Reference : Smart cloud collocation: a unified workflow from CAD to enhanced solutions
Dissertations and theses : Doctoral thesis
Engineering, computing & technology : Computer science
Engineering, computing & technology : Mechanical engineering
Engineering, computing & technology : Multidisciplinary, general & others
Smart cloud collocation: a unified workflow from CAD to enhanced solutions
Jacquemin, Thibault Augustin Marie mailto [University of Luxembourg > Faculty of Science, Technology and Medecine (FSTM) > >]
University of Luxembourg, ​​Luxembourg
Docteur en Sciences de l'Ingénieur
xxv, 181 + 26
Bordas, Stéphane mailto
Zilian, Andreas mailto
Hale, Jack mailto
Sbalzarini, Ivo
Adam, Laurent
[en] CAD to collocation ; Generalized visibility criterion ; Discretization adaptivity from CAD ; Generalized Finite Difference (GFD) ; Discretization-Corrected Particle Strength Exchange method (DC PSE) ; Stencil selection ; Concave problems ; Singular problems ; Error indication ; Linear elasticity
[en] Computer Aided Design (CAD) software packages are used in the industry to design mechanical systems. Then, calculations are often performed using simulation software packages to improve the quality of the design. To speed up the development costs, companies and research centers have been trying to ease the integration of the computation phase in the design phase. The collocation methods have the potential of easing such integration thanks to their meshless nature. The geometry discretization step which is a key element of all computational method is simplified compared to mesh-based methods such as the finite element method.

We propose in this thesis a unified workflow that allows the solution of engineering problems defined by partial differential equations (PDEs) directly from input CAD files. The scheme is based on point collocation methods and proposed techniques to enhance the solution. We introduce the idea of “smart clouds”. Smart clouds refer to point cloud discretizations that are aware of the exact CAD geometry, appropriate to solve a defined problem using a point collocation method and that contain information used to improve locally the solution.

We introduce a unified node selection algorithm based on a generalization of the visibility criterion. The proposed algorithm leads to a significant reduction of the error for concave problems and does not have any drawback for convex problems. The point collocation methods rely on many parameters. We select in this thesis parameters for the Generalized Finite Difference (GFD) method and the Discretization-Corrected Particle Strength Exchange (DC PSE) method that we deem appropriate for most problems from the field of linear elasticity. We also show that solution improvement techniques, based on the use of Voronoi diagrams or on a stabilization of the PDE, do not lead to a reduction of the error for all of the considered benchmark problems. These methods shall therefore be used with care. We propose two types of a posteriori error indicators that both succeed in identifying the areas of the domain where the error is the greatest: a ZZ-type and a residual-type error indicator. We couple these indicators to a h-adaptive refinement scheme and show that the approach is effective. Finally, we show the performance of Algebraic Multigrid (AMG) preconditions on the solution of linear systems compared to other preconditioning/solution methods. This family of preconditioners necessitates the selection of a large number of parameters. We assess the impact of some of them on the solution time for a 3D problem from the field of linear elasticity. Despite the performance of AMG preconditions, ILU preconditioners may be preferred thanks to their ease of usage and robustness to lead to a convergence of the solution.
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