Andrey N. Chernikov

Learn More
Given the importance of parallel mesh generation in large-scale scientific applications and the proliferation of multilevel SMT-based architectures, it is imperative to obtain insight on the interaction between meshing algorithms and these systems. We focus on Parallel Constrained Delaunay Mesh (PCDM) generation. We exploit coarse-grain parallelism at the(More)
We present a theoretical framework for developing parallel guaranteed quality De-launay mesh generation software, that allows us to use commercial off-the-shelf sequential Delaunay meshers for two-dimensional geometries. In this paper, we describe our approach for constructing uniform meshes, in other words, the meshes in which all elements have(More)
A number of approaches have been suggested for the selection of the positions of Steiner points in Delaunay mesh refinement. In particular, one can define an entire region (called picking region or selection disk) inside the circumscribed sphere of a poor quality element such that any point can be chosen for insertion from this region. The two main results(More)
—In this paper, we present a Delaunay refinement algorithm for meshing 3D medical images. We prove that (a) all the tetrahedra of the output mesh have radius-edge ratio less than 2, (b) all the boundary facets have planar angles larger than 30 degrees, (c) the symmetric (2-sided) Hausdorff distance between the object surface and mesh boundary is bounded(More)
—This paper describes the design of a flexible load balancing framework and runtime software system for supporting the development of adaptive applications on distributed-memory parallel computers. The runtime system supports a global namespace, transparent object migration, automatic message forwarding and routing, and automatic load balancing. These(More)
We describe a parallel scheduler, for guaranteed quality parallel mesh generation and refinement methods. We prove a sufficient condition for the new points to be independent, which permits the concurrent insertion of more than two points without destroying the conformity and Delaunay properties of the mesh. The scheduling technique we present is much more(More)
Mesh generation is a critical step in high fidelity computational simulations. High quality and high density meshes are required to accurately capture the complex physical phenomena. A parallel framework has been developed to generate large-scale meshes in a short period of time. A coarse volume mesh is generated first to provide the basis of block(More)
We develop the first ever fully functional three-dimensional guaranteed quality parallel graded Delaunay mesh generator. First, we prove a criterion and a sufficient condition of Delaunay-independence of Steiner points in three dimensions. Based on these results, we decompose the iteration space of the sequential Delaunay refinement algorithm by selecting(More)
We present a novel algorithm for tetrahedral image-to-mesh conversion which allows for guaranteed bounds on the smallest dihedral angle and on the distance between the boundaries of the mesh and the boundaries of the tissues. The algorithm produces a small number of mesh elements that comply with these bounds. We also describe and evaluate our(More)