and operator-splitting equipment (coupled to finite-element approximations). It starts with an outline of the mechanical and mathematical frameworks of the thought of functions in addition to a common research of the fundamental numerical equipment also used to check them. those principles are then utilized to precise periods of mechanical difficulties.

Show description

Read Online or Download Augmented Lagrangian and operator-splitting methods in nonlinear mechanics PDF

Best fluid dynamics books

Augmented Lagrangian and operator-splitting methods in nonlinear mechanics

A necessity for a deeper figuring out of the convergence homes of augmented Lagrangian algorithms and in their courting to operator-splitting tools equivalent to alternating-methods path and the improvement of extra effective algorithms caused the authors to write down this e-book. the quantity is orientated to purposes in continuum mechanics.

The Navier-Stokes equations

The Navier-Stokes equations have been firmly validated within the nineteenth Century because the approach of nonlinear partial differential equations which describe the movement of most typically happening fluids in air and water, and because that point designated options were sought through scientists. jointly those recommendations permit a transparent perception into the habit of fluids, supplying a automobile for novel mathematical equipment and an invaluable fee for computations in fluid dynamics, a box within which theoretical learn is now ruled via computational equipment.

Thermal Spray Fundamentals: From Powder to Part

This booklet offers readers with the basics useful for realizing thermal spray know-how. assurance contains in-depth discussions of varied thermal spray tactics, feedstock fabrics, particle-jet interactions, and linked but very severe themes: diagnostics, present and rising purposes, floor technological know-how, and pre and post-treatment.

Theoretical and Applied Aerodynamics: and Related Numerical Methods

This booklet covers classical and smooth aerodynamics, theories and similar numerical equipment, for senior and first-year graduate engineering scholars, including:-The classical power (incompressible) stream theories for low pace aerodynamics of skinny airfoils and low and high point ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics.

Extra resources for Augmented Lagrangian and operator-splitting methods in nonlinear mechanics

Example text

2. Weak formulations. 2). This leads to a FIG. 2. 4). 40 CHAPTER 2 problem of the form which is completely specified as soon as the set K of kinematically admissible displacement fields and the space V of test functions (virtual displacements) are defined. 4) and proceeding by analogy with the linear case, we may choose The superscript s is such that the integral makes sense for any u in K and any v in V. 7) for K and V, corresponds to the classical weak formulation of equilibrium problems in compressible finite elasticity.

7. <+oo, be given. Let Fj be a measurable subset of F whose interior in T is not empty. 3. Basic tools for existence theory. Existence theory is important from the numerical point of view because it helps in the choice of consistent approximation techniques and numerical methods for the solution of the underlying problem. In this book, existence results will be based mainly on three fundamental theorems. 8. ) Let V be a Hilbert space, a ( - , - ) a continuous bilinear form on Vx V, and L ( - ) a continuous linear form on V.

The existence of solutions follows, then, from a direct application of the generalized Weierstrass theorem on W M (fl). To check the uniqueness of the solution when the internal dissipation potential is strictly convex, consider a solution v of the above problem, an arbitrary element w of Xj different from v, and compute J((w+v)/2). 1. 1 is still applicable to materials associated with potentials that are nondifferentiable and not strictly convex such as where Dt denotes the eigenvalues of D. This corresponds to Tresca-type viscoplasticity (see Chap.

Download PDF sample

Rated 4.32 of 5 – based on 31 votes