SCG '86 Proceedings of the second annual symposium on Computational geometry
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Merging free trees in parallel for efficient Voronoi diagram construction
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A comparison of sequential Delaunay triangulation algorithms
Computational Geometry: Theory and Applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Dynamic-mesh finite element method for Lagrangian computational fluid dynamics
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Parallel Delaunay triangulation based on circum-circle criterion
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
A bézier-based approach to unstructured moving meshes
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Simulation of blood flow through a microvessel branching
BioMed'06 Proceedings of the 24th IASTED international conference on Biomedical engineering
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Many important phenomena in science and engineering, including our motivating problem of microstructural blood flow, can be modeled as flows with dynamic interfaces. The major challenge faced in simulating such flows is resolving the interfacial motion. Lagrangian methods are ideally suited for such problems, since interfaces are naturally represented and propagated. However, the material description of motion results in dynamic meshes, which become hopelessly distorted unless they are regularly regenerated. Lagrangian methods are particularly challenging on parallel computers, because scalable dynamic mesh methods remain elusive. Here, we present a parallel dynamic mesh Lagrangian method for flows with dynamic interfaces. We take an aggressive approach to dynamic meshing by triangulating the propagating grid points at every timestep using a scalable parallel Delaunay algorithm. Contrary to conventional wisdom, we show that the costs of the dynamic mesh components (triangulation,coarsening, refinement, and partitioning) can be made small relative to the flow solver.