Improved recovery of admissible stress in domain decomposition methods - application to heterogeneous structures and new error bounds for FETI-DP

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization

Performance Analysis of Optimization Methods in PSE Applications. Mathematical Programming Versus Grid-based Multi-parametric Genetic Algorithms

Due to their large variety of applications in the PSE area, complex optimisation problems are of high interest for the scientific community. As a consequence, a great effort is made for developing efficient solution techniques. The choice of the relevant technique for the treatment of a given problem has already been studied for batch plant design issues. However,most works reported in the dedicated literature classically considered item sizes as continuous variables. In a view of realism, a similar approach is proposed in this paper, with discrete variables representing equipment capacities. The numerical results enable to evaluate the performances of two mathematical programming (MP) solvers embedded within the GAMS package and a genetic algorithm (GA), on a set of seven increasing complexity examples. The necessarily huge number of runs for the GA could be performed within a computational framework basedon a grid infrastructure; however, since the MP methods were tackled through single-computer computations, the CPU time comparison are reported for this one-PC working mode. On the one hand, the high combinatorial effect induced by the new discrete variables heavily penalizes the GAMS modules, DICOPTþþand SBB. On the other hand, the Genetic Algorithm proves its superiority, providing quality solutions within acceptable computational times, whatever the considered example

Accurate,robust and harmonized implementation of morpho-functional imaging in treatment planning for personalized radiotherapy

In this work we present a methodology able to use harmonized PET/CT imaging in dose painting by number (DPBN) approach by means of a robust and accurate treatment planning system. Image processing and treatment planning were performed by using a Matlab-based platform, called CARMEN, in which a full Monte Carlo simulation is included. Linear programming formulation was developed for a voxel-by-voxel robust optimization and a specific direct aperture optimization was designed for an efficient adaptive radiotherapy implementation. DPBN approach with our methodology was tested to reduce the uncertainties associated with both, the absolute value and the relative value of the information in the functional image. For the same H&N case, a single robust treatment was planned for dose prescription maps corresponding to standardized uptake value distributions from two different image reconstruction protocols: One to fulfill EARL accreditation for harmonization of [18F]FDG PET/CT image, and the other one to use the highest available spatial resolution. Also, a robust treatment was planned to fulfill dose prescription maps corresponding to both approaches, the dose painting by contour based on volumes and our voxel-by-voxel DPBN. Adaptive planning was also carried out to check the suitability of our proposal. Different plans showed robustness to cover a range of scenarios for implementation of harmonizing strategies by using the highest available resolution. Also, robustness associated to discretization level of dose prescription according to the use of contours or numbers was achieved. All plans showed excellent quality index histogram and quality factors below 2%. Efficient solution for adaptive radiotherapy based directly on changes in functional image was obtained. We proved that by using voxel-by-voxel DPBN approach it is possible to overcome typical drawbacks linked to PET/CT images, providing to the clinical specialist confidence enough for routinely implementation of functional imaging for personalized radiotherapy.Junta de Andalucía (FISEVI, reference project CTS 2482)European Regional Development Fund (FEDER