Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media

In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of multilevel methods and the recently proposed preconditioner based on additive Schur complement approximation by J. Kraus (see [8]). The main results are the design and a theoretical and numerical justification of an iterative method for such problems that is robust with respect to the contrast of the media, defined as the ratio between the maximum and minimum values of the coefficient (related to the permeability/conductivity).Comment: 28 page

Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method inherits the advantages of both the EDG method and the HDG method to make itself well-suited for turbulence simulations. We propose a minimal residual Newton algorithm for solving the nonlinear system arising from the IEDG discretization of the Navier-Stokes equations. The preconditioned GMRES algorithm is based on a restricted additive Schwarz (RAS) preconditioner in conjunction with a block incomplete LU factorization at the subdomain level. The proposed approach is applied to the ILES of transitional turbulent flows over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both design and off-design conditions. The high-order ILES results show good agreement with a subgrid-scale LES model discretized with a second-order finite volume code while using significantly less degrees of freedom. This work shows that high-order accuracy is key for predicting transitional turbulent flows without a SGS model.Comment: 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201

Predictive control using an FPGA with application to aircraft control

Alternative and more efficient computational methods can extend the applicability of MPC to systems with tight real-time requirements. This paper presents a “system-on-a-chip” MPC system, implemented on a field programmable gate array (FPGA), consisting of a sparse structure-exploiting primal dual interior point (PDIP) QP solver for MPC reference tracking and a fast gradient QP solver for steady-state target calculation. A parallel reduced precision iterative solver is used to accelerate the solution of the set of linear equations forming the computational bottleneck of the PDIP algorithm. A numerical study of the effect of reducing the number of iterations highlights the effectiveness of the approach. The system is demonstrated with an FPGA-inthe-loop testbench controlling a nonlinear simulation of a large airliner. This study considers many more manipulated inputs than any previous FPGA-based MPC implementation to date, yet the implementation comfortably fits into a mid-range FPGA, and the controller compares well in terms of solution quality and latency to state-of-the-art QP solvers running on a standard PC

Preconditioned fully implicit PDE solvers for monument conservation

Mathematical models for the description, in a quantitative way, of the damages induced on the monuments by the action of specific pollutants are often systems of nonlinear, possibly degenerate, parabolic equations. Although some the asymptotic properties of the solutions are known, for a short window of time, one needs a numerical approximation scheme in order to have a quantitative forecast at any time of interest. In this paper a fully implicit numerical method is proposed, analyzed and numerically tested for parabolic equations of porous media type and on a systems of two PDEs that models the sulfation of marble in monuments. Due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required and every step implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate iterative or multi-iterative solvers, with special attention to preconditioned Krylov methods and to multigrid procedures. Numerical experiments for the validation of the analysis complement this contribution.Comment: 26 pages, 13 figure