Computational modeling and simulation of real-world problems, e.g., various applications in the automotive, aerospace, and biomedical industries, often involve geometric objects which are bounded by curved surfaces. The geometric modeling of such objects can be performed via high-order meshes. Such a mesh, when paired with a high-order partial differential equation (PDE) solver, can realize more accurate solution results with a decreased number of mesh elements (in comparison to a low-order mesh). There are several types of high-order mesh generation approaches, such as direct methods, a posteriori methods, and isogeometric analysis (IGA)-based spline modeling approaches. In this paper, we propose a direct, high-order, curvilinear tetrahedral mesh generation method using an advancing front technique. After generating the mesh, we apply mesh optimization to improve the quality and to take advantage of the degrees of freedom available in the initially straight-sided quadratic elements. Our method aims to generate high-quality tetrahedral mesh elements from various types of boundary representations including the cases where no computer-aided design files are available. Such a method is essential, for example, for generating meshes for various biomedical models where the boundary representation is obtained from medical images instead of CAD files. We present several numerical examples of second-order tetrahedral meshes generated using our method based on input triangular surface meshes.
more »
« less
A direct high-order curvilinear triangular mesh generation method using an advancing front technique
In this paper, we propose a novel method of generating high-order curvilinear triangular meshes using an advancing front approach. Our method relies on a direct approach to generate meshes on geometries with curved boundaries. Our advancing front method yields high-quality triangular elements in each iteration which omits the need for
post-processing steps. We present several numerical examples of second-order curvilinear triangular meshes of patient-specific anatomical models generated using our technique on boundary meshes obtained from biomedical images.
more »
« less
- NSF-PAR ID:
- 10192420
- Date Published:
- Journal Name:
- Proceedings of the 2020 International Conference on Computational Science (ICCS 2020)
- Volume:
- 12138
- Page Range / eLocation ID:
- 72-85
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Faithful, accurate, and successful cardiac biomechanics and electrophysiological simulations require patient-specific geometric models of the heart. Since the cardiac geometry consists of highly-curved boundaries, the use of high-order meshes with curved elements would ensure that the various curves and features present in the cardiac geometry are well-captured and preserved in the corresponding mesh. Most other existing mesh generation techniques require computer-aided design files to represent the geometric boundary, which are often not available for biomedical applications. Unlike such methods, our technique takes a high-order surface mesh, generated from patient medical images, as input and generates a high-order volume mesh directly from the curved surface mesh. In this paper, we use our direct high-order curvilinear tetrahedral mesh generation method [1] to generate several second-order cardiac meshes. Our meshes include the left ventricle myocardia of a healthy heart and hearts with dilated and hypertrophic cardiomyopathy. We show that our high-order cardiac meshes do not contain inverted elements and are of sufficiently high quality for use in cardiac finite element simulations.more » « less
-
more » « less
Summary We present an algorithm to simulate curvilinear hydraulic fractures in plane strain and axisymmetry. We restrict our attention to sharp fractures propagating in an isotropic, linear elastic medium and driven by the injection of a laminar, Newtonian fluid governed by lubrication theory, and we require the existence of a finite lag region between the fluid front and the crack tip. The key novelty of our approach is in how we discretize the evolving crack and fluid domains: we utilize universal meshes (UMs), a technique to create conforming triangulations of a problem domain by only perturbing nodes of a universal background mesh in the vicinity of the boundary. In this way, we construct meshes, which conform to the crack and to the fluid front. This allows us to build standard piecewise linear finite element spaces and to monolithically solve the quasistatic hydraulic fracture problem for the displacement field in the rock and the pressure in the fluid. We demonstrate the performance of our algorithms through three examples: a convergence study in plane strain, a comparison with experiments in axisymmetry, and a novel case of a fracture in a narrow pay zone.
-
Boundary element methods (BEM) have been successfully applied towards solving a broad array of complicated electromagnetic problems. Most BEM approaches rely on flat triangular discretizations and discretization via the Method of Moments (MoM) and low-order basis functions. Although more complicated from an implementation standpoint, it has been shown that high-order methods based on curvilinear patch mesh discretizations can significantly outperform low-order MoM in both accuracy and computational efficiency. In this work, we review a new high-order Nyström method based on using Chebyshev basis functions with curvilinear elements that we have recently developed, present a few scattering examples, and discuss related on-going and future work.more » « less
-
One challenge in the generation of high-order meshes is that mesh tangling can occur as a consequence of moving the new boundary nodes to the true curved boundary. In this paper, we propose a new optimization-based method that uses signed angles to untangle invalid second- and third-order triangular meshes. Our proposed method consists of two passes. In the first pass, we loop over each high-order interior edge node and minimize an objective function based on the signed angles of the pair of triangles that share the node. In the second pass, we loop over face nodes and move them to the mean of the high-order nodes of the triangle to which the face node belongs. We present several numerical examples in two dimensions with second- and third-order elements that demonstrate the capabilities of our method for untangling invalid meshes.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-50417-5_6
