Browsing by Subject "Lagrange multipliers"

Now showing 1 - 7 of 7

Open Access
An animation system for fracturing of rigid objects
(Springer, Berlin, Heidelberg, 2005) Küçükyilmaz, Ayşe; Özgüç, Bülent
This paper describes a system for the animation of fracturing brittle objects. The system combines rigid body simulation methods with a constraint-based model to animate fracturing of arbitrary polyhedral shaped objects under impact. The objects are represented as sets of masses, where pairs of adjacent masses are connected via a distance-preserving linear constraint. Lagrange multipliers are used to compute the forces exerted by those constraints, where these forces determine how and where the object will break. However, a problem with existing systems is that the initial body models exhibit well-defined uniformity, which makes the generated animations unrealistic. This work introduces a method for generating more realistic cracks without any performance loss. This method is easy to implement and applicable on different models. © Springer-Verlag Berlin Heidelberg 2005.
Open Access
Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers
(John Wiley and Sons Ltd, 2014) Temizer, I.
SUMMARY: A computational contact homogenization framework is established for the modeling and simulation of soft matter friction. The main challenges toward the realization of the framework are (1) the establishment of a frictional contact algorithm that displays an optimal combination of accuracy, efficiency, and robustness and plays a central role in (2) the construction of a micromechanical contact test within which samples of arbitrary size may be embedded and which is not restricted to a single deformable body. The former challenge is addressed through the extension of mixed variational formulations of contact mechanics to a mortar-based isogeometric setting where the augmented Lagrangian approach serves as the constraint enforcement method. The latter challenge is addressed through the concept of periodic embedding, with which a periodically replicated C1-continuous interface topography is realized across which not only pending but also ensuing contact among simulation cells will be automatically captured. Two-dimensional and three-dimensional investigations with unilateral/bilateral periodic/random roughness on two elastic micromechanical samples demonstrate the overall framework and the nature of the macroscopic frictional response. © 2014 John Wiley & Sons, Ltd.
Open Access
A derivation of Lovász' theta via augmented lagrange duality
(E D P Sciences, 2003) Pınar, M. Ç.
A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemar´echal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resulting relaxation is easily transformed to the well-known Lov´asz θ number.
Open Access
Image reconstruction for Magnetic Particle Imaging using an Augmented Lagrangian Method
(IEEE, 2017) Ilbey S.; Top C.B.; Çukur, Tolga; Sarıtaş, Emine Ülkü; Guven H.E.
Magnetic particle imaging (MPI) is a relatively new imaging modality that images the spatial distribution of superparamagnetic iron oxide nanoparticles administered to the body. In this study, we use a new method based on Alternating Direction Method of Multipliers (a subset of Augmented Lagrangian Methods, ADMM) with total variation and l1 norm minimization, to reconstruct MPI images. We demonstrate this method on data simulated for a field free line MPI system, and compare its performance against the conventional Algebraic Reconstruction Technique. The ADMM improves image quality as indicated by a higher structural similarity, for low signal-to-noise ratio datasets, and it significantly reduces computation time. © 2017 IEEE.
Open Access
An interior point method for isogeometric contact
(Elsevier, 2014) Temizer, I.; Abdalla, M. M.; Gürdal, Z.
The interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented Lagrangian approach. The method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region. The derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by NURBS-based isogeometric volume discretizations. Various interior point algorithms are discussed, including a primal-dual approach that satisfies the unilateral contact constraints exactly, in addition to two primal approaches that retain an arbitrary barrier parameter. The developed algorithms can easily be pursued starting from an augmented Lagrangian implementation. Numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework, but also highlight current limitations that suggest paths for future research. Overall, the results indicate that the interior point method can challenge the augmented Lagrangian method in contact mechanics, even displaying potential for higher efficiency and robustness. © 2014 Elsevier B.V.
Open Access
Marginal allocation algorithm for nonseparable functions
(Taylor & Francis, 1999) Yüceer, Ü.
Marginal allocation algorithm is implemented to discrete allocation problems with nonseparable objective functions subject to a single linear constraint. A Lagrangian analysis shows that the algorithm generates a sequence of undominated allocations under the condition of discretely convex objective functions and Lagrangian functions. The case of separable functions is proven to be a special case. An application is provided to illustrate the method and various size randomly chosen problems are run to demonstrate the efficiency of the marginal allocation algorithm.
Open Access
Optimizing local memory allocation and assignment through a decoupled approach
(Springer, 2010-10) Diouf, B.; Öztürk, Özcan; Cohen, A.
Software-controlled local memories (LMs) are widely used to provide fast, scalable, power efficient and predictable access to critical data. While many studies addressed LM management, keeping hot data in the LM continues to cause major headache. This paper revisits LM management of arrays in light of recent progresses in register allocation, supporting multiple live-range splitting schemes through a generic integer linear program. These schemes differ in the grain of decision points. The model can also be extended to address fragmentation, assigning live ranges to precise offsets. We show that the links between LM management and register allocation have been underexploited, leaving much fundamental questions open and effective applications to be explored. © 2010 Springer-Verlag.