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The volume penalization method, which allows to impose no-slip boundary conditions, is assessed for wall-bounded flows. For the numerical solution of the penalized equations a spectral method is used. Considering a two-dimensional Poiseuille flow, the solution of the Navier-Stokes penalized equation is computed analytically and the convergence of the numerical solution is studied. To illustrate the properties of the approach we compute a three-dimensional turbulent channel flow imposing a constant flow rate. The obtained results are compared with reference data of Kim et al. [10]. [ABSTRACT FROM AUTHOR]

In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations. Iterative solution methods are the methods of choice for these large linear systems. We start with a short introduction of Basic Iterative Methods. Thereafter preconditioned Krylov subspace methods, which are state of the art, are describeed. A distinction is made between various classes of matrices. At the end of the lecture notes many references are given to state of the art Scientific Computing methods. Here, we will discuss a number of books which are nice to use for an overview of background material. First of all the books of Golub and Van Loan [19] and Horn and Johnson [26] are classical works on all aspects of numerical linear algebra. These books also contain most of the material, which is used for direct solvers. Varga [50] is a good starting point to study the theory of basic iterative methods. Krylov subspace methods and multigrid are discussed in Saad [38] and Trottenberg, Oosterlee and Schüller [42]. Other books on Krylov subspace methods are [1, 6, 21, 34, 39]. [ABSTRACT FROM AUTHOR]

We present a shape-oriented data assimilation strategy suitable for front-tracking problems through the example of wildfire. The concept of "front" is used to model, at regional scales, the burning area delimitation that moves, undergoes shape and topological changes under heterogeneous orography, biomass fuel and micrometeorology. The simulation-observation discrepancies are represented using a front shape similarity measure deriving from image processing and based on the Chan-Vese contour fitting functional. We show that consistent corrections of the front location and uncertain physical parameters can be obtained using this measure applied on a level-set fire growth model solving for an eikonal equation. This study involves a Luenberger observer for state estimation, including a topological gradient term to track multiple fronts, and of a reduced-order Kalman filter for joint parameter estimation. We also highlight the need – prior to parameter estimation – for sensitivity analysis based on the same discrepancy measure, and for instance using polynomial chaos metamodels, to ensure a meaningful inverse solution is achieved. The performance of the shape-oriented data assimilation strategy is assessed on a synthetic configuration subject to uncertainties in front initial position, near-surface wind magnitude and direction. The use of a robust front shape similarity measure paves the way toward the direct assimilation of infrared images and is a valuable asset in the perspective of data-driven wildfire modeling. [ABSTRACT FROM AUTHOR]

This article describes the implementation of an all-in-one numerical procedure within the runtime StarPU. In order to limit the complexity of the method, for the sake of clarity of the presentation of the non-classical task-driven programming environment, we have limited the numerics to first order in space and time. Results show that the task distribution is efficient if the tasks are numerous and individually large enough so that the task heap can be saturated by tasks which computational time covers the task management overhead. Next, we also see that even though they are mostly faster on graphic cards, not all the tasks are suitable for GPUs, which brings forward the importance of the task scheduler. Finally, we look at a more realistic system of conservation laws with an expensive source term, what allows us to conclude and open on future works involving higher local arithmetic intensity, by increasing the order of the numerical method or by enriching the model (increased number of parameters and therefore equations). [ABSTRACT FROM AUTHOR]

In this paper we investigate the feasibility of applying the Parareal algorithm [5, 6] for quasi-static nonlinear structural analysis problems. We describe how this proposal has been realized and present some preliminary numerical results of applying this algorithm to a beam undergoing nonlinear deflection with a contact boundary condition. Further numerical experiments are needed to provide an evidence for the effciency of the method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop some techniques for automation of the mappings (between working and reference domains) required by reduced basis methods: the development of geometry mappings is indeed often a substantial impediment to the implementation of reduced basis techniques, especially in the context of the reduced basis element method (RBEM) and the reduced basis component method (RBCM). In the RBCM context, the geometry mappings are applied at the level of components. The methods have been tested on various cases to understand the limits of the approach and try to foresee and overcome the possible failures. [ABSTRACT FROM AUTHOR]

Because of the non-local nature of the integral kernels at play, the discretization of boundary integral equations leads to dense matrices, which would imply high computational complexity. Acceleration techniques, such as hierarchical matrix strategies combined with Adaptive Cross Approximation (ACA), are available in literature. Here we apply such a technique to the solution of an elastostatic problem, arising from industrial applications, posed at the surface of highly irregular cracks networks. [ABSTRACT FROM AUTHOR]

In magnetically confined plasmas used in Tokamak, turbulence is respon-sible for specific transport that limits the performance of this kind of reactors. Gyroki-netic simulations are able to capture ion and electron turbulence that give rise to heat losses, but require also state-of-the-art HPC techniques to handle computation costs. Such simulations are a major tool to establish good operating regime in Tokamak such as ITER, which is currently being built. Some of the key issues to address more re- alistic gyrokinetic simulations are: efficient and robust numerical schemes, accurate geometric description, good parallelization algorithms. The framework of this work is the Semi-Lagrangian setting for solving the gyrokinetic Vlasov equation and the Gy-sela code. In this paper, a new variant for the interpolation method is proposed that can handle the mesh singularity in the poloidal plane at r = 0 (polar system is used for the moment in Gysela). A non-uniform meshing of the poloidal plane is proposed instead of uniform one in order to save memory and computations. The interpolation method, the gyroaverage operator, and the Poisson solver are revised in order to cope with non-uniform meshes. A mapping that establish a bijection from polar coordinates to more realistic plasma shape is used to improve realism. Convergence studies are provided to establish the validity and robustness of our new approach. [ABSTRACT FROM AUTHOR]

Modeling turbulent transport is a major goal in order to predict confinement performance in a tokamak plasma. The gyrokinetic framework considers a computational domain in five dimensions to look at kinetic issues in a plasma; this leads to huge computational needs. Therefore, optimization of the code is an especially important aspect, especially since coprocessors and complex manycore architectures are foreseen as building blocks for Exascale systems. This project aims to evaluate the applicability of two auto-tuning approaches with the BOAST and StarPU tools on the GYSELA code in order to circumvent performance portability issues. A specific computation intensive kernel is considered in order to evaluate the benefit of these methods. StarPU enables to match the performance and even sometimes outperform the hand-optimized version of the code while leaving scheduling choices to an automated process. BOAST on the other hand reveals to be well suited to get a gain in terms of execution time on four architectures. Speedups in-between 1.9 and 5.7 are obtained on a cornerstone computation intensive kernel. [ABSTRACT FROM AUTHOR]

To answer the need for an efficient and robust geothermal simulation tool going beyond existing code capabilities in terms of geological and physical complexity, we have started to develop a parallel geothermal simulator based on unstructured meshes. The model takes into account complex geology including fault and fracture networks acting as major heat and mass transfer corridors and complex physics coupling the mass and energy conservations to the thermodynamic equilibrium between the gas and liquid phases. The objective of this Cemracs project was to focus on well modeling which is a key missing ingredient in our current simulator in order to perform realistic geothermal studies both in terms of monitoring and in terms of history matching. The well is discretized by a set of edges of the mesh in order to represent efficiently slanted or multi-branch wells on unstructured meshes. The connection with the 3D matrix and the 2D fracture network at each node of the well is accounted for using Peaceman's approach. The non-isothermal flow model inside the well is based on the usual single unknown approach assuming the hydrostatic and thermodynamical equilibrium inside the well. The parallelization of the well model is implemented in such a way that the assembly of the Jacobian at each Newton step and the computation of the pressure drops inside the well can be done locally on each process without MPI communications. [ABSTRACT FROM AUTHOR]

In [2], 1D×1D two-species Vlasov-Poisson simulations are performed by the semi-Lagrangian method. Thanks to a classical first order dispersion analysis, we are able to check the validity of their simulations; the extension to second order is performed and shown to be relevant for explaining further details. In order to validate multi-dimensional effects, we propose a 2D × 2D single species test problem that has true 2D effects coming from the sole second order dispersion analysis. Finally, we perform, in the same code, full 2D × 2D non linear two-species simulations with mass ratio 0:01, and consider the mixing of semi-Lagrangian and Particle-in-Cell methods. [ABSTRACT FROM AUTHOR]

In this paper we present and implement the Palindromic Discontinuous Galerkin (PDG) method in dimensions higher than one. The method has already been exposed and tested in [4] in the one-dimensional context. The PDG method is a general implicit high order method for approximating systems of conservation laws. It relies on a kinetic interpretation of the conservation laws containing stiff relaxation terms. The kinetic system is approximated with an asymptotic-preserving high order DG method. We describe the parallel implementation of the method, based on the StarPU runtime library. Then we apply it on preliminary test cases. [ABSTRACT FROM AUTHOR]

This paper presents a FEM-BEM coupling method suitable for the numerical simulation of the electromagnetic scattering of objects composed of dielectric materials and perfect electric conduc- tors. The originality of the approach lies in part in the use of the newly proposed Sparse Cardinal Sine Decomposition SCSD) method for the BEM part of the computation and the fact that the simulation software is almost entirely written in MATLAB. The performance of the method is illustrated by the computation of the electromagnetic scattering by an UAV-like object with two RAM regions proposed in the workshop ISAE EM 2016. [ABSTRACT FROM AUTHOR]