Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model
We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are impl...
Ausführliche Beschreibung
Autor*in: |
Artemov, Anton G. [verfasserIn] Rudberg, Elias [verfasserIn] Rubensson, Emanuel H. [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2019 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Parallel computing - Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984, 89 |
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Übergeordnetes Werk: |
volume:89 |
DOI / URN: |
10.1016/j.parco.2019.102548 |
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Katalog-ID: |
ELV003083098 |
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100 | 1 | |a Artemov, Anton G. |e verfasserin |0 (orcid)0000-0002-6333-6869 |4 aut | |
245 | 1 | 0 | |a Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
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520 | |a We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. | ||
650 | 4 | |a Parallel computing | |
650 | 4 | |a Sparse matrix algorithms | |
650 | 4 | |a Scalable algorithms | |
650 | 4 | |a Large-scale computing | |
650 | 4 | |a Algorithm analysis | |
700 | 1 | |a Rudberg, Elias |e verfasserin |4 aut | |
700 | 1 | |a Rubensson, Emanuel H. |e verfasserin |4 aut | |
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2019 |
allfields |
10.1016/j.parco.2019.102548 doi (DE-627)ELV003083098 (ELSEVIER)S0167-8191(19)30139-5 DE-627 ger DE-627 rda eng 004 620 DE-600 54.25 bkl Artemov, Anton G. verfasserin (orcid)0000-0002-6333-6869 aut Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. Parallel computing Sparse matrix algorithms Scalable algorithms Large-scale computing Algorithm analysis Rudberg, Elias verfasserin aut Rubensson, Emanuel H. verfasserin aut Enthalten in Parallel computing Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984 89 Online-Ressource (DE-627)265784115 (DE-600)1466340-5 (DE-576)074890999 1872-7336 nnns volume:89 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.25 Parallele Datenverarbeitung AR 89 |
spelling |
10.1016/j.parco.2019.102548 doi (DE-627)ELV003083098 (ELSEVIER)S0167-8191(19)30139-5 DE-627 ger DE-627 rda eng 004 620 DE-600 54.25 bkl Artemov, Anton G. verfasserin (orcid)0000-0002-6333-6869 aut Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. Parallel computing Sparse matrix algorithms Scalable algorithms Large-scale computing Algorithm analysis Rudberg, Elias verfasserin aut Rubensson, Emanuel H. verfasserin aut Enthalten in Parallel computing Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984 89 Online-Ressource (DE-627)265784115 (DE-600)1466340-5 (DE-576)074890999 1872-7336 nnns volume:89 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.25 Parallele Datenverarbeitung AR 89 |
allfields_unstemmed |
10.1016/j.parco.2019.102548 doi (DE-627)ELV003083098 (ELSEVIER)S0167-8191(19)30139-5 DE-627 ger DE-627 rda eng 004 620 DE-600 54.25 bkl Artemov, Anton G. verfasserin (orcid)0000-0002-6333-6869 aut Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. Parallel computing Sparse matrix algorithms Scalable algorithms Large-scale computing Algorithm analysis Rudberg, Elias verfasserin aut Rubensson, Emanuel H. verfasserin aut Enthalten in Parallel computing Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984 89 Online-Ressource (DE-627)265784115 (DE-600)1466340-5 (DE-576)074890999 1872-7336 nnns volume:89 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.25 Parallele Datenverarbeitung AR 89 |
allfieldsGer |
10.1016/j.parco.2019.102548 doi (DE-627)ELV003083098 (ELSEVIER)S0167-8191(19)30139-5 DE-627 ger DE-627 rda eng 004 620 DE-600 54.25 bkl Artemov, Anton G. verfasserin (orcid)0000-0002-6333-6869 aut Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. Parallel computing Sparse matrix algorithms Scalable algorithms Large-scale computing Algorithm analysis Rudberg, Elias verfasserin aut Rubensson, Emanuel H. verfasserin aut Enthalten in Parallel computing Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984 89 Online-Ressource (DE-627)265784115 (DE-600)1466340-5 (DE-576)074890999 1872-7336 nnns volume:89 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.25 Parallele Datenverarbeitung AR 89 |
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10.1016/j.parco.2019.102548 doi (DE-627)ELV003083098 (ELSEVIER)S0167-8191(19)30139-5 DE-627 ger DE-627 rda eng 004 620 DE-600 54.25 bkl Artemov, Anton G. verfasserin (orcid)0000-0002-6333-6869 aut Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. Parallel computing Sparse matrix algorithms Scalable algorithms Large-scale computing Algorithm analysis Rudberg, Elias verfasserin aut Rubensson, Emanuel H. verfasserin aut Enthalten in Parallel computing Amsterdam [u.a.] : North-Holland, Elsevier Science, 1984 89 Online-Ressource (DE-627)265784115 (DE-600)1466340-5 (DE-576)074890999 1872-7336 nnns volume:89 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.25 Parallele Datenverarbeitung AR 89 |
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Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
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Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
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parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
title_auth |
Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
abstract |
We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. |
abstractGer |
We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. |
abstract_unstemmed |
We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. |
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Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model |
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