Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

Fortmeier, Oliver; Bücker, H. Martin

doi:10.1016/j.jcp.2011.02.005

Cited by 10 publications

(4 citation statements)

References 41 publications

(51 reference statements)

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“…It was also applied to the FEM with first‐order accuracy and the DG method on triangular grids with second‐order accuracy . For triangular grids, the method was further improved for parallel performance . Last, the method was applied to DG‐FEM simulations on structured, quadrilateral grids and was improved for second‐order and third‐order accuracy .…”

Section: Introductionmentioning

confidence: 99%

Interface‐preserving level‐set reinitialization for DG‐FEM

Utz

Kummer

Oberlack

2016

Numerical Methods in Fluids

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Summary This paper presents a contribution to level‐set reinitialization in the context of discontinuous Galerkin finite element methods. We focus on high‐order polynomials for the discretization and level set geometries, which are comparable to the element size. In contrast to hyperbolic and geometric reinitialization techniques, our method relies on solving a nonlinear elliptic PDE iteratively. We critically compare two different variants of the algorithm experimentally in numerical studies. The results demonstrate that the method is stable for nontrivial test cases and shows high‐order accuracy. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Interface‐preserving level‐set reinitialization for DG‐FEM

Utz

Kummer

Oberlack

2016

Numerical Methods in Fluids

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“…In Section 4, we show that such partitioning problems, with general communication volumes, can be minimized greedily using a standard hypergraph partitioner. To measure the performance of this strategy, we partition a finite element triangulation from a real-world application taken from [18] in Section 5 and measure the resulting communication volumes and communication times of DROPS for up to 1024 processes. We compare partitionings obtained by the Mondriaan hypergraph partitioner [19] together with PaToH [20] to those generated by partitioning the undirected graph model using METIS [21].…”

Section: Introductionmentioning

confidence: 99%

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

et al. 2013

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A hypergraph model for mapping applications with an all-neighbor communication pattern to distributed-memory computers is proposed, which originated in finite element triangulations. Rather than approximating the communication volume for linear algebra operations, this new model represents the communication volume exactly. To this end, a hypergraph partitioning problem is formulated where the objective function involves a new metric. This metric, the kðk À 1Þ-metric, accurately models the communication volume for an all-neighbor communication pattern occurring in a concrete finite element application. It is a member of a more general class of metrics, which also contains more widely used metrics, such as the cut-net and the ðk À 1Þ-metric. In addition, we develop a heuristic to minimize the communication volume in the new kðk À 1Þ-metric. For the solution of several real-world finite element problems, experimental results based on this new heuristic demonstrate a small reduction in communication volume compared to a standard graph partitioner and do not show significant reductions in communication volume compared to a hypergraph partitioner using the common ðk À 1Þ-metric. However, for this set of problems, the new approach does reduce actual communication times. As a by-product, we observe that it also tends to reduce the number of messages. Furthermore, the new approach dramatically reduces the communication volume for a set of sparse matrix problems that are more irregularly-structured than finite element problems.

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“…The problem is now reduced to locating the nearest point → for each target vertex near the level set. In [23], a bruteforce approach is proposed to search → in all adjacent cells in an explicit manner. We have employed this approach, together with a minor improvement, to search → more reliably.…”

mentioning

confidence: 99%

“…Compared to its original form, in Procedure 1 we have added steps 10 -13 to ensure that the outputted nearest point is the globally nearest one. Other details about the procedure can be found in [23] and are not discussed here. The method proposed here is referred to as "explicit correction (EC)" below.…”

mentioning

confidence: 99%

Robust Three-Dimensional Level-Set Method for Evolving Fronts on Complex Unstructured Meshes

Wei

Bao

Liu

et al. 2018

Mathematical Problems in Engineering

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With a purpose to evolve the surfaces of complex geometries in their normal direction at arbitrarily defined velocities, we have developed a robust level-set approach which runs on three-dimensional unstructured meshes. The approach is built on the basis of an innovative spatial discretization and corresponding gradient-estimating approach. The numerical consistency of the estimating method is mathematically proven. A correction technology is utilized to improve accuracy near sharp geometric features. Validation tests show that the proposed approach is able to accurately handle geometries containing sharp features, computation regions having irregular shapes, discontinuous speed fields, and topological changes. Results of the test problems fit well with the reference results produced by analytical or other numerical methods and converge to reference results as the meshes refine. Compared to level-set method implementations on Cartesian meshes, the proposed approach makes it easier to describe jump boundary conditions and to perform coupling simulations.

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Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

Cited by 10 publications

References 41 publications

Interface‐preserving level‐set reinitialization for DG‐FEM

Interface‐preserving level‐set reinitialization for DG‐FEM

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

Robust Three-Dimensional Level-Set Method for Evolving Fronts on Complex Unstructured Meshes

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