All-at-once preconditioning in PDE-constrained optimization

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques

Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure

The deal.II Library, Version 8.3

deal.II version 8.3 was released August 1, 2015. This paper provides an overview of the new features of this release and serves as a citable reference for the deal.II software library version 8.3. deal.II is an object-oriented finite element library used around the world in the development of finite element solvers. It is available for free under the GNU Lesser General Public License (LGPL) from the deal.II homepage at http://www.dealii.org/

Endogenous hormonal status of embryogenic callus in cocos (Cocos nucifera L.) explants

Trabajo presentado en un evento que no se pudo identificar.The application of optimum concentrations of hormones according to specific culture stages plays an important role, especially in plants which are concerned lo be recalcitrant for propagation in vitro, like Cocos nucifera L. The teasibility of the clonal propagation of coconut via somatic embryogenesis using inmature inflorescences as source of explants has been demostrated by Branton and Blake (1984). But yet there is no advanced technique for the mass producction of clonal palms available. One reason among others might be the inconsistent in vitro responses of coconut cultures observed In various clonal propagation experiments (Ebert. 1993). The present study was done to elucidate the endogenous hormonal changes In coconut explants, focusing on the 4-months period of embryogenic callus formation in rachilla explant cultures.UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Agroalimentarias::Centro para Investigaciones en Granos y Semillas (CIGRAS

FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics

Developing multiphysics finite element methods (FEM) and scalable HPC implementations can be very challenging in terms of software complexity and performance, even more so with the addition of goal-oriented adaptive mesh refinement. To manage the complexity we in this work present general adaptive stabilized methods with automated implementation in the FEniCS-HPC automated open source software framework. This allows taking the weak form of a partial differential equation (PDE) as input in near-mathematical notation and automatically generating the low-level implementation source code and auxiliary equations and quantities necessary for the adaptivity. We demonstrate new optimal strong scaling results for the whole adaptive framework applied to turbulent flow on massively parallel architectures down to 25000 vertices per core with ca. 5000 cores with the MPI-based PETSc backend and for assembly down to 500 vertices per core with ca. 20000 cores with the PGAS-based JANPACK backend. As a demonstration of the power of the combination of the scalability together with the adaptive methodology allowing prediction of gross quantities in turbulent flow we present an application in aerodynamics of a full DLR-F11 aircraft in connection with the HiLift-PW2 benchmarking workshop with good match to experiments

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem

Parameter identification through mode isolation for reaction-diffusion systems on arbitrary geometries

We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many natural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of do- mains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary

The deal.II Library, Version 9.1

This paper provides an overview of the new features of the finite element library deal.II, version 9.1

Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

Magnetic Induction Tomography (MIT) is a non‐invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, a widely‐used open source finite element library