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'''Parallel mesh generation''' in [[numerical analysis]] is a new research area between the boundaries of two [[scientific computing]] disciplines: [[computational geometry]] and [[parallel computing]]<ref name="Chrisochoides">Nikos Chrisochoides, Parallel Mesh Generation, Chapter in ''Numerical Solution of Partial Differential Equations on Parallel Computers'', (Eds. Are Magnus Bruaset, Aslak Tveito), Springer-Verlag, pp 237-259, 2005.</ref>. Parallel mesh generation methods decompose the original [[mesh generation]] problem into smaller subproblems which are solved (meshed) in parallel using multiple processors or threads. The existing parallel mesh generation methods can be classified in terms of two basic attributes:
#the sequential technique used for meshing the individual subproblems and
▲'''Parallel mesh generation''' in [[numerical analysis]] is a new research area between the boundaries of two [[scientific computing]] disciplines: [[computational geometry]] and [[parallel computing]]<ref name="Chrisochoides">Nikos Chrisochoides, Parallel Mesh Generation, Chapter in Numerical Solution of Partial Differential Equations on Parallel Computers, (Eds. Are Magnus Bruaset, Aslak Tveito), Springer-Verlag, pp 237-259, 2005.</ref>. Parallel mesh generation methods decompose the original [[mesh generation]] problem into smaller subproblems which are solved (meshed) in parallel using multiple processors or threads. The existing parallel mesh generation methods can be classified in terms of two basic attributes: (1) the sequential technique used for meshing the individual subproblems and (2) the degree of coupling between the subproblems. One of the challenges in parallel mesh generation is to develop parallel meshing software using off-the-shelf sequential meshing codes.
#the degree of coupling between the subproblems. One of the challenges in parallel mesh generation is to develop parallel meshing software using off-the-shelf sequential meshing codes.
==Overview==
Parallel mesh generation procedures in general decompose the original 2-dimensional (2D) or 3-dimensional (3D) mesh generation problem into N smaller subproblems which are solved (i.e., meshed) concurrently using P processors or threads<ref name="Chrisochoides"/>. The subproblems can be formulated to be either tightly coupled<ref>Nikos Chrisochoides and Demian Nave. Parallel [[Delaunay]] mesh generation kernel. Int. J. Numer. Meth. Engng., 58:161--176, 2003</ref><ref>Lohner, J.Camberos, and M.Marshal. Parallel Unstructured Grid
Generation. Chapter in ''Unstructured Scientific Computation on Scalable Multiprocessors''. (Eds. Piyush Mehrotra and Joel Saltz), pp 31--64, MIT Press, 1990.</ref>, partially coupled<ref>H. de Cougny and M.Shephard. Parallel volume meshing using face removals and hierarchical repartitioning. Comp. Meth. Appl. Mech. Engng.,
174(3-4):275--298, 1999.</ref><ref>Andrey Chernikov and Nikos Chrisochoides. Parallel Guaranteed Quality Planar Delaunay Mesh Refinement Concurrent Point Insertion. ''SIAM Journal for Scientific Computing'', Vol. 28, No. 5, pp 1907-1926, 2006.</ref> or even decoupled<ref>J. Galtier and P. L. George. Prepartitioning as a way to mesh subdomains in parallel. Special Symposium on Trends in Unstructured Mesh Generation, pp 107--122. ASME/ASCE/SES, 1997.</ref><ref>Leonidas Linardakis and Nikos Chrisochoides. Delaunay Decoupling Method for Parallel Guaranteed Quality Planar Mesh Generation. ''SIAM Journal for Scientific Computing'', Vol. 27, No. 4, pp 1394-1423, 2006.</ref>. The coupling of the subproblems determines the intensity of the communication and the amount/type of synchronization required between the subproblems.
The challenges in parallel mesh generation methods are: to maintain stability of the parallel mesher (i.e., retain the quality of finite elements generated by state-of-the-art sequential codes) and at the same time achieve 100% code re-use (i.e., leverage the continuously evolving and fully functional off-the-shelf sequential meshers) without substantial deterioration of the scalability of the parallel mesher.
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While many solvers have been ported to parallel machines, grid generators have left behind. Still the preprocessing step of mesh generation remains a sequential bottleneck in the simulation cycle. That is why the need for developing of stable 3D parallel grid generator is well-justified. Work in this direction is carried out by several institutions. <ref>[http://www.itwm.fhg.de Fraunhofer Institute for Industrial Mathematics
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Another parallel mesh generator is '''D3D''', <ref>
== Challenges in parallel mesh generation ==
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ended and permanent which makes the task of delivering state-of-the-art parallel mesh generation codes even more difficult.
An area with immediate high benefits to parallel mesh generation is ___domain decomposition. The DD problem as it is posed in <ref>Chrisochoides N., ''A Survey of Parallel Mesh Generation Methods'', Brown University, Providence RI - 2005.</ref>is still open for 3D geometries and its solution will help to deliver stable and scalable methods that rely on off-the-shelf mesh generation codes for Delaunay and Advancing Front Techniques.
Finally, a long term investment to parallel mesh generation is to attract the attention of mathematicians with open problems in mesh generation and broader impact in mathematics.
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