A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination

We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To reduce the complexity of the estimation for high resolution images and the time of computations, we implement a multi-level parallel approach based on the domain decomposition with the Schwarz overlapping method. The second level of parallelism uses the massively parallel solver MUMPS. We perform some numerical simulations to show the efficiency of our approach and to validate it on classical and real-world image sequences

Cell organization in soft media due to active mechanosensing

Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one unifying principle, namely that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness. Using linear elasticity theory to model the extracellular environment, we calculate optimal cell organization for several situations of interest and find excellent agreement with experiments for fibroblasts, both on elastic substrates and in collagen gels: cells orient in the direction of external tensile strain, they orient parallel and normal to free and clamped surfaces, respectively, and they interact elastically to form strings. Our method can be applied for rational design of tissue equivalents. Moreover our results indicate that the concept of contact guidance has to be reevaluated. We also suggest that cell-matrix contacts are upregulated by large effective stiffness in the environment because in this way, build-up of force is more efficient.Comment: Revtex, 7 pages, 4 Postscript files include

Domain Decomposition Based High Performance Parallel Computing\ud

The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers. Parallel sparse direct solvers are not found to exhibit good scalability. Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study. The scalability of both Newton and modified Newton algorithms are tested

Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization

Schwarz methods are attractive parallel solvers for large scale linear systems obtained when partial differential equations are discretized. For hybridizable discontinuous Galerkin (HDG) methods, this is a relatively new field of research, because HDG methods impose continuity across elements using a Robin condition, while classical Schwarz solvers use Dirichlet transmission conditions. Robin conditions are used in optimized Schwarz methods to get faster convergence compared to classical Schwarz methods, and this even without overlap, when the Robin parameter is well chosen. We present in this paper a rigorous convergence analysis of Schwarz methods for the concrete case of hybridizable interior penalty (IPH) method. We show that the penalization parameter needed for convergence of IPH leads to slow convergence of the classical additive Schwarz method, and propose a modified solver which leads to much faster convergence. Our analysis is entirely at the discrete level, and thus holds for arbitrary interfaces between two subdomains. We then generalize the method to the case of many subdomains, including cross points, and obtain a new class of preconditioners for Krylov subspace methods which exhibit better convergence properties than the classical additive Schwarz preconditioner. We illustrate our results with numerical experiments.Comment: 25 pages, 5 figures, 3 tables, accepted for publication in SINU

Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwell's equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy

An efficient nonlinear cardinal B-spline model for high tide forecasts at the Venice Lagoon

An efficient class of nonlinear models, constructed using cardinal B-spline (CBS) basis functions, are proposed for high tide forecasts at the Venice lagoon. Accurate short term predictions of high tides in the lagoon can easily be calculated using the proposed CBS models