Parallel Algorithm Oriented Mesh Database

Abstract.In this paper, we present a new point of view for efficiently managing general parallel mesh representations. Taking as a slarting point the Algorithm Oriented Mesh Database (AOMD) of [1] we extend the concepts to a parallel mesh representation. The important aspects of parallel adaptivity and dynamic load balancing are discussed. We finally show how AOMD can be effectively interfaced with mesh adaptive partial differential equation solvers. Results of the calculation of an elasticity problem and of a transient fluid dynamics problem involving thousands of mesh refinements, and load balancings are finally presented.

[1]  M. F. Webster,et al.  The use of dynamic data structures in finite element applications , 1992 .

[2]  Y. Kallinderis,et al.  Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes , 1993 .

[3]  David H. Sharp,et al.  The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces , 1987 .

[4]  Mark S. Shephard,et al.  An Object-Oriented Framework for Reliable Numerical Simulations , 1999, Engineering with Computers.

[5]  B. Hendrickson,et al.  Zoltan: A Dynamic Load-Balancing Library for Parallel Applications , 2000 .

[6]  Mark S. Shephard,et al.  Parallel refinement and coarsening of tetrahedral meshes , 1999 .

[7]  J. Peraire,et al.  TVD ALGORITHMS FOR THE SOLUTION OF THE COMPRESSIBLE EULER EQUATIONS ON UNSTRUCTURED MESHES , 1994 .

[8]  Jean-François Remacle,et al.  An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems , 2003, SIAM Rev..

[9]  Y. Kallinderis,et al.  Parallel dynamic load-balancing algorithm for three-dimensional adaptive unstructured grids , 1994 .

[10]  Robert M. O'Bara,et al.  p-Version Mesh Generation Issues , 2002, IMR.

[11]  Joseph E. Flaherty,et al.  A hierarchical partition model for adaptive finite element computation , 2000 .

[12]  Dimitri J. Mavriplis,et al.  Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes , 1997 .

[13]  Jean-François Remacle,et al.  Transient Mesh Adaptation Using Conforming and Non Conforming Mesh Modifications , 2002, IMR.

[14]  Charbel Farhat,et al.  Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics , 1993 .

[15]  Masahito Hasegawa Under Consideration for Publication in J. Functional Programming Girard Translation and Logical Predicates , 2000 .

[16]  Graham F. Carey,et al.  A class of data structures for 2‐D and 3‐D adaptive mesh refinement , 1988 .

[17]  Leonid Oliker,et al.  Efficient load balancing and data remapping for adaptive grid calculations , 1997, SPAA '97.

[18]  Mark S. Shephard,et al.  a General Topology-Based Mesh Data Structure , 1997 .

[19]  Yannis Kallinderis,et al.  Octree partitioning of hybrid grids for parallel adaptive viscous flow simulations , 1998 .

[20]  Jean-François Remacle,et al.  An algorithm oriented mesh database , 2003, IMR.

[21]  R. LeVeque Numerical methods for conservation laws , 1990 .

[22]  Philippe A. Tanguy,et al.  Efficient data structures for adaptive remeshing with the FEM , 1990 .

[23]  Rainald Löhner,et al.  Some useful data structures for the generation of unstructured grids , 1988 .