108,010 research outputs found
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
Segregated Runge–Kutta time integration of convection-stabilized mixed finite element schemes for wall-unresolved LES of incompressible flows
In this work, we develop a high-performance numerical framework for the large eddy simulation (LES) of incompressible flows. The spatial discretization of the nonlinear system is carried out using mixed finite element (FE) schemes supplemented with symmetric projection stabilization of the convective term and a penalty term for the divergence constraint. These additional terms introduced at the discrete level have been proved to act as implicit LES models. In order to perform meaningful wall-unresolved simulations, we consider a weak imposition of the boundary conditions using a Nitsche’s-type scheme, where the tangential component penalty term is designed to act as a wall law. Next, segregated Runge–Kutta (SRK) schemes (recently proposed by the authors for laminar flow problems) are applied to the LES simulation of turbulent flows. By the introduction of a penalty term on the trace of the acceleration, these methods exhibit excellent stability properties for both implicit and explicit treatment of the convective terms. SRK schemes are excellent for large-scale simulations, since they reduce the computational cost of the linear system solves by splitting velocity and pressure computations at the time integration level, leading to two uncoupled systems. The pressure system is a Darcy-type problem that can easily be preconditioned using a traditional block-preconditioning scheme that only requires a Poisson solver. At the end, only coercive systems have to be solved, which can be effectively preconditioned by multilevel domain decomposition schemes, which are both optimal and scalable. The framework is applied to the Taylor–Green and turbulent channel flow benchmarks in order to prove the accuracy of the convection-stabilized mixed FEs as LES models and SRK time integrators. The scalability of the preconditioning techniques (in space only) has also been proven for one step of the SRK scheme for the Taylor–Green flow using uniform meshes. Moreover, a turbulent flow around a NACA profile is solved to show the applicability of the proposed algorithms for a realistic problem.Peer ReviewedPostprint (author's final draft
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear
model reduction method that operates on fully discretized computational models.
It achieves dimension reduction by a Petrov--Galerkin projection associated
with residual minimization; it delivers computational efficency by a
hyper-reduction procedure based on the `gappy POD' technique. Originally
presented in Ref. [1], where it was applied to implicit nonlinear
structural-dynamics models, this method is further developed here and applied
to the solution of a benchmark turbulent viscous flow problem. To begin, this
paper develops global state-space error bounds that justify the method's design
and highlight its advantages in terms of minimizing components of these error
bounds. Next, the paper introduces a `sample mesh' concept that enables a
distributed, computationally efficient implementation of the GNAT method in
finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability
of GNAT for parameterized problems is highlighted with the solution of an
academic problem featuring moving discontinuities. Finally, the capability of
this method to reduce by orders of magnitude the core-hours required for
large-scale CFD computations, while preserving accuracy, is demonstrated with
the simulation of turbulent flow over the Ahmed body. For an instance of this
benchmark problem with over 17 million degrees of freedom, GNAT outperforms
several other nonlinear model-reduction methods, reduces the required
computational resources by more than two orders of magnitude, and delivers a
solution that differs by less than 1% from its high-dimensional counterpart
ParMooN - a modernized program package based on mapped finite elements
{\sc ParMooN} is a program package for the numerical solution of elliptic and
parabolic partial differential equations. It inherits the distinct features of
its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and
finite element spaces, implementation of mapped finite elements as their
definition can be found in textbooks, and a geometric multigrid preconditioner
with the option to use different finite element spaces on different levels of
the multigrid hierarchy. After having presented some thoughts about in-house
research codes, this paper focuses on aspects of the parallelization for a
distributed memory environment, which is the main novelty of {\sc ParMooN}.
Numerical studies, performed on compute servers, assess the efficiency of the
parallelized geometric multigrid preconditioner in comparison with some
parallel solvers that are available in the library {\sc PETSc}. The results of
these studies give a first indication whether the cumbersome implementation of
the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie
Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant
number 67571
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