259 research outputs found

    Binarized-octree generation for Cartesian adaptive mesh refinement around immersed geometries

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    We revisit the generation of balanced octrees for adaptive mesh refinement (AMR) of Cartesian domains with immersed complex geometries. In a recent short note (Hasbestan and Senocak, 2017) [42], we showed that the data locality of the Z-order curve in a hashed linear-octree generation method may not be perfect because of potential collisions in the hash table. Building on that observation, we propose a binarized-octree generation method that complies with the Z-order curve exactly. Similar to a hashed linear-octree generation method, we use Morton encoding to index the nodes of an octree, but use a red-black tree in place of the hash table. Red-black tree is a special kind of a binary tree, which we use for insertion and deletion of elements during mesh adaptation. By strictly working with the bitwise representation of an octree, we remove computer hardware limitations on the depth of adaptation on a single processor. Additionally, we introduce a geometry encoding technique for rapidly tagging a solid geometry for mesh refinement. Our results for several geometries with different levels of adaptations show that the binarized-octree generation method outperforms the linear-octree generation method in terms of runtime performance at the expense of only a slight increase in memory usage. The current AMR capability, rebl-AMR, is available as open-source software

    Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework

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    [EN] Geometry plays a key role in contact and shape optimization problems in which the accurate representation of the exact geometry and the use of adaptive analysis techniques are crucial to obtaining accurate computationally-efficient Finite Element (FE) simulations. We propose a novel algorithm to generate 3D h-adaptive meshes for an Immersed Boundary Method (IBM) based on Cartesian grids and the so-called NEFEM (NURBS-Enhanced FE Method) integration techniques. To increase the accuracy of the results at the minimum computational cost we seek to keep the efficient Cartesian structure of the mesh during the whole analysis process while considering the exact boundary representation of domains given by NURBS or T-Splines. Within the framework of Cartesian grids, the two significant contributions of this paper are: (a) the methodology used for the mesh-geometry intersection, which represents a considerable challenge due to their independence; and (b) the robust procedure used to generate the integration subdomains that exactly represent the CAD model. The numerical examples given show the proper convergence of the method, its capacity to mesh complex 3D geometries and that Cartesian grid-based IBM can be considered a robust and reliable tool in terms of accuracy and computational cost.The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through Project DPI2013-46317-R and the FPI program (BES-2011-044080), also the Generalitat Valenciana for the assistance received through Project PROMETEO/2016/007.Marco, O.; Ródenas, J.; Navarro-Jiménez, J.; Tur Valiente, M. (2017). Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. Computers & Structures. 193:87-109. doi:10.1016/j.compstruc.2017.08.004S8710919

    Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komplizierter Mikrostruktur

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    Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained.Moderne bildgebende Verfahren wie Mikro-Computertomographie (μCT), Magnetresonanztomographie (MRT) und Rasterelektronenmikroskopie (SEM) liefern nicht-invasiv hochauflösende Bilder der Mikrostruktur von Materialien. Sie bilden die Grundlage der geometrischen Modelle der hochauflösenden bildbasierten Analysis. Allerdings erreichen vor allem in 3D die Diskretisierungen dieser Modelle leicht die Größe von 100 Mill. Freiheitsgraden und erfordern umfangreiche Hardware-Ressourcen in Bezug auf Hauptspeicher und Rechenleistung, um das numerische Modell zu lösen. Der Fokus dieser Arbeit liegt daher darin, numerische Lösungsmethoden zu kombinieren und anzupassen, um den Speicherplatzbedarf und die Rechenzeit zu reduzieren und damit eine Ausführung der bildbasierten Analyse auf modernen Computer-Desktops zu ermöglichen. Daher ist als numerisches Modell eine einfache Gitterdiskretisierung der voxelbasierten (Pixel mit der Tiefe als dritten Dimension) Geometrie gewählt, die die Oberflächenerstellung weglässt und eine reduzierte Speicherung der finiten Elementen und einen matrixfreien Lösungsalgorithmus ermöglicht. Dies wiederum verringert den Aufwand von fast allen angewandten gitterbasierten Lösungsverfahren und führt zu Speichereffizienz und numerisch stabilen Algorithmen für die Mikrostrukturmodelle. Es werden zwei Varianten der Anpassung der matrixfreien Lösung präsentiert, die Element-für-Element Methode und eine Knoten-Kanten-Variante. Die Methode der konjugierten Gradienten in Kombination mit dem Mehrgitterverfahren als sehr effizienten Vorkonditionierer wird für den matrixfreien Lösungsalgorithmus adaptiert. Der stufige Verlauf der Materialgrenzen durch die voxelbasierte Diskretisierung wird durch Elemente geglättet, die am Integrationspunkt unterschiedliche Materialinformationen enthalten und über Teilzellen integriert werden (embedded boundary elements). Die Effizienz der matrixfreien Verfahren bleibt erhalten

    Robust volume mesh generation for non-watertight geometries

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    Nowadays large part of the time needed to perform a numerical simulation is spent in preprocessing, especially in the geometry cleaning operations and mesh generation. Furthermore, these operations are not easy to automatize because they depend strongly on each geometrical model and they often need human interaction. Many of these operations are needed to obtain a watertight geometry. Even with a clean geometry, classical unstructured meshing methods (like Delaunay or Advancing Front based ones) present critical weak points like the need of a given quality in the boundary mesh or a relatively smooth size transition. These aspects decrease their robustness and imply an extra effort in order to reach the final mesh. Octree based meshers try to relax some of these requirements. In the present work an octree based mesher for unstructured tetrahedra is presented. The proposed mesher ensures the mesh generation avoiding most of the geometry cleaning operations. It is based in the following steps: fit an octree onto the model, refine it following given criteria, apply a tetrahedra pattern to the octree cells and adapt the tetrahedra close to the contours in order to represent accurately the boundary shape. An important and innovative aspect of the proposed algorithm is it ensures the final mesh preserves the topology and the geometric features of the original model. The method uses a Ray Casting based algorithm for the identification of the inner and outer parts of the volumes involved in the model. This technique allows the mesh generation of volumes even with non-watertight boundaries, and also opens the use of the mesher for immersed methods only applying slight modifications to the algorithm. The main advantages of the presented mesher are: robustness, no need for watertight boundaries, independent on the contour mesh quality, preservation of geometrical features (corners and ridges), original geometric topology guaranteed, accurate representation of the contours, valid for immersed methods, and fast performance. A lot of time in the preprocessing part of the numerical simulation is saved thanks to the robustness of the mesher, which allows skipping most of the geometry cleaning operations. A shared memory parallel implementation of the algorithm has been done. The effectiveness of the algorithm and its implementation has been verified by some validation examples.En l'actualitat gran part del temps emprat per córrer una simulació numèrica està dedicat al preprocés, especialment a les operacions de neteja de geometria i generació de malla. A més, aquestes operacions no són fàcils d'automatitzar degut a la seva forta dependència del model geomètric i sovint necessiten d’interacció humana. Moltes d'aquestes operacions són necessàries per aconseguir una definició topológicament hermètica de la geometria. Inclús amb una geometria neta, els mètodes clàssics de mallat (com els basats en Delaunay o avançament frontal) presenten punts febles crítics com la necessitat d'una certa qualitat de les malles de contorn o una transició de mides relativament suau. Aquests aspectes disminueixen la seva robustesa i impliquen un esforç extra a l'hora d'obtenir la malla final. Els mètodes de mallat basats en estructures octree relaxen alguns d'aquests requeriments. En aquest treball es presenta un mallador basat en octree per tetraedres no estructurats. Un dels aspectes claus d'aquest mallador és que garanteix la generació de malla evitant moltes de les operacions de neteja de geometria. Es basa en els següents passos: encaixar un octree al model, refinar-lo seguint certs criteris, aplicar un patró de tetraedres a les cel•les de l'octree i adaptar-los a les zones properes als contorns a fi i efecte de representar acuradament la forma del domini. Un aspecte important i innovador de l'algorisme proposat és que manté la topologia del model a la malla final i preserva les seves característiques geomètriques. El mètode presentat utilitza un algorisme basat en la tècnica Ray Casting per la identificació de les parts interiors i exteriors dels volums del model. Aquesta tècnica permet la generació de malla de volums inclús amb contorns que no tanquen hermèticament, i també obre l’ús del mallador a mètodes “immersed” aplicant només petites modificacions a l'algorisme. Els principals avantatges del mallador presentat són: robustesa, no necessitat de definicions hermètiques dels contorns, independent de la qualitat de la malla de contorn, preservació de característiques geomètriques (cantonades i arestes abruptes), topologia original de la geometria garantida, representació precisa dels contorns, vàlid per mètodes “immersed” i ràpid rendiment. L’ús del mallador estalvia molt de temps en la part del preprocés de la simulació numèrica gràcies a la seva robustesa que permet obviar la majoria d'operacions de neteja de geometria. S'ha dut a terme una implementació paral•lela amb memòria compartida de l'algorisme. L'efectivitat del mateix i la seva implementació ha estat verificada mitjançant exemples de validació

    Kinetic Solvers with Adaptive Mesh in Phase Space

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    An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems
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