arXiv subjects

Ernst Rank

Publications and source records attributed to Ernst Rank.

35 records · Page 2Linked to original sources

arXiv2019

Direct structural analysis of domains defined by point clouds

This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a regular background grid of finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficient information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.

cs.CE↗

arXiv2019

Integrating CAD and Numerical Analysis: 'Dirty Geometry' handling using the Finite Cell Method

This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with "dirty geometries". FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the boundary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an effective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also "dirty geometries", i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm being insensitive to most CAD model flaws is proposed to identify the affiliation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.

cs.CE↗

arXiv2018

From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry

During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the model's interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out efficiently and robustly

cs.CE↗

arXiv2018

A design-through-analysis approach using the Finite Cell Method (ECCOMAS Congress 2016)

Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects' surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that B-Rep models are not necessarily watertight. These 'dirty geometries' cause major difficulties in computational analysis because even basic geometric operations such as point-in-membership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to B-Rep models, CSG models are intrinsically water-tight. To run a finite element simulation on a water-tight CSG model, two alternatives are possible: (i) it can either be converted to a B-Rep-model to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a design-through analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable point-in-membership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the point-in-membership test as a sequence of CSG-operations, and discuss advantages and limitations on complex models of relevance in mechanical engineering.

cs.CE↗

arXiv2018

Residual stresses in metal deposition modeling: discretizations of higher order

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This application demands for the solution of a coupled thermo-elasto-plastic problem on transient meshes within which history variables need to be managed dynamically on non-boundary conforming discretizations. To this end, we propose to combine the multi-level hp-method and the finite cell method. The former was specifically designed to treat high-order finite element discretizations on transient meshes, while the latter offers a remedy to retain high-order convergence rates also in cases where the physical boundary does not coincide with the boundary of the discretization. We investigate the performance of the method at two analytical and one experimental benchmark.

math.NA↗

arXiv2018

Robust and parallel scalable iterative solutions for large-scale finite cell analyses

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which signifi- cantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.

math.NA↗

arXiv2018

A review of the finite cell method for nonlinear structural analysis of complex CAD and image-based geometric models

The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. For the analysis of complex geometries, it circumvents expensive and potentially error-prone meshing procedures, while maintaining high rates of convergence. The present contribution provides an overview of recent accomplishments in the FCM with applications in structural mechanics. First, we review the basic components of the technology using the p- and B-spline versions of the FCM. Second, we illustrate the typical solution behavior for linear elasticity in 1D. Third, we show that it is straightforward to extend the FCM to nonlinear elasticity. We also outline that the FCM can be extended to applications beyond structural mechanics, such as transport processes in porous media. Finally, we demonstrate the benefits of the FCM with two application examples, i.e. the vibration analysis of a ship propeller described by T-spline CAD surfaces and the nonlinear compression test of a CT-based metal foam.

math.NA↗

arXiv2018

Parallelization of the multi-level hp-adaptive finite cell method

The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a hp-scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level hp-scheme is presented that is adapted to the scheme's simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the scheme's parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.

cs.DC↗

arXiv2018

Dynamic load balancing strategies for hierarchical p-FEM solvers

Equation systems resulting from a p-version FEM discretisation typically require a special treatment as iterative solvers are not very efficient here. Applying hierarchical concepts based on a nested dissection approach allow for both the design of sophisticated solvers as well as for advanced parallelisation strategies. To fully exploit the underlying computing power of parallel systems, dynamic load balancing strategies become an essential component.

cs.DC↗

arXiv2018

Computational steering of complex flow simulations

Computational Steering, the combination of a simulation back-end with a visualisation front-end, offers great possibilities to exploit and optimise scenarios in engineering applications. Due to its interactivity, it requires fast grid generation, simulation, and visualisation and, therefore, mostly has to rely on coarse and inaccurate simulations typically performed on rather small interactive computing facilities and not on much more powerful high-performance computing architectures operated in batch-mode. This paper presents a steering environment that intends to bring these two worlds - the interactive and the classical HPC world - together in an integrated way. The environment consists of efficient fluid dynamics simulation codes and a steering and visualisation framework providing a user interface, communication methods for distributed steering, and parallel visualisation tools. The gap between steering and HPC is bridged by a hierarchical approach that performs fast interactive simulations for many scenario variants increasing the accuracy via hierarchical refinements in dependence of the time the user wants to wait. Finally, the user can trigger large simulations for selected setups on an HPC architecture exploiting the pre-computations already done on the interactive system.

cs.CE↗

arXiv2018

Numerical simulation of transport in porous media: some problems from micro to macro scale

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of tracers is strongly influenced by pore scale velocity structure and large scale inhomogeneities in the permeability field. The velocity structure on the pore scale is investigated by direct numerical simulations of the 3D velocity field in a random sphere pack. The velocity probability density functions are strongly skewed, including some negative velocities. The large probability for very small velocities might be the reason for non-Fickian dispersion in the initial phase of contaminant transport. We present a method to determine large scale distributions of the permeability field from point-wise velocity measurements. The adjoint-based optimisation algorithm delivers fully satisfying agreement between input and estimated permeability fields. Finally numerical methods for convection dominated tracer transports are investigated from a theoretical point of view. It is shown that high order Finite Element Methods can reduce or even eliminate non-physical oscillations in the solution without introducing additional numerical diffusivity.

math.NA↗

arXiv2018

A high-performance interactive computing framework for engineering applications

To harness the potential of advanced computing technologies, efficient (real time) analysis of large amounts of data is as essential as are front-line simulations. In order to optimise this process, experts need to be supported by appropriate tools that allow to interactively guide both the computation and data exploration of the underlying simulation code. The main challenge is to seamlessly feed the user requirements back into the simulation. State-of-the-art attempts to achieve this, have resulted in the insertion of so-called check- and break-points at fixed places in the code. Depending on the size of the problem, this can still compromise the benefits of such an attempt, thus, preventing the experience of real interactive computing. To leverage the concept for a broader scope of applications, it is essential that a user receives an immediate response from the simulation to his or her changes. Our generic integration framework, targeted to the needs of the computational engineering domain, supports distributed computations as well as on-the-fly visualisation in order to reduce latency and enable a high degree of interactivity with only minor code modifications. Namely, the regular course of the simulation coupled to our framework is interrupted in small, cyclic intervals followed by a check for updates. When new data is received, the simulation restarts automatically with the updated settings (boundary conditions, simulation parameters, etc.). To obtain rapid, albeit approximate feedback from the simulation in case of perpetual user interaction, a multi-hierarchical approach is advantageous. Within several different engineering test cases, we will demonstrate the flexibility and the effectiveness of our approach.

cs.DC↗

arXiv2018

Ensuring domain consistency in an adaptive framework with distributed topology for fluid flow simulations

Top-tier parallel computing clusters continue to accumulate more and more computational power with more and better CPUs and Networks. This allows, especially for environmental simulations, computations with larger domain sizes and better resolution. One of the challenges becoming increasingly important is the decomposition and distribution of the overall work load. State-of-the-art parallel codes usually use solutions that involve complete knowledge of the domain topology, which will lead to communication and memory bottlenecks when computing very large domains. To meet this challenge, the authors propose a new strategy for decentralised domain management, based on a proven hierarchic data structure. On the way of developing a framework where individual sub-domains only have local knowledge of their surroundings, this contribution describes the communication patterns used in ensuring a consistent domain, without the need for expensive global broadcast messages. Furthermore, the routines necessary to deal with adaptive changes in domain topology, due to refinement, coarsening and migration of sub-domains to different computational resources, are discussed in detail.

cs.DC↗

arXiv2018

Framework for the hybrid parallelisation of simulation codes

Writing efficient hybrid parallel code is tedious, error-prone, and requires good knowledge of both parallel programming and multithreading such as MPI and OpenMP, resp. Therefore, we present a framework which is based on a job model that allows the user to incorporate his sequential code with manageable effort and code modifications in order to be executed in parallel on clusters or supercomputers built from modern multi-core CPUs. The primary application domain of this framework are simulation codes from engineering disciplines as those are in many cases still sequential and due to their memory and runtime demands prominent candidates for parallelisation.

cs.DC↗

arXiv2018

A sliding window technique for interactive high-performance computing scenarios

Interactive high-performance computing is doubtlessly beneficial for many computational science and engineering applications whenever simulation results should be visually processed in real time, i.e. during the computation process. Nevertheless, interactive HPC entails a lot of new challenges that have to be solved - one of them addressing the fast and efficient data transfer between a simulation back end and visualisation front end, as several gigabytes of data per second are nothing unusual for a simulation running on some (hundred) thousand cores. Here, a new approach based on a sliding window technique is introduced that copes with any bandwidth limitations and allows users to study both large and small scale effects of the simulation results in an interactive fashion.

cs.CE↗

arXiv2018

Interactive data exploration for high-performance fluid flow computations through porous media

Huge data advent in high-performance computing (HPC) applications such as fluid flow simulations usually hinders the interactive processing and exploration of simulation results. Such an interactive data exploration not only allows scientiest to 'play' with their data but also to visualise huge (distributed) data sets in both an efficient and easy way. Therefore, we propose an HPC data exploration service based on a sliding window concept, that enables researches to access remote data (available on a supercomputer or cluster) during simulation runtime without exceeding any bandwidth limitations between the HPC back-end and the user front-end.

cs.CE↗

arXiv2018

Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small length-scale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phase-field profile. In the classical approach, phase-field models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations.

cs.CE↗