SIAM IMR24: Program

Highly Anisotropic Battery Meshing

François Protais, Siemens DISW
Yuri Nesterenko,
Scott Canann,

Link to paper

Keywords: Anisotropic meshing, Cell design, Periodic Global Parametrization

Abstract

Cell design became a major challenge in the path for a greener future. Simcenter STAR-CCM+ introduced new tools to facilitate the design exploration of batteries. We present our new meshing approach that automates the discretization process, while ensuring the fastest simulation time, so as to maximize Engineers’ productivity. We produce highly anisotropic meshes on a curved stack of materials while respecting local sizing constraints. Our method is a two steps process, we first generate a high-quality quad-dominant anisotropic mesh on the top of the battery, that is then swept using standard approaches to obtain a volume mesh used for simulation. The surface mesh is obtained using our new quasi-structured approach. We apply the Periodic Global Parametrization method [1] to the process of creating the highly anisotropic mesh. This enables precise size variation control, while maximizing element quality. Our meshes are generated to offer similar convergence quality and speed to carefully hand-crafted structured meshes, while requiring a minimal user interaction, thus being orders of magnitude faster to generate.

Barycentrics for Incompatible Neighbors

Eugene Wachspress, retired

Link to paper

Keywords: barycentric, incompatible elements, Wachspress coordinates

Abstract

When vertices on common sides of adjacent elements do not align the elements are incompatible. Continuity is lost. This may occur, for example, when mesh refinement is used to reduce error over a portion of the mesh. Various schemes restore continuity. One may introduce transition elements or restrict approximation along the side to the coarse mesh variation. This note introduces a new scheme. The barycentric coordinates of the incompatible elements are modified to retain continuity.

On Why Mesh Untangling May Not be Required

Bhagyashree Prabhune, Oak Ridge National Lab
Krishnan Suresh, University of Wisconsin, Madison

Link to paper

Keywords: Mesh untangling, hexahedral elements, finite element method

Abstract

If a finite element mesh contains elements with negative Jacobian, it is said to tangled. Tangled meshes lead to erroneous results during finite element analysis. Consequently, many untangling methods have been proposed; however, untangling is not always achievable. To address this challenge, the authors recently introduced the isoparametric tangled finite element method (i-TFEM), allowing the use of tangled meshes in finite element analysis. By introducing minor modifications to standard FEM, i-TFEM offers an easy implementation and reduces to standard FEM for non-tangled meshes. It efficiently handles complex configurations of tangled elements, making it suitable for real-world scenarios, including linear/non-linear elasticity, free and forced vibrations, and thermal for quadrilateral, hexahederal and higher order triangular elements. Numerical experiments demonstrate the accuracy and applicability of the method to real-world tangled meshes. The numerical results also emphasizes the importance of reevaluating the notion of mesh quality for tangled meshes.

Curved Hexahedral Block-Structure Generation by Advancing Front

Claire Roche, CEA
Jérôme Breil,
Simon Calderan,
Hocquellet Thierry,
Franck Ledoux, CEA

Link to paper

Keywords: Mesh Generation, Block-Structured Mesh, Hexahedral Mesh, Curved Blocking

Abstract

This work aims to provide a method to generate block-structured meshes suitable for Computational Fluid Dynamics (CFD) simulations of flows around vehicles during atmospheric re-entry. This method takes as input a tetrahedral mesh of the domain, and the quadrangular block discretization of the vehicle surface. A linear blocking is obtained using an advancing front algorithm. This means it is incrementally created from the vehicle surface, layer by layer. Then, this linear blocking is curved, and we generate the final mesh. Some results of blocking and corresponding meshes generated with our algorithm are shown.

3D Mesh Regularization Based on a Weighted Line Sweeping Method

Guillaume Damour, CEA
Sébastien Guisset, CEA
Jérôme Breil, CEA

Link to paper

Keywords: Regularization method, Arbitrary Lagrangian-Eulerian (ALE), untangling method

Abstract

Mesh regularization methods are employed in computational simulations, particularly when dealing with problems modeled using the Lagrangian formalism. Indeed solving complex engineering problems using the Euler equations within a Lagrangian framework presents a critical challenge. In complex engineering applications that involve simulating strong shock waves, the computational mesh can deform significantly, closely tracking the movements of materials or fluids. In such cases, deteriorated or tangled meshes may compromise the integrity of the simulation. Combining regularization methods with Lagrangian simulation becomes indispensable, leading to the development of the Arbitrary Lagrangian-Eulerian (ALE) framework. In this work, we propose a regularization method for block-structured meshes which could be used within a 3D ALE code. Our proposed method aims to prevent mesh tangling while preserving the interesting physical characteristics of the Lagrangian mesh.

Asymptotic Analysis of Compound Volume+Shape Metrics for Mesh Optimization

Veselin A. Dobrev, Lawrence Livermore National Lab
Patrick Knupp, Dihedral LLC
Tzanio Kolev, Lawrence Livermore National Lab
Ketan Mittal, Lawrence Livermore National Lab
Robert N. Rieben, Lawrence Livermore National Lab
Michael Stees, Lawrence Livermore National Lab
Vladimir Tomov, Lawrence Livermore National Lab

Link to paper

Keywords: mesh quality, volume+shape balance, mesh adaptivity

Abstract

Mesh optimization metrics of type Volume+Shape (VS) are critical in controlling local volume, skew, and aspect ratio in computational meshes. Such metrics can be viewed as being intermediate between pure shape metrics and pure volume metrics. In most applications using VS metrics one wants the optimal mesh to display a good balance between shape and volume characteristics. Many existing VS metrics are shape-dominated or volume-dominated, meaning that they do not give good balance between shape and volume. To achieve balance, some of the existing VS metrics contain a user parameter to adjust the balance in one direction or the other. Unfortunately this parameter is currently determined by trial and error because the parameter is not intuitively linked to a definition of balance. In this work we study the asymptotic properties of different compound metrics and find the ones that provide good balance between shape and volume. This asymptotic approach is motivated, presented, and tested by numerical experiments. The experiments confirm the expected behavior of the metrics and yields volume-shape balance in the optimized mesh.

Mixed-Order Meshes through rp-Adaptivity for Surface Fitting to Implicit Geometries

Ketan Mittal, Lawrence Livermore National Lab
Veselin A. Dobrev, Lawrence Livermore National Lab
Patrick Knupp, Dihedral LLC
Tzanio Kolev, Lawrence Livermore National Lab
Franck Ledoux, CEA
Claire Roche, CEA-CESTA
Vladimir Tomov, Lawrence Livermore National Lab

Link to paper

Keywords: rp-adaptivity, mixed order meshes, surface fitting, high-order meshes

Abstract

Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes. Existing techniques for high-order mesh generation typically output meshes with same polynomial order for all elements. However, high order elements away from curvilinear boundaries or interfaces increase the computational cost of the simulation without increasing geometric accuracy. Prior work [5, 21] has presented one such approach for generating body-fitted uniform-order meshes that takes a given mesh and morphs it to align with the surface of interest prescribed as the zero isocontour of a level-set function. We extend this method to generate mixed-order meshes such that curved surfaces of the domain are discretized with high-order elements, while low-order elements are used elsewhere. Numerical experiments demonstrate the robustness of the approach and show that it can be used to generate a mixed-order mesh that is much more efficient than a high uniform-order mesh. The proposed approach is purely algebraic, and extends to different types of elements (quadrilaterals/triangles/tetrahedron/hexahedra) in two- and three- dimensions. Authors are anonymized for double-blind review.

High-Order Curvilinear Mesh Generation from Third-Party Meshes

Kaloyan S Kirilov, Imperial College London
Joaquim Peiró, Imperial College London
Jingtian Zhou, Imperial College London
Mashy D Green, Kings College London
David Moxey, Kings College London

Link to paper

Keywords: High-Order Mesh Generation, CAD-Mesh Connectivity, Complex Geometries, Mesh Curving

Abstract

A posteriori mesh curving techniques are established as the primary tool for generating high-order isoparametric meshes. However, this approach relies on an accurate CAD parametrisation of the underlying mesh objects which is not commonly made available as part of the mesh. Therefore, we present a method for reconstructing the missing CAD-mesh parametrisation and hence generating high-order meshes for complex geometries using modern mesh curving and optimisation techniques. The methodology imports an arbitrarily sourced straight-sided linear mesh. The linear mesh entities are then associated with their corresponding CAD BRep counterparts, followed by curving methods for order elevation, projections and, consequently, optimisations. Mesh modification techniques are used to achieve the desired mesh resolution and quality. We present and illustrate all steps of the proposed workflow through a simple geometry and a complex automotive one.

Keywords:

Abstract

Keywords:

Abstract

Keywords:

Abstract

Reconstruction of CAD Models into Single Trimmed Surfaces

Rebecca Rasmussen, Brigham Young University
Kendrick Shepherd, Brigham Young University

Link to paper

Keywords: Spline reconstruction; Fitting; Isogeometric analysis; Shell analysis; CAD; Mesh

Abstract

Classical methods by which computer-aided design (CAD) geometries are represented for both design and analysis involve meshing. This poses problems, as the meshing process takes a significant amount of time and labor, results in an approximate representation of the geometry of interest, and typically generates models capable only of low-order analyses. This research focuses on accurately and efficiently rebuilding given CAD surfaces or meshes into single trimmed surfaces (rather than a piecewise-linear approximation/representation), making them suitable for use in isogeometric analysis.

Visualization of Metric Fields for Four-dimensional Applications

Jude Anderson,
David Williams, Pennsylvania State University

Keywords: Metric field, mesh adaptation, visualization

Abstract

The metric field in a three-dimensional (3D) simulation domain can be visualized using an array of ellipsoids. The presence of deformed or skewed ellipsoids indicates an area of interest in the simulation that would benefit from mesh refinement and increased anisotropy of elements. For example, in computational fluid dynamics, boundary layers and shockwaves are typical flow features that require mesh refinement, and will display skewed ellipsoids in a plot of the metric field. Previous efforts to visualize metric fields have been limited to 2D and 3D applications. However, there has been recent interest in the development of 4D space-time applications. For example, one may consult the recent PhD thesis of Philip Caplan entitled “Four-Dimensional Anisotropic Mesh Adaptation for Spacetime Numerical Simulations,” MIT, 2019. To our knowledge, no one has attempted to visualize 4D metric fields by plotting 4D hyperellipsoids. Here, we propose the first method for visualizing these hyperellipsoids. In particular, we develop a method for approximating the surface of a hyperellipsoid using a polytope with tetrahedral facets. The facets can be uniformly subdivided in order to approximate the hyperellipsoid surface as closely as desired. Our approach for constructing these 4D polytopes is merely a higher-dimensional extension of the so-called ‘geodesic polyhedra’ which are often used to approximate spherical surfaces in 3D. Once the tetrahedral facets of our polytopes are constructed, they can be plotted using standard, 3D visualization techniques in conjunction with a non-orthogonal projection of the temporal axis. The resulting metric visualization is meant to provide an improved understanding of complex, space-time metric fields.

Manifold Meshing of Point Clouds with Guaranteed Smallest Edge Length

Henriette Lipschütz, Freie Universität Berlin
Ulrich Reitebuch, Freie Universität Berlin
Konrad Polthier, Freie Universität Berlin
Martin Skrodzki, TU Delft

Link to paper

Keywords: mesh generation, manifold mesh, high-quality triangulation, guaranteed smallest edge length

Abstract

Point clouds and polygonal meshes are widely used when modeling real world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or cultural preservation. Based on these raw data, polygonal meshes are created to, for example, run various simulations. For such applications, the utilized meshes must be of high quality. This paper presents an algorithm to derive triangle meshes from unstructured point clouds. The occurring edges have a close to uniform length and their lengths are bounded from below. Theoretical results guarantee the output to be manifold, provided suitable input and parameter choices. Further, the paper presents several experiments establishing that the algorithms can compete with widely used competitors in terms of quality of the output and timing. Furthermore, the output is stable under moderate levels of noise.

Robust Surface Remeshing Based on Conformal Welding

Wei Chen, Capital Normal University
Siquan Sun, Stony Brook University
Yue Wang, Stony Brook University
Na Lei, Dalian University of Technology
Chander Sadasivan, Stony Brook University
Apostolos Tassiopoulos, Stony Brook University
Shikui Chen, Stony Brook University
Hang Si, Cadence Design Systems Inc.
Xianfeng Gu, Stony Brook University

Link to paper

Keywords: Surface remeshing, Conformal welding, Surface Ricce flow

Abstract

High quality surface mesh generation is a challenging problem in the meshing field. Conformal uniformization has the potential to conquer the difficulty, which maps the surface onto a planar domain, triangulate the image with high quality using planar mesh generation method, and pull back the planar triangulation to the surface. Since the mapping preserves angles, the surface triangulation quality is guaranteed. Existing conformal parameterization method may induce self-intersections near the boundary. This work proposes a novel algorithm to eliminate the self-overlapping based on conformal welding theory, so to improve the robustness of the remeshing algorithm. The proposed algorithm constructs a planar annulus with high quality triangulation, then weld the input surface with the annulus along their corresponding boundary components. The welded surface has well defined Riemannian metric and can be conformally mapped onto a convex planar domain by using the dynamic discrete surface Ricci flow method. This method guarantees the conformal mapping restricted on the input surface is a global embedding, and resolve the problem of self-intersections in the neighborhood of the boundary. The conformal welding method has been tested to remesh real car models. The experimental results demonstrate the method is highly effective in practice and greatly improves the robustness of the remeshing algorithm based on conformal uniformization.

Optimal Surface Quadrilateral Mesh Generation

Zhou Zhao, Stony Brook University
Siyu Fang, Stony Brook University
Na Lei, Dalian University of Technology
Yuanpeng Liu, Stony Brook University
Yiming Zhu, Stony Brook University
Chander Sadasivan, Stony Brook University
Apostolos Tassiopoulos, Stony Brook University
Shikui Chen, Stony Brook University
Xianfeng Gu, Stony Brook University

Link to paper

Keywords: mesh generation, quad-mesh, optimal

Abstract

Structured mesh generation has fundamental importance, but controlling the qualities of structured meshes remains a challenge. This work proposes a rigorous and practical algorithm to generate quadrilateral meshes on topological poly-annuli with the least number of singularities. It is shown that each quad-mesh with $4k$ vertex degree induces a holomorphic differential. All the holomorphic differentials form a finite-dimensional linear space. A geometric distortion energy is proposed to measure the local area distortion. One can achieve quad-meshes as uniformly as possible by optimizing the distortion energy in the linear space. Experimental results show the proposed algorithm is able to improve the uniformity of the quad-meshes, and the method has the potential to be generalized to handle quad-meshes with other constraints.

CAD Dimensional Reduction for Shell Modeling using Reinforcement Learning

Steven Owen, Sandia National Laboratories
Armida J. Carbajal, Sandia National Laboratories
Matthew G. Peterson, Sandia National Laboratories
Corey D. Ernst, Sandia National Laboratories

Link to paper

Keywords: machine learning, reinforcement learning, shell finite elements, dimensional reduction

Abstract

This study presents advancements in shell model preparation, enhancing the design to simulation workflow. An approach is introduced to efficiently reduce thin CAD volumes to sheet body equivalents while maintaining geometric and topological integrity. Machine learning techniques, including supervised and reinforcement learning, guide reduction actions. Thin volume assembly reduction for shell modeling employs a multi-agent reinforcement learning algorithm to establish interconnected sheet bodies with designated attributes. Central to this approach is a novel supervised learning method predicting suitable dimensional reduction operations within a CAD tool. Developed tools enable efficient management of thin volume assemblies, contributing to accurate shell model generation with potential applications in design to simulation workflows.