Three-dimensional image-based modeling by combining SBFEM and transfinite element shape functions

Gravenkamp, Hauke; Saputra, Albert A.; Eisenträger, Sascha

doi:10.1007/s00466-020-01884-4

Cited by 10 publications

(4 citation statements)

References 61 publications

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“…The aim of this paper is to derive a priori error estimates of SBFEM approximations for the case of Laplace's equation. Although numerical experiments in the literature point that optimal rates of convergence are obtained using SBFEM approximations [16,17], the mathematical demonstrations that give support to the observed numerical results are new contributions of the current work. For that, we explore two different aspects of SBFEM spaces, shared with Duffy's approximations [18] or with virtual harmonic spaces [19].…”

Section: Introductionmentioning

confidence: 62%

Error estimates for the Scaled Boundary Finite Element Method

Coelho,

Devloo,

Gomes

2020

Preprint

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The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions, where the shape functions approximate local Dirichlet problems with piecewise polynomial trace data. Using this operator adaptation approach, and by imposing a starlike scaling requirement on the subregions, the representation of local SBFEM shape functions in radial and surface directions are obtained from eigenvalues and eigenfunctions of an ODE system, whose coefficients are determined by the element geometry and the trace polynomial spaces. The aim of this paper is to derive a priori error estimates for SBFEM's solutions of harmonic test problems. For that, the SBFEM spaces are characterized in the context of Duffy's approximations for which a gradient-orthogonality constraint is imposed. As a consequence, the scaled boundary functions are gradient-orthogonal to any function in Duffy's spaces vanishing at the mesh skeleton, a mimetic version of a well-known property valid for harmonic functions. This orthogonality property is applied to provide a priori SBFEM error estimates in terms of known finite element interpolant errors of the exact solution. Similarities with virtual harmonic approximations are also explored for the understanding of SBFEM convergence properties. Numerical experiments with 2D and 3D polytopal meshes confirm optimal SBFEM convergence rates for two test problems with smooth solutions. Attention is also paid to the approximation of a point singular solution by using SBFEM close to the singularity and finite element approximations elsewhere, revealing optimal accuracy rates of standard regular contexts.

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Section: Introductionmentioning

confidence: 62%

Error estimates for the Scaled Boundary Finite Element Method

Coelho,

Devloo,

Gomes

2020

Preprint

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“…In this study, the two constraint conditions were the node delay and energy consumption constraint. e purpose of constraint allocation was to determine the allocation plan in the shortest time possible and to fairly allocate the best guaranteed time slot (GTS) resources in each superframe period to ensure communication quality of service (QoS) [24]. Common target allocation problems can be solved by the genetic algorithm, ant colony optimization algorithm, Markov chain state optimization algorithm, and other methods.…”

Section: Stitching Data Optimization Based On Simulatedmentioning

confidence: 99%

Applications of 3D Image Using Internet of Things in the Exhibition of Classical Architecture Art Style

Xie

Wen

Deng

2021

Mobile Information Systems

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Classical architecture is an architectural, cultural heritage with specific historical value. It is also a city with historical and cultural heritage and even a testimony of the profound historical culture of a country. Therefore, urbanization is unavoidable, and it directly influences historical buildings. This study aims to combine the three-dimensional image techniques and the Internet of Things (IoT) technology to research the development of classical architectural artistic style. This article presents the acquisition equipment, methods, precautions, and data processing of real-life 3D image data of the classical architectural heritage. We realized the online publishing of real-world 3D services of classical architectural heritage through the real-world 3D display system developed through the Internet of Things and mobile terminals. The model was verified through simulation tests. The combination of image processing techniques and analysis methods such as simulated annealing improved the accuracy of the prediction model. The proposed model can provide data support for policy formulation, technical intervention, and targeted field investigation on architectural heritage by screening research objects.

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“…CT-scans are voxel models and directly describe the volume of an investigated artifact. These can be used as a direct input for a large variety of methods for computational analysis [4,5,6,7,8].…”

Section: Geometric Modelsmentioning

confidence: 99%

Enforcing essential boundary conditions on domains defined by point clouds

Hartmann¹,

Kollmannsberger²

2021

Preprint

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This paper develops and investigates a new method for the application of Dirichlet boundary conditions for computational models defined by point clouds. Point cloud models often stem from laser or structured-light scanners which are used to scan existing mechanical structures for which CAD models either do not exist or from which the artifact under investigation deviates in shape or topology. Instead of reconstructing a CAD model from point clouds via surface reconstruction and a subsequent boundary conforming mesh generation, a direct analysis without pre-processing is possible using embedded domain finite element methods. These methods use non-boundary conforming meshes which calls for a weak enforcement of Dirichlet boundary conditions. For point cloud based models, Dirichlet boundary conditions are usually imposed using a diffuse interface approach. This leads to a significant computational overhead due to the necessary computation of domain integrals. Additionally, undesired side effects on the gradients of the solution arise which can only be controlled to some extent. This paper develops a new sharp interface approach for point cloud based models which avoids both issues. The computation of domain integrals is circumvented by an implicit approximation of corresponding Voronoi diagrams of higher order and the resulting sharp approximation avoids the side-effects of diffuse approaches. Benchmark examples from the graphics as well as the computational mechanics community are used to verify the algorithm. All algorithms are implemented in the FCMLab framework and provided at https://gitlab.lrz.de/cie_sam_public/fcmlab/. Further, we discuss challenges and limitations of point cloud based analysis w.r.t. application of Dirichlet boundary conditions.

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Three-dimensional image-based modeling by combining SBFEM and transfinite element shape functions

Cited by 10 publications

References 61 publications

Error estimates for the Scaled Boundary Finite Element Method

Error estimates for the Scaled Boundary Finite Element Method

Applications of 3D Image Using Internet of Things in the Exhibition of Classical Architecture Art Style

Enforcing essential boundary conditions on domains defined by point clouds

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