Multithread parallelization of Lepp-bisection algorithms
Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation...
Uloženo v:
| Vydáno v: | Applied numerical mathematics Ročník 62; číslo 4; s. 473 - 488 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.04.2012
|
| Témata: | |
| ISSN: | 0168-9274, 1873-5460 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained. |
|---|---|
| AbstractList | Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained. |
| Author | Rivara, Maria-Cecilia Rodriguez, Pedro Montenegro, Rafael Jorquera, Gaston |
| Author_xml | – sequence: 1 givenname: Maria-Cecilia surname: Rivara fullname: Rivara, Maria-Cecilia email: mcrivara@dcc.uchile.cl organization: Department of Computer Science, University of Chile, Santiago, Chile – sequence: 2 givenname: Pedro surname: Rodriguez fullname: Rodriguez, Pedro email: prodrigu@dcc.uchile.cl organization: Department of Computer Science, University of Chile, Santiago, Chile – sequence: 3 givenname: Rafael surname: Montenegro fullname: Montenegro, Rafael email: rafa@dma.ulpg.es organization: University of Las Palmas de Gran Canaria, University Institute for Intelligent Systems and Numerical Applications for Engineering, Spain – sequence: 4 givenname: Gaston surname: Jorquera fullname: Jorquera, Gaston email: gjorquera@dcc.uchile.cl organization: Department of Computer Science, University of Chile, Santiago, Chile |
| BookMark | eNqFkDtPwzAURi1UJNrCL2DpyJJwnYftDAyo4iUVscBsOc41uHIe2AkS_HrclokBpk-yzrmSz4LMur5DQs4ppBQou9ymauimNs2A0hR4GueIzKngeVIWDGZkHimRVBkvTsgihC0AlGUBcyIeJzfa8c2jalaD8so5dPZLjbbvVr1ZbXAYktoG1PsX5V57H_E2nJJjo1zAs59dkpfbm-f1fbJ5untYX28SnedsTCoGRQMGtKi54bzIKk1rXvGyrJqqLjmnwjQN17lihcm0USXWQgBkSogaucqX5OJwd_D9-4RhlK0NGp1THfZTkJRxWgADlke0OqDa9yF4NFLbcf-T0SvrJAW5qyW3cl9L7mpJ4DJOdPNf7uBtq_znP9bVwcJY4MOil0Fb7DQ21sdisuntn_43ZFmHdA |
| CitedBy_id | crossref_primary_10_1007_s00366_020_01253_y crossref_primary_10_1137_140973840 |
| Cites_doi | 10.1137/0916074 10.1137/080723028 10.1145/1271.1274 10.1002/nme.1620360308 10.1016/0045-7825(91)90017-Z 10.1007/BF01553881 10.1016/j.jpdc.2009.03.005 10.1145/78607.78614 10.1093/comjnl/21.3.243 10.1002/cnm.1630080502 10.1016/j.tcs.2007.03.004 10.1016/S0010-4485(00)00125-1 10.1007/s00366-006-0013-2 10.1016/S0168-874X(96)00039-X 10.1002/(SICI)1097-0207(19970930)40:18<3313::AID-NME214>3.0.CO;2-# 10.1016/j.cad.2008.11.004 10.1090/S0025-5718-1980-0583497-1 10.1016/0956-0521(94)90013-2 10.1006/jagm.1995.1021 10.1016/j.jpdc.2009.03.009 10.1007/BF02274210 10.1016/S0925-7721(01)00047-5 10.2514/3.12386 10.1016/S0925-7721(01)00054-2 10.1002/nme.1620200412 10.1137/0713021 10.1016/j.apnum.2008.12.011 10.1145/1322436.1322442 10.1109/HPDC.1999.805291 10.1016/S0167-8191(97)00056-2 10.1137/S106482759528065X 10.1090/S0025-5718-1975-0375068-5 10.1002/(SICI)1097-0207(19970615)40:11<1957::AID-NME147>3.0.CO;2-6 10.1090/S0025-5718-1983-0689473-5 10.1002/nme.1620281212 10.1090/S0025-5718-1979-0521285-4 |
| ContentType | Journal Article |
| Copyright | 2011 IMACS |
| Copyright_xml | – notice: 2011 IMACS |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.apnum.2011.07.011 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 1873-5460 |
| EndPage | 488 |
| ExternalDocumentID | 10_1016_j_apnum_2011_07_011 S0168927411001292 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HMJ HVGLF HZ~ IHE J1W KOM M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SSW SSZ T5K TN5 VH1 VOH WH7 WUQ XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c336t-9604d0f0c8b7f77429c1b797559d9b57718fdd7c3a64f2cfa5eb88002a88be7a3 |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000301902200016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-9274 |
| IngestDate | Thu Sep 25 08:36:33 EDT 2025 Sat Nov 29 02:29:51 EST 2025 Tue Nov 18 21:19:31 EST 2025 Fri Feb 23 02:32:57 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Finite element method Parallel multithread refinement Lepp-bisection algorithm Triangulation refinement Longest edge bisection |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c336t-9604d0f0c8b7f77429c1b797559d9b57718fdd7c3a64f2cfa5eb88002a88be7a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1671406063 |
| PQPubID | 23500 |
| PageCount | 16 |
| ParticipantIDs | proquest_miscellaneous_1671406063 crossref_citationtrail_10_1016_j_apnum_2011_07_011 crossref_primary_10_1016_j_apnum_2011_07_011 elsevier_sciencedirect_doi_10_1016_j_apnum_2011_07_011 |
| PublicationCentury | 2000 |
| PublicationDate | April 2012 2012-04-00 20120401 |
| PublicationDateYYYYMMDD | 2012-04-01 |
| PublicationDate_xml | – month: 04 year: 2012 text: April 2012 |
| PublicationDecade | 2010 |
| PublicationTitle | Applied numerical mathematics |
| PublicationYear | 2012 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Rivara, Calderón, Federov, Chrisochoides (br0400) 2006; 22 Williams (br0500) 1991 Borouchaki, George (br0080) 1997; 40 Jones, Plassmann (br0210) 1997; 25 Ruppert (br0420) 1995; 18 Jones, Plassmann (br0190) 1994; 5 Boissonnat, Devillers, Pion, Teillaud, Yvinec (br0070) 2002; 22 Nambiar, Valera, Lawrence, Morgan, Amil (br0270) 1993; 36 Manber (br0250) 1991 Rosenberg, Stenger (br0410) 1975; 29 Babuska, Aziz (br0040) 1976; 13 Lawson (br0230) 1977 Weiss (br0490) 2006 Chernikov, Chrisochoides (br0140) 2009; 31 Rauber, Runger (br0280) 2010 George, Hecht, Saltel (br0160) 1991; 92 J.G. Castaños, J.E. Savage, Pared: a framework for the adaptive solution of PDEs, in: 8th IEEE Symposium on High Performance Distributed Computing, 1999. Rivara, Calderon (br0370) 2010; 42 Jones, Plassmann (br0200) 1997; 18 Muthukrishnan, Shiakolas, Nambiar, Lawrence (br0260) 1995; 33 Rivara (br0360) 2009; 59 Shewchuk (br0450) 2002; 22 Shephard, Guerinoni, Flaherty, Ludwig, Baehmann (br0430) 1988 Chernikov, Chrisochoides (br0130) 2008; 34 José G. Cataños, John E. Savage, Parallel refinement of unstructured meshes, in: Proc. IASTED Conference on Parallel and Distributed Computing and Systems (PDCSʼ99), Boston, 1999. Rivara (br0320) 1986 Baker (br0060) 1994 Grama, Gupta, Karypis, Kumar (br0170) 2003 Stynes (br0470) 1979; 33 Cataños, Savage (br0120) 2000 Liu, Joe (br0240) 1995; 16 Rivara (br0310) 1986 Sibson (br0460) 1978; 21 Rivara, Palma (br0380) 1997; vol. 220 Karp, Flatt (br0220) 1990; 33 Rivara (br0330) 1989; 28 Antonopoulos, Blagajevic, Chernikov, Chrisochoides, Nikolopoulos (br0030) 2009; 69 Rivara, Levin (br0350) 1992; 8 Shephard, Flaherty, Bottasso, de Cougny, Ozturan, Simone (br0440) 1997; 23 Chew (br0150) 1989; 4 Rivara, Hitschfeld, Simpson (br0390) 2001; 33 Baker (br0050) 1989; 5 Rivara (br0300) 1984; 20 Adler (br0010) 1983; 40 Gutierrez, Gutierrez, Rivara (br0180) 2007; 382 Rivara (br0290) 1984; 10 Rivara (br0340) 1997; 40 Antonopoulos, Blagajevic, Chernikov, Chrisochoides, Nikolopoulos (br0020) 2009; 69 Breshears (br0090) 2009 Stynes (br0480) 1980; 35 10.1016/j.apnum.2011.07.011_br0110 Grama (10.1016/j.apnum.2011.07.011_br0170) 2003 Gutierrez (10.1016/j.apnum.2011.07.011_br0180) 2007; 382 Antonopoulos (10.1016/j.apnum.2011.07.011_br0030) 2009; 69 Jones (10.1016/j.apnum.2011.07.011_br0210) 1997; 25 Rivara (10.1016/j.apnum.2011.07.011_br0340) 1997; 40 Baker (10.1016/j.apnum.2011.07.011_br0060) 1994 Liu (10.1016/j.apnum.2011.07.011_br0240) 1995; 16 Chernikov (10.1016/j.apnum.2011.07.011_br0140) 2009; 31 Rivara (10.1016/j.apnum.2011.07.011_br0360) 2009; 59 Breshears (10.1016/j.apnum.2011.07.011_br0090) 2009 10.1016/j.apnum.2011.07.011_br0100 Rivara (10.1016/j.apnum.2011.07.011_br0370) 2010; 42 Rivara (10.1016/j.apnum.2011.07.011_br0400) 2006; 22 Rivara (10.1016/j.apnum.2011.07.011_br0330) 1989; 28 Muthukrishnan (10.1016/j.apnum.2011.07.011_br0260) 1995; 33 Baker (10.1016/j.apnum.2011.07.011_br0050) 1989; 5 Shephard (10.1016/j.apnum.2011.07.011_br0440) 1997; 23 Stynes (10.1016/j.apnum.2011.07.011_br0470) 1979; 33 Borouchaki (10.1016/j.apnum.2011.07.011_br0080) 1997; 40 Shephard (10.1016/j.apnum.2011.07.011_br0430) 1988 Chew (10.1016/j.apnum.2011.07.011_br0150) 1989; 4 Boissonnat (10.1016/j.apnum.2011.07.011_br0070) 2002; 22 Jones (10.1016/j.apnum.2011.07.011_br0200) 1997; 18 Rivara (10.1016/j.apnum.2011.07.011_br0290) 1984; 10 Stynes (10.1016/j.apnum.2011.07.011_br0480) 1980; 35 Rivara (10.1016/j.apnum.2011.07.011_br0380) 1997; vol. 220 Rivara (10.1016/j.apnum.2011.07.011_br0300) 1984; 20 Babuska (10.1016/j.apnum.2011.07.011_br0040) 1976; 13 Rauber (10.1016/j.apnum.2011.07.011_br0280) 2010 Rosenberg (10.1016/j.apnum.2011.07.011_br0410) 1975; 29 Karp (10.1016/j.apnum.2011.07.011_br0220) 1990; 33 Lawson (10.1016/j.apnum.2011.07.011_br0230) 1977 Rivara (10.1016/j.apnum.2011.07.011_br0310) 1986 Rivara (10.1016/j.apnum.2011.07.011_br0320) 1986 Sibson (10.1016/j.apnum.2011.07.011_br0460) 1978; 21 Nambiar (10.1016/j.apnum.2011.07.011_br0270) 1993; 36 Antonopoulos (10.1016/j.apnum.2011.07.011_br0020) 2009; 69 Rivara (10.1016/j.apnum.2011.07.011_br0390) 2001; 33 Ruppert (10.1016/j.apnum.2011.07.011_br0420) 1995; 18 Adler (10.1016/j.apnum.2011.07.011_br0010) 1983; 40 Rivara (10.1016/j.apnum.2011.07.011_br0350) 1992; 8 Cataños (10.1016/j.apnum.2011.07.011_br0120) 2000 George (10.1016/j.apnum.2011.07.011_br0160) 1991; 92 Shewchuk (10.1016/j.apnum.2011.07.011_br0450) 2002; 22 Manber (10.1016/j.apnum.2011.07.011_br0250) 1991 Weiss (10.1016/j.apnum.2011.07.011_br0490) 2006 Williams (10.1016/j.apnum.2011.07.011_br0500) 1991 Chernikov (10.1016/j.apnum.2011.07.011_br0130) 2008; 34 Jones (10.1016/j.apnum.2011.07.011_br0190) 1994; 5 |
| References_xml | – volume: 5 start-page: 161 year: 1989 end-page: 175 ident: br0050 article-title: Automatic mesh generation for complex three dimensional regions using a constrained Delaunay triangulation publication-title: Engineering with Computers – volume: 10 start-page: 242 year: 1984 end-page: 264 ident: br0290 article-title: Design and data structure for fully adaptive, multigrid finite-element software publication-title: ACM Transactions on Mathematical Software – volume: 29 start-page: 390 year: 1975 end-page: 395 ident: br0410 article-title: A lower bound on the angles of triangles constructed by bisecting the longest side publication-title: Mathematics of Computation – start-page: 709 year: 1988 end-page: 718 ident: br0430 article-title: Finite octree mesh generation for three-dimensional flow analysis publication-title: Numerical Grid Generation in Computational Fluid Mechanics – volume: 23 start-page: 1327 year: 1997 end-page: 1347 ident: br0440 article-title: Parallel automatic adaptive analysis publication-title: Parallel Computing – volume: 25 start-page: 41 year: 1997 end-page: 60 ident: br0210 article-title: Adaptive refinement of unstructured finite element meshes publication-title: Finite Elements in Analysis and Design – year: 1991 ident: br0250 article-title: Introduction to Algorithms. A Creative Approach – volume: 13 start-page: 214 year: 1976 end-page: 226 ident: br0040 article-title: On the angle condition in the finite element method publication-title: SIAM Journal on Numerical Analysis – volume: 18 start-page: 548 year: 1995 end-page: 585 ident: br0420 article-title: A Delaunay refinement algorithm for quality 2-dimensional mesh generation publication-title: Journal of Algorithms – volume: 20 start-page: 745 year: 1984 end-page: 756 ident: br0300 article-title: Algorithms for refining triangular grids suitable for adaptive and multigrid techniques publication-title: International Journal for Numerical Methods in Engineering – volume: 18 start-page: 686 year: 1997 end-page: 708 ident: br0200 article-title: Parallel algorithms for adaptive mesh refinement publication-title: SIAM Journal on Scientific Computing – volume: 33 start-page: 539 year: 1990 end-page: 543 ident: br0220 article-title: Measuring parallel processor performance publication-title: Communications of the ACM – year: 2006 ident: br0490 article-title: Data Structures and Algorithm Analysis in C++ – volume: 33 start-page: 928 year: 1995 end-page: 932 ident: br0260 article-title: Simple algorithm for adaptative refinement of three-dimensional finite element tetrahedral meshes publication-title: AIAA Journal – volume: 59 start-page: 2218 year: 2009 end-page: 2235 ident: br0360 article-title: Lepp-bisection algorithms, applications and mathematical properties publication-title: Applied Numerical Mathematics – volume: 92 start-page: 269 year: 1991 end-page: 288 ident: br0160 article-title: Automatic mesh generator with specified boundary publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 40 start-page: 571 year: 1983 end-page: 574 ident: br0010 article-title: On the bisection method for triangles publication-title: Mathematics of Computation – volume: 31 start-page: 3387 year: 2009 end-page: 3403 ident: br0140 article-title: Generalized two-dimensional Delaunay mesh refinement publication-title: SIAM Journal on Scientific Computing – volume: 42 start-page: 58 year: 2010 end-page: 66 ident: br0370 article-title: Lepp terminal centroid method for quality triangulation publication-title: Computer-Aided Design – start-page: 201 year: 1991 end-page: 213 ident: br0500 article-title: Adaptive parallel meshes with complex geometry publication-title: Numerical Grid Generation in Computational Fluid Dynamics and Related Fields – volume: 28 start-page: 2889 year: 1989 end-page: 2906 ident: br0330 article-title: Selective refinement/derefinement algorithms for sequences of nested triangulations publication-title: International Journal for Numerical Methods in Engineering – volume: 33 start-page: 263 year: 2001 end-page: 277 ident: br0390 article-title: Terminal edges Delaunay (small angle based) algorithm for the quality triangulation problem publication-title: Computer-Aided Design – volume: 36 start-page: 499 year: 1993 end-page: 509 ident: br0270 article-title: An algorithm for adaptive refinement of triangular finite element meshes publication-title: International Journal for Numerical Methods in Engineering – year: 2009 ident: br0090 article-title: The Art of Concurrency: A Thread Monkeyʼs Guide to Writing Parallel Applications – start-page: 190 year: 1986 end-page: 199 ident: br0310 article-title: A dynamic multigrid algorithm suitable for partial differential equations with singular solutions publication-title: Recent Advances in Systems Modelling and Optimization – volume: 4 start-page: 97 year: 1989 end-page: 108 ident: br0150 article-title: Constrained Delaunay triangulations publication-title: Algorithmica – volume: 40 start-page: 1957 year: 1997 end-page: 1975 ident: br0080 article-title: Aspects of 2-D Delaunay mesh generation publication-title: International Journal for Numerical Methods in Engineering – start-page: 161 year: 1977 end-page: 194 ident: br0230 article-title: Software for publication-title: Mathematical Software III – volume: 8 start-page: 281 year: 1992 end-page: 290 ident: br0350 article-title: A 3D refinement algorithm suitable for adaptive and multigrid techniques publication-title: Communications in Applied Numerical Methods – year: 2003 ident: br0170 article-title: Introduction to Parallel Computing – volume: 22 start-page: 5 year: 2002 end-page: 19 ident: br0070 article-title: Triangulations in CGAL publication-title: Computational Geometry: Theory and Applications – volume: 40 start-page: 3313 year: 1997 end-page: 3324 ident: br0340 article-title: New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations publication-title: International Journal for Numerical Methods in Engineering – reference: José G. Cataños, John E. Savage, Parallel refinement of unstructured meshes, in: Proc. IASTED Conference on Parallel and Distributed Computing and Systems (PDCSʼ99), Boston, 1999. – volume: 382 start-page: 131 year: 2007 end-page: 138 ident: br0180 article-title: Complexity on the bisection method publication-title: Theoretical Computer Science – start-page: 61 year: 1994 end-page: 75 ident: br0060 article-title: Triangulations, mesh generation and point placement strategies publication-title: Computing the Future – start-page: 823 year: 2000 end-page: 832 ident: br0120 article-title: Repartitioning unstructured adaptive meshes publication-title: IPDPS – volume: 22 start-page: 536 year: 2006 end-page: 544 ident: br0400 article-title: Parallel decoupled terminal-edge bisection method for 3D mesh generation publication-title: Engineering with Computers – volume: 34 start-page: 1 year: 2008 end-page: 20 ident: br0130 article-title: Algorithm 872: Parallel 2d constrained Delaunay mesh generation publication-title: ACM Transactions on Mathematical Software – volume: 69 year: 2009 ident: br0020 article-title: Algorithm software, and hardware optimizations for Delaunay mesh generation on simultaneous multithreaded architectures publication-title: Journal on Parallel and Distributed Computing – start-page: 359 year: 1986 end-page: 370 ident: br0320 article-title: Adaptive finite element refinement and fully irregular and conforming triangulations publication-title: Accuracy Estimates and Adaptive Refinements in Finite Element Computations – volume: 22 start-page: 21 year: 2002 end-page: 74 ident: br0450 article-title: Delaunay refinement algorithms for triangular mesh generation publication-title: Computational Geometry: Theory and Applications – year: 2010 ident: br0280 article-title: Parallel Programming for Multicore and Cluester Systems – volume: 16 start-page: 1269 year: 1995 end-page: 1291 ident: br0240 article-title: Quality local refinement of tetrahedral meshes based on bisection publication-title: SIAM Journal on Scientific Computing – volume: 21 start-page: 243 year: 1978 end-page: 245 ident: br0460 article-title: Locally equiangular triangulations publication-title: Computer Journal – volume: 35 start-page: 1195 year: 1980 end-page: 1202 ident: br0480 article-title: On faster convergence of the bisection method for all triangles publication-title: Mathematics of Computation – reference: J.G. Castaños, J.E. Savage, Pared: a framework for the adaptive solution of PDEs, in: 8th IEEE Symposium on High Performance Distributed Computing, 1999. – volume: 5 start-page: 297 year: 1994 end-page: 309 ident: br0190 article-title: Computational results for parallel unstructured mesh computations publication-title: Computing Systems Engineering – volume: 69 year: 2009 ident: br0030 article-title: A multigrain Delaunay mesh generation method for multicore SMT-based architectures publication-title: Journal of Parallel and Distributed Computing – volume: 33 start-page: 1195 year: 1979 end-page: 1202 ident: br0470 article-title: On faster convergence of the bisection method for certain triangles publication-title: Mathematics of Computation – volume: vol. 220 start-page: 1 year: 1997 end-page: 8 ident: br0380 article-title: New LEPP algorithms for quality polygon and volume triangulation: Implementation issues and practical behavior publication-title: Trends in Unstructured Mesh Generation – volume: 16 start-page: 1269 year: 1995 ident: 10.1016/j.apnum.2011.07.011_br0240 article-title: Quality local refinement of tetrahedral meshes based on bisection publication-title: SIAM Journal on Scientific Computing doi: 10.1137/0916074 – volume: 31 start-page: 3387 year: 2009 ident: 10.1016/j.apnum.2011.07.011_br0140 article-title: Generalized two-dimensional Delaunay mesh refinement publication-title: SIAM Journal on Scientific Computing doi: 10.1137/080723028 – volume: 10 start-page: 242 year: 1984 ident: 10.1016/j.apnum.2011.07.011_br0290 article-title: Design and data structure for fully adaptive, multigrid finite-element software publication-title: ACM Transactions on Mathematical Software doi: 10.1145/1271.1274 – volume: 36 start-page: 499 year: 1993 ident: 10.1016/j.apnum.2011.07.011_br0270 article-title: An algorithm for adaptive refinement of triangular finite element meshes publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620360308 – start-page: 61 year: 1994 ident: 10.1016/j.apnum.2011.07.011_br0060 article-title: Triangulations, mesh generation and point placement strategies – volume: 92 start-page: 269 year: 1991 ident: 10.1016/j.apnum.2011.07.011_br0160 article-title: Automatic mesh generator with specified boundary publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/0045-7825(91)90017-Z – volume: 4 start-page: 97 year: 1989 ident: 10.1016/j.apnum.2011.07.011_br0150 article-title: Constrained Delaunay triangulations publication-title: Algorithmica doi: 10.1007/BF01553881 – start-page: 823 year: 2000 ident: 10.1016/j.apnum.2011.07.011_br0120 article-title: Repartitioning unstructured adaptive meshes – volume: 69 year: 2009 ident: 10.1016/j.apnum.2011.07.011_br0020 article-title: Algorithm software, and hardware optimizations for Delaunay mesh generation on simultaneous multithreaded architectures publication-title: Journal on Parallel and Distributed Computing doi: 10.1016/j.jpdc.2009.03.005 – volume: 33 start-page: 539 year: 1990 ident: 10.1016/j.apnum.2011.07.011_br0220 article-title: Measuring parallel processor performance publication-title: Communications of the ACM doi: 10.1145/78607.78614 – volume: 21 start-page: 243 issue: 1978 year: 1978 ident: 10.1016/j.apnum.2011.07.011_br0460 article-title: Locally equiangular triangulations publication-title: Computer Journal doi: 10.1093/comjnl/21.3.243 – volume: 8 start-page: 281 year: 1992 ident: 10.1016/j.apnum.2011.07.011_br0350 article-title: A 3D refinement algorithm suitable for adaptive and multigrid techniques publication-title: Communications in Applied Numerical Methods doi: 10.1002/cnm.1630080502 – year: 2006 ident: 10.1016/j.apnum.2011.07.011_br0490 – volume: 382 start-page: 131 year: 2007 ident: 10.1016/j.apnum.2011.07.011_br0180 article-title: Complexity on the bisection method publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2007.03.004 – volume: 33 start-page: 263 year: 2001 ident: 10.1016/j.apnum.2011.07.011_br0390 article-title: Terminal edges Delaunay (small angle based) algorithm for the quality triangulation problem publication-title: Computer-Aided Design doi: 10.1016/S0010-4485(00)00125-1 – volume: 22 start-page: 536 year: 2006 ident: 10.1016/j.apnum.2011.07.011_br0400 article-title: Parallel decoupled terminal-edge bisection method for 3D mesh generation publication-title: Engineering with Computers doi: 10.1007/s00366-006-0013-2 – start-page: 190 year: 1986 ident: 10.1016/j.apnum.2011.07.011_br0310 article-title: A dynamic multigrid algorithm suitable for partial differential equations with singular solutions – volume: vol. 220 start-page: 1 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0380 article-title: New LEPP algorithms for quality polygon and volume triangulation: Implementation issues and practical behavior – start-page: 161 year: 1977 ident: 10.1016/j.apnum.2011.07.011_br0230 article-title: Software for C1 surface interpolation – volume: 25 start-page: 41 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0210 article-title: Adaptive refinement of unstructured finite element meshes publication-title: Finite Elements in Analysis and Design doi: 10.1016/S0168-874X(96)00039-X – volume: 40 start-page: 3313 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0340 article-title: New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/(SICI)1097-0207(19970930)40:18<3313::AID-NME214>3.0.CO;2-# – volume: 42 start-page: 58 year: 2010 ident: 10.1016/j.apnum.2011.07.011_br0370 article-title: Lepp terminal centroid method for quality triangulation publication-title: Computer-Aided Design doi: 10.1016/j.cad.2008.11.004 – year: 2009 ident: 10.1016/j.apnum.2011.07.011_br0090 – volume: 35 start-page: 1195 year: 1980 ident: 10.1016/j.apnum.2011.07.011_br0480 article-title: On faster convergence of the bisection method for all triangles publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1980-0583497-1 – volume: 5 start-page: 297 year: 1994 ident: 10.1016/j.apnum.2011.07.011_br0190 article-title: Computational results for parallel unstructured mesh computations publication-title: Computing Systems Engineering doi: 10.1016/0956-0521(94)90013-2 – volume: 18 start-page: 548 year: 1995 ident: 10.1016/j.apnum.2011.07.011_br0420 article-title: A Delaunay refinement algorithm for quality 2-dimensional mesh generation publication-title: Journal of Algorithms doi: 10.1006/jagm.1995.1021 – volume: 69 issue: 7 year: 2009 ident: 10.1016/j.apnum.2011.07.011_br0030 article-title: A multigrain Delaunay mesh generation method for multicore SMT-based architectures publication-title: Journal of Parallel and Distributed Computing doi: 10.1016/j.jpdc.2009.03.009 – volume: 5 start-page: 161 year: 1989 ident: 10.1016/j.apnum.2011.07.011_br0050 article-title: Automatic mesh generation for complex three dimensional regions using a constrained Delaunay triangulation publication-title: Engineering with Computers doi: 10.1007/BF02274210 – volume: 22 start-page: 21 year: 2002 ident: 10.1016/j.apnum.2011.07.011_br0450 article-title: Delaunay refinement algorithms for triangular mesh generation publication-title: Computational Geometry: Theory and Applications doi: 10.1016/S0925-7721(01)00047-5 – volume: 33 start-page: 928 year: 1995 ident: 10.1016/j.apnum.2011.07.011_br0260 article-title: Simple algorithm for adaptative refinement of three-dimensional finite element tetrahedral meshes publication-title: AIAA Journal doi: 10.2514/3.12386 – year: 2003 ident: 10.1016/j.apnum.2011.07.011_br0170 – volume: 22 start-page: 5 year: 2002 ident: 10.1016/j.apnum.2011.07.011_br0070 article-title: Triangulations in CGAL publication-title: Computational Geometry: Theory and Applications doi: 10.1016/S0925-7721(01)00054-2 – start-page: 201 year: 1991 ident: 10.1016/j.apnum.2011.07.011_br0500 article-title: Adaptive parallel meshes with complex geometry – volume: 20 start-page: 745 year: 1984 ident: 10.1016/j.apnum.2011.07.011_br0300 article-title: Algorithms for refining triangular grids suitable for adaptive and multigrid techniques publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620200412 – volume: 13 start-page: 214 year: 1976 ident: 10.1016/j.apnum.2011.07.011_br0040 article-title: On the angle condition in the finite element method publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/0713021 – volume: 59 start-page: 2218 year: 2009 ident: 10.1016/j.apnum.2011.07.011_br0360 article-title: Lepp-bisection algorithms, applications and mathematical properties publication-title: Applied Numerical Mathematics doi: 10.1016/j.apnum.2008.12.011 – volume: 34 start-page: 1 issue: 1 year: 2008 ident: 10.1016/j.apnum.2011.07.011_br0130 article-title: Algorithm 872: Parallel 2d constrained Delaunay mesh generation publication-title: ACM Transactions on Mathematical Software doi: 10.1145/1322436.1322442 – ident: 10.1016/j.apnum.2011.07.011_br0100 doi: 10.1109/HPDC.1999.805291 – year: 2010 ident: 10.1016/j.apnum.2011.07.011_br0280 – volume: 23 start-page: 1327 issue: 9 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0440 article-title: Parallel automatic adaptive analysis publication-title: Parallel Computing doi: 10.1016/S0167-8191(97)00056-2 – volume: 18 start-page: 686 issue: 3 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0200 article-title: Parallel algorithms for adaptive mesh refinement publication-title: SIAM Journal on Scientific Computing doi: 10.1137/S106482759528065X – start-page: 709 year: 1988 ident: 10.1016/j.apnum.2011.07.011_br0430 article-title: Finite octree mesh generation for three-dimensional flow analysis – volume: 29 start-page: 390 year: 1975 ident: 10.1016/j.apnum.2011.07.011_br0410 article-title: A lower bound on the angles of triangles constructed by bisecting the longest side publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1975-0375068-5 – volume: 40 start-page: 1957 year: 1997 ident: 10.1016/j.apnum.2011.07.011_br0080 article-title: Aspects of 2-D Delaunay mesh generation publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/(SICI)1097-0207(19970615)40:11<1957::AID-NME147>3.0.CO;2-6 – year: 1991 ident: 10.1016/j.apnum.2011.07.011_br0250 – volume: 40 start-page: 571 year: 1983 ident: 10.1016/j.apnum.2011.07.011_br0010 article-title: On the bisection method for triangles publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1983-0689473-5 – volume: 28 start-page: 2889 year: 1989 ident: 10.1016/j.apnum.2011.07.011_br0330 article-title: Selective refinement/derefinement algorithms for sequences of nested triangulations publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620281212 – volume: 33 start-page: 1195 year: 1979 ident: 10.1016/j.apnum.2011.07.011_br0470 article-title: On faster convergence of the bisection method for certain triangles publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1979-0521285-4 – ident: 10.1016/j.apnum.2011.07.011_br0110 – start-page: 359 year: 1986 ident: 10.1016/j.apnum.2011.07.011_br0320 article-title: Adaptive finite element refinement and fully irregular and conforming triangulations |
| SSID | ssj0005540 |
| Score | 1.9588393 |
| Snippet | Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 473 |
| SubjectTerms | Algorithms Charge Finite element method Lepp-bisection algorithm Longest edge bisection Mathematical analysis Parallel multithread refinement Refining Synchronism Terminals Triangles Triangulation Triangulation refinement |
| Title | Multithread parallelization of Lepp-bisection algorithms |
| URI | https://dx.doi.org/10.1016/j.apnum.2011.07.011 https://www.proquest.com/docview/1671406063 |
| Volume | 62 |
| WOSCitedRecordID | wos000301902200016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5460 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005540 issn: 0168-9274 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ba9swFBZZuoe97D7adRsejL10Lq4dW9JjKekuhGyUFPImji25uHi251zoz--RJTlpy0r3sBcnOLKS6Duci3TOdwj5hDYT8KPQDyFKfbTQgQ8Is6-po1gEQSpVVyg8odMpm8_5r8GgcbUw65JWFbu64s1_hRrvIdi6dPYf4O4nxRv4HkHHK8KO1wcBb0pqESKQB5rYuyxVaYstuwMB1TQYDi-U7RFeXtQtDrek5Y6P1vqm1coc6JQHv3t6101yfLGGrkuRLvgpwD9RWVEWvZo_qyVG_iu7Q61kW_fgakasSl2YEpszyF3efpfJ06KlMtN-Be2Zbu9L6ASPPp3FblUmqEpD04PH6dok3JKp0ZbiHJmGJtYGj0yrvzvq3ew0XB5Cg__f8q_Sw8Cq6xtk2tOf4vR8MhGz8Xz2ufnj6z5j-jzeNl15RHZCGnM2JDvH38fzH5u0oLgrou1_vWOq6nIC73zv37yZW3a9c1Zmz8lTG2V4x0Y6XpCBql6SZxZVz-rzxSvCtoTFuyUsXp17N4XF2wjLa3J-Op6dfPNtLw0_i6Jk6WsOHhnkQcZSmqPLH_LsKKWcYkApeRpTdFFyKWkWQTLKwyyHWKVMBxPAWKooRG_IsKortUs8qTJARxHnVRi7gwTOKQcFuZJBSJN4j4RuTURmieZ1v5NSuIzCS9EtpNALKQIq8GWPfOkfagzPyv3DE7fYwrqKxgUUKCr3P_jRQSNQkerTMahUvVqIo0RzV2I8H719wJh98mQj9O_IcNmu1HvyOFsvi0X7wQrVNST4mY8 |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Multithread+parallelization+of+Lepp-bisection+algorithms&rft.jtitle=Applied+numerical+mathematics&rft.au=Rivara%2C+Maria-Cecilia&rft.au=Rodriguez%2C+Pedro&rft.au=Montenegro%2C+Rafael&rft.au=Jorquera%2C+Gaston&rft.date=2012-04-01&rft.issn=0168-9274&rft.volume=62&rft.issue=4&rft.spage=473&rft.epage=488&rft_id=info:doi/10.1016%2Fj.apnum.2011.07.011&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-9274&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-9274&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-9274&client=summon |