An adaptive octree finite element method for PDEs posed on surfaces

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk finite element space is defined on an octree grid which is locally refined or coarsened depending on error indicators and estimated values of the surface curvatures. The cartesian structure of the bulk mesh leads to easy and efficient adaptation process, while the trace finite element method makes fitting the mesh to the surface unnecessary. The number of degrees of freedom involved in computations is consistent with the two-dimension nature of surface PDEs. No parametrization of the surface is required; it can be given implicitly by a level set function. In practice, a variant of the marching cubes method is used to recover the surface with the second order accuracy. We prove the optimal order of accuracy for the trace finite element method in $H^1$ and $L^2$ surface norms for a problem with smooth solution and quasi-uniform mesh refinement. Experiments with less regular problems demonstrate optimal convergence with respect to the number of degrees of freedom, if grid adaptation is based on an appropriate error indicator. The paper shows results of numerical experiments for a variety of geometries and problems, including advection-diffusion equations on surfaces. Analysis and numerical results of the paper suggest that combination of cartesian adaptive meshes and the unfitted (trace) finite elements provide simple, efficient, and reliable tool for numerical treatment of PDEs posed on surfaces

Particlization in hybrid models

In hybrid models, which combine hydrodynamical and transport approaches to describe different stages of heavy-ion collisions, conversion of fluid to individual particles, particlization, is a non-trivial technical problem. We describe in detail how to find the particlization hypersurface in a 3+1 dimensional model, and how to sample the particle distributions evaluated using the Cooper-Frye procedure to create an ensemble of particles as an initial state for the transport stage. We also discuss the role and magnitude of the negative contributions in the Cooper-Frye procedure.Comment: 18 pages, 28 figures, EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics"; version accepted for publication, typos and error in Eq.(1) corrected, the purpose of sampling and change from UrQMD to fluid clarified, added discussion why attempts to cancel negative contributions of Cooper-Frye are not applicable her

Hardware Parallel Architecture of a 3D Surface Reconstruction: Marching Cubes Algorithm

International audienceIn this paper we present a study of the algorithmic and architectural exploration methodology for a parallelism of the 3D reconstructing algorithm (Marching Cubes) and its optimized implementation on FPGA.We aim at defining a parallel multiprocessor architecture implementing this algorithm in an optimal way and Elementary Processor (EP) architecture dedicated to this algorithm. We use the SynDEx tool which adapts the AAA (Algorithm Architecture Adequacy) methodology, to find a good compromise between the computing power, the functionality of each PE, the optimization constraint (time, area), and the parallelization efficiency. Then, we describe a first implementation of PE on FPGA

Shape from Shading through Shape Evolution

In this paper, we address the shape-from-shading problem by training deep networks with synthetic images. Unlike conventional approaches that combine deep learning and synthetic imagery, we propose an approach that does not need any external shape dataset to render synthetic images. Our approach consists of two synergistic processes: the evolution of complex shapes from simple primitives, and the training of a deep network for shape-from-shading. The evolution generates better shapes guided by the network training, while the training improves by using the evolved shapes. We show that our approach achieves state-of-the-art performance on a shape-from-shading benchmark

Reducing artifacts in surface meshes extracted from binary volumes

We present a mesh filtering method for surfaces extracted from binary volume data which guarantees a smooth and correct representation of the original binary sampled surface, even if the original volume data is inaccessible or unknown. This method reduces the typical block and staircase artifacts but adheres to the underlying binary volume data yielding an accurate and smooth representation. The proposed method is closest to the technique of Constrained Elastic Surface Nets (CESN). CESN is a specialized surface extraction method with a subsequent iterative smoothing process, which uses the binary input data as a set of constraints. In contrast to CESN, our method processes surface meshes extracted by means of Marching Cubes and does not require the binary volume. It acts directly and solely on the surface mesh and is thus feasible even for surface meshes of inaccessible or unknown volume data. This is possible by reconstructing information concerning the binary volume from artifacts in the extracted mesh and applying a relaxation method constrained to the reconstructed information

Isosurface Extraction in the Visualization Toolkit Using the Extrema Skeleton Algorithm

Generating isosurfaces is a very useful technique in data visualization for understanding the distribution of scalar data. Often, when the size of the data set is really large, as in the case with data produced by medical imaging applications, engineering simulations or geographic information systems applications, the use of traditional methods like marching cubes makes repeated generation of isosurfaces a very time consuming task. This thesis investigated the use of the Extrema Skeleton algorithm to speed up repeated isosurface generation in the visualization package, Visualization Toolkit (VTK). The objective was to reduce the number of non-isosurface cells visited to generate isosurfaces, and to compare the Extrema Skeleton method with the Marching Cubes method by monitoring parameters like time taken for the isosurfacing process and number of cells visited. The results of this investigation showed that the Extrema Skeleton method was faster for most of the datasets tested. For simple datasets with less than 10% isosurface cells and complex datasets with less than 5% isosurface cells, the Extrema Skeleton method was found to be significantly faster than the Marching Cubes method. The time gained by the Extrema Skeleton method for datasets with greater than 15% isosurface cells was found to be insignificant. Based on the results of this study, implementing the Extrema Skeleton method for the VTK software is a change worth making because typical VTK users deal with datasets for which the Extrema Skeleton method is significantly faster and also with datasets for which it is marginally faster than the Marching Cubes method

Numerical studies of flow in porous media using an unstructured approach

Flow and transport in porous media is relevant to many areas of engineering and science including groundwater hydrology and the recovery of oil and gas. Porous materials are characterized by the unique shape and connectivity of the internal void structures which give rise to a large range in macroscopic transport properties. Historically an inability to accurately describe the internal pore-structure has prevented detailed study of the role of pore structure on transport. In recent decades however, the combination of high resolution imaging technologies with computational modeling has seen the development of fundamental pore-scale techniques for studying flow in porous media. Image-based pore-scale modeling of transport phenomena has become an important tool for understanding the complicated relationships between pore structure and measurable macroscopic properties, including permeability and formation factor. This has commonly been achieved by a network-based approach where the pore space is idealized as a series of pores connected by throats, or by a grid-based approach where the voxels of a 3D image represent structured quadrilateral elements or nodal locations. In this work however, image-based unstructured meshing techniques are used to represent voxelised pore spaces by grids comprising entirely of tetrahedral elements. These unstructured tetrahedral grids are used in finite element models to calculate permeability and formation factor. Solutions to the Stokes equations governing creeping, or Darcy flow, are used to validate the finite element approach employed in this work, and to assess the impact of different image-based unstructured meshing strategies on predicted permeability. Testing shows that solutions to the Stokes equations by a P2P1 tetrahedral element are significantly more accurate than solutions based on a P1P1 element, while permeability is shown to be sensitive to structural changes to the pore space induced by different meshing approaches. The modeling approach is also used to investigate the relationship of an electric and hydraulic definition of tortuosity to the Carman-Kozeny equation. The results of simulations using a number of computer generated porous structures indicate that an electrical tortuosity based on computed formation factor is well correlated with the tortuosity suggested by the Carman-Kozeny equation

Graphical Computing Solution for Industrial Plant Engineering

When preparing an engineering operation on an industrial plant, reliable and updated models of the plant must be available for correct decisions and planning. However, especially in the case of offshore oil and gas installations, it can hazardous and expensive to send an engineering party to assess and update the model of the plant. To reduce the cost and risk of modelling the plant, there are methods for quickly generating a 3D representation, such as LiDAR and stereoscopic reconstruction. However, these methods generate large files with no inherit cohesion. To address this, we propose to find a solution to efficiently transform point clouds from stereoscopic reconstruction into small mesh files that can be streamed or shared across teams. With that in mind, different techniques for treating point clouds and generating meshes were tested independently to measure their performance and effectiveness on an artifact-rich data set, such as the ones this work is aimed for. Afterwards, the techniques were combined into pipelines and compared with each other in terms of efficiency, file size output, and quality. With all results in place, the best solution from the ones tested was identified and validated with large real-world data sets.Master's Thesis in InformaticsINF39

VolRoverN: Enhancing Surface and Volumetric Reconstruction for Realistic Dynamical Simulation of Cellular and Subcellular Function

Establishing meaningful relationships between cellular structure and function requires accurate morphological reconstructions. In particular, there is an unmet need for high quality surface reconstructions to model subcellular and synaptic interactions among neurons and glia at nanometer resolution. We address this need with VolRoverN, a software package that produces accurate, efficient, and automated 3D surface reconstructions from stacked 2D contour tracings. While many techniques and tools have been developed in the past for 3D visualization of cellular structure, the reconstructions from VolRoverN meet specific quality criteria that are important for dynamical simulations. These criteria include manifoldness, water-tightness, lack of self- and object-object-intersections, and geometric accuracy. These enhanced surface reconstructions are readily extensible to any cell type and are used here on spiny dendrites with complex morphology and axons from mature rat hippocampal area CA1. Both spatially realistic surface reconstructions and reduced skeletonizations are produced and formatted by VolRoverN for easy input into analysis software packages for neurophysiological simulations at multiple spatial and temporal scales ranging from ion electro-diffusion to electrical cable models