Overlapping Schwarz Decomposition for Constrained Quadratic Programs

We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have recently shown that they are also effective at solving structured optimization problems. In the proposed scheme, we consider QPs whose algebraic structure can be represented by graphs. The graph domain is partitioned into overlapping subdomains (yielding a set of coupled subproblems), solutions for the subproblems are computed in parallel, and convergence is enforced by updating primal-dual information in the overlapping regions. We show that convergence is guaranteed if the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. Convergence results rely on a key property of graph-structured problems that is known as exponential decay of sensitivity. Here, we establish conditions under which this property holds for constrained QPs (as those found in network optimization and optimal control), thus extending existing work that addresses unconstrained QPs. The numerical behavior of the Schwarz scheme is demonstrated by using a DC optimal power flow problem defined over a network with 9,241 nodes

Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation

Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints fail to satisfy a standard constraint qualification such as the linear independence constraint qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. As a result, the developed nonlinear programming theory may not be applied to MPCC class directly. Nowadays, a natural and popular approach is try to find some suitable approximations of an MPCC so that it can be solved by solving a sequence of nonlinear programs. This work aims to solve the MPCC using nonlinear programming techniques, namely the SQP and the regularization scheme. Some algorithms with two iterative processes, the inner and the external, were developed. A set of AMPL problems from MacMPEC database [7] were tested. The algorithms performance comparative analysis was carried out

An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics (2011

DejaVu: Intra-operative Simulation for Surgical Gesture Rehearsal

International audienceAdvances in surgical simulation and surgical augmented reality have changed the way surgeons prepare for practice and conduct medical procedures. Despite considerable interest from surgeons, the use of simulation is still predominantly confined to pre-operative training of surgical tasks and the lack of robustness of surgical augmented reality means that it is seldom used for surgical guidance. In this paper, we present DejaVu, a novel surgical simulation approach for intra-operative surgical gesture rehearsal. With DejaVu we aim at bridging the gap between pre-operative surgical simulation and crucial but not yet robust intra-operative surgical augmented reality. By exploiting intra-operative images we produce a simulation that faithfully matches the actual procedure without visual discrepancies and with an underlying physical modelling that performs real-time deformation of organs and surrounding tissues, surgeons can interact with the targeted organs through grasping, pulling or cutting to immediately rehearse their next gesture. We present results on different in vivo surgical procedures and demonstrate the feasibility of practical use of our system

The use of Artificial Neural Networks to estimate seismic damage and derive vulnerability functions for traditional masonry

This paper discusses the adoption of Artificial Intelligence-based techniques to estimate seismic damage, not with the goal of replacing existing approaches, but as a mean to improve the precision of empirical methods. For such, damage data collected in the aftermath of the 1998 Azores earthquake (Portugal) is used to develop a comparative analysis between damage grades obtained resorting to a classic damage formulation and an innovative approach based on Artificial Neural Networks (ANNs). The analysis is carried out on the basis of a vulnerability index computed with a hybrid seismic vulnerability assessment methodology, which is subsequently used as input to both approaches. The results obtained are then compared with real post-earthquake damage observation and critically discussed taking into account the level of adjustment achieved by each approach. Finally, a computer routine that uses the ANN as an approximation function is developed and applied to derive a new vulnerability curve expression. In general terms, the ANN developed in this study allowed to obtain much better approximations than those achieved with the original vulnerability approach, which has revealed to be quite non-conservative. Similarly, the proposed vulnerability curve expression was found to provide a more accurate damage prediction than the traditional analytical expressions.SFRH/BPD/122598/2016info:eu-repo/semantics/publishedVersio

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intra-joint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.Fundação para a Ciência e a Tecnologia (FCT