Mixed‐element Octree: a meshing technique toward fast and real‐time simulations in biomedical applications

Abstract

This article introduces a meshing technique focused on fast and real-time simulation in a biomedical context. We describe in details our algorithm, which starts from a basic Octree regarding the constraints imposed by the simulation, and then, mixed-element patterns are applied over transitions between coarse and fine regions. The use of surface patterns, also composed by mixed elements, allows us to better represent curved domains decreasing the odds of creating invalid elements by adding as few nodes as possible. In contrast with other meshing techniques, we let the user define regions of greater refinement, and as a consequence of that refinement, we add as few nodes as possible to produce a mesh that is topologically correct. Therefore, our meshing technique gives more control on the number of nodes of the final mesh. We show several examples where the quality of the final mesh is acceptable, even without using quality filters. We believe that this new meshing technique is in the correct direction toward real-time simulation in the biomedical field.

Fast Quadtree/Octree adaptive meshing and re-meshing with linear mixed elements

“…As an alternative, mixed-element meshes have been more developed, counting with a larger set of patterns to handle transitions [4,16,17]. Moreover, in a previous work [14], we were able to implement all mixed-element transition cases, avoiding any unnecessary refinement propagation (see [8] for implementation details).…”

“…In Fig. 2(d) quadrant Q 2 was finally refined due to balancing and now edge (6,9) holds [0, Q 5 , Q 14 ] and edge (2,9) (9,14) with [0, Q 9 , Q 11 ] are adequately updated, remembering that only the most refined edges need to support up-to-date information on neighbors.…”

Finite element models of the human tongue: a mixed-element mesh approach

“…Three types of meshes were tested: a coarse and fine all-tetrahedral mesh (Figure 2(b)) generated using the AN-SYS meshing algorithm; a coarse and fine all-hexahedral mesh (Figure 2(c)) also generated using the ANSYS meshing algorithm; and five mixed-element meshes (Figure 2(d)) generated using the automatic mixed-element meshing algorithm developed in [19]. In this case, all the octants at the boundary of the cylinder have the same size but the discretization of the cylinder's inner section was performed differently.…”

“…The goal of the present study is to evaluate the performance of a mixed-element meshing technique we recently developed [19]. The modeling context of this study is incompressible materials at large strains.…”

Relations between Geometric Parameters and Numerical Simulation Accuracy in Modeling Signal Transmission in the Presynaptic Bouton

“…The above mentioned dynamical processes are often described by using differential equations [5][6][7], including−for a long time−partial ones [8][9][10]. The equation of this type can not, usually, be solved analytically, and therefore numerical methods have to be used [10][11][12][13]. In order to perform the calculations quickly and accurately, the appropriately designed mesh, in the nodes of which the calculations will be made, should be created.…”