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The X-ray flux provided by X-ray free-electron lasers and storage rings offers new spatiotemporal possibilities to study in-situ and operando dynamics, even using single pulses of such facilities. X-ray Multi-Projection Imaging (XMPI) is a novel technique that enables volumetric information using single pulses of such facilities and avoids centrifugal forces induced by state-of-the-art time-resolved 3D methods such as time-resolved tomography. As a result, XMPI can acquire 3D movies (4D) at least three orders of magnitude faster than current methods. However, it is exceptionally challenging to reconstruct 4D from highly sparse projections as acquired by XMPI with current algorithms. Here, we present 4D-ONIX, a Deep Learning (DL)-based approach that learns to reconstruct 3D movies (4D) from an extremely limited number of projections. It combines the computational physical model of X-ray interaction with matter and state-of-the-art DL methods. We demonstrate the potential of 4D-ONIX to generate high-quality 4D by generalizing over multiple experiments with only two projections per timestamp for binary droplet collisions. We envision that 4D-ONIX will become an enabling tool for 4D analysis, offering new spatiotemporal resolutions to study processes not possible before.

We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge-Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete solution. However, in practice they differ in several important respects, including the terminology used to describe them, the structure of the resulting software, and the interaction with nonlinear solvers. Challenges and merits of the two approaches are discussed with the goal of providing the practitioner with sufficient consideration to choose which path to follow. Additionally, implementations of the two methods are provided as a starting point for further development. Numerical experiments validate the theoretical accuracy of these codes and demonstrate their utility, even for 4D problems., Comment: updated 3D experiments, fixed typos

This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial differential equations (PDE). Although the C++ interfaces of DUNE-FEM-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work easier user interfaces based on Python and the Unified Form Language are provided to open DUNE-FEM-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first order hyperbolic PDEs., Comment: 36 pages, 15 figures, various Python code examples

The Open Porous Media (OPM) initiative is a community effort that encourages open innovation and reproducible research for simulation of porous media processes. OPM coordinates collaborative software development, maintains and distributes open-source software and open data sets, and seeks to ensure that these are available under a free license in a long-term perspective. In this paper, we present OPM Flow, which is a reservoir simulator developed for industrial use, as well as some of the individual components used to make OPM Flow. The descriptions apply to the 2019.10 release of OPM., Comment: 43 pages, 22 figures

This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state [1, 2]. This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper., Comment: 69 pages, 14 figures, 4 tables and various code examples

In this paper we present a framework for solving two phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid adaptivity and local choice of polynomial degree. The method is implemented using the new Python frontend Dune-FemPy to the open source framework Dune. The code used for the simulations is made available as Jupyter notebook and can be used through a Docker container. We present a number of time stepping approaches ranging from a classical IMPES method to fully coupled implicit scheme. The implementation of the discretization is very flexible allowing for test different formulations of the two phase flow model and adaptation strategies., Comment: Keywords: DG, hp-adaptivity, Two-phase flow, IMPES, Fully implicit, Dune, Python, Porous media. 28 pages, 9 figures, various code snippets

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and also the geometric quality of the produced meshes., Comment: 18 pages

Distributed adaptive conforming refinement requires multiple iterations of the serial refinement algorithm and global communication as the refinement can be propagated over several processor boundaries. We show bounds on the maximum number of iterations. The algorithm is implemented within the software package DUNE-ALUGrid., Comment: 18 pages, 13 pictures, 4 algorithms

In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of the sources from the ALUgrid library and the binding to the DUNE software framework. The main changes include user defined load balancing, parallel grid construction, and an redesign of the 2d grid which can now also be used for parallel computations. In addition many improvements have been introduced into the code to increase the parallel efficiency and to decrease the memory footprint. The original ALUGrid library is widely used within the DUNE community due to its good parallel performance for problems requiring local adaptivity and dynamic load balancing. Therefore, this new model will benefit a number of DUNE users. In addition we have added features to increase the range of problems for which the grid manager can be used, for example, introducing a 3d tetrahedral grid using a parallel newest vertex bisection algorithm for conforming grid refinement. In this paper we will discuss the new features, extensions to the DUNE interface, and explain for various examples how the code is used in parallel environments., Comment: 25 pages, 11 figures

The compact Discontinuous Galerkin 2 (CDG2) method was successfully tested for elliptic problems, scalar convection-diffusion equations and compressible Navier-Stokes equations. In this paper we use the newly developed DG method to solve a mathematical model for early stages of atherosclerotic plaque formation. Atherosclerotic plaque is mainly formed by accumulation of lipid-laden cells in the arterial walls which leads to a heart attack in case the artery is occluded or a thrombus is built through a rupture of the plaque. After describing a mathematical model and the discretization scheme, we present some benchmark tests comparing the CDG2 method to other commonly used DG methods. Furthermore, we take parallelization and higher order discretization schemes into account., Comment: preprint