Parallel Fortran-MPI software for numerical inversion of the Laplace transform and its application to oscillatory water levels in groundwater environments
A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwate...
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| Published in | Environmental modelling & software : with environment data news Vol. 20; no. 3; pp. 279 - 284 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.03.2005
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1364-8152 1873-6726 |
| DOI | 10.1016/j.envsoft.2004.05.006 |
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| Abstract | A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery)
Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. |
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| AbstractList | A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery) Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery) Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. |
| Author | Zhan, Xiaoyong |
| Author_xml | – sequence: 1 givenname: Xiaoyong surname: Zhan fullname: Zhan, Xiaoyong email: xyz@ku.edu organization: Kansas Geological Survey, The University of Kansas, 1930 Constant Avenue, Lawrence, KS 66047, USA |
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| Cites_doi | 10.1145/361953.361969 10.1145/326147.326148 10.1029/WR025i010p02129 10.1145/326147.326149 10.1029/WR021i009p01397 10.1137/0903022 10.1145/321921.321931 |
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| Keywords | Groundwater environment Numerical inversion of the Laplace transform Message Passing Interface (MPI) Oscillatory water levels Fortran |
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| References | Shapiro (BIB8) 1989; 25 Miller (BIB6) 2003 Kipp (BIB5) 1985; 21 Valkó, Vojta (BIB7) 2003 D'Amore, Laccetti, Murli (BIB2) 1999; 25 Stehfest (BIB9) 1970; 13 de Hoog, Knight, Stokes (BIB4) 1982; 3 Crump (BIB1) 1976; 23 D'Amore, Laccetti, Murli (BIB3) 1999; 25 de Hoog (10.1016/j.envsoft.2004.05.006_BIB4) 1982; 3 D'Amore (10.1016/j.envsoft.2004.05.006_BIB2) 1999; 25 Miller (10.1016/j.envsoft.2004.05.006_BIB6) Crump (10.1016/j.envsoft.2004.05.006_BIB1) 1976; 23 Valkó (10.1016/j.envsoft.2004.05.006_BIB7) Shapiro (10.1016/j.envsoft.2004.05.006_BIB8) 1989; 25 Stehfest (10.1016/j.envsoft.2004.05.006_BIB9) 1970; 13 Kipp (10.1016/j.envsoft.2004.05.006_BIB5) 1985; 21 D'Amore (10.1016/j.envsoft.2004.05.006_BIB3) 1999; 25 |
| References_xml | – year: 2003 ident: BIB6 article-title: Miscellaneous TOMS (& CACM) algorithms – volume: 21 start-page: 1397 year: 1985 end-page: 1408 ident: BIB5 article-title: Type curve analysis of inertial effects in the response of a well to a slug test publication-title: Water Resour. Res – volume: 23 start-page: 89 year: 1976 end-page: 96 ident: BIB1 article-title: Numerical inversion of Laplace transform using a Fourier series approximation publication-title: J. ACM – volume: 25 start-page: 306 year: 1999 end-page: 315 ident: BIB3 article-title: Algorithm 796: a Fortran software package for the numerical inversion of the Laplace transform based on Fourier series method publication-title: ACM Trans. Math. Softw – volume: 13 start-page: 47 year: 1970 end-page: 49 ident: BIB9 article-title: Numerical inversions of Laplace transforms publication-title: Commun. ACM – year: 2003 ident: BIB7 article-title: Numerical inversion of Laplace transform: a challenge for developers of numerical methods – volume: 25 start-page: 2129 year: 1989 end-page: 2137 ident: BIB8 article-title: Interpretation of oscillatory water levels in observation wells during aquifer tests in fractured rock publication-title: Water Resour. Res – volume: 25 start-page: 279 year: 1999 end-page: 305 ident: BIB2 article-title: An implementation of a Fourier series method for the numerical inversion of the Laplace transform publication-title: ACM Trans. Math. Softw – volume: 3 start-page: 357 year: 1982 end-page: 366 ident: BIB4 article-title: An improved method for numerical inversion of Laplace transforms publication-title: SIAM J. Sci. Stat. Comput – volume: 13 start-page: 47 issue: 1 year: 1970 ident: 10.1016/j.envsoft.2004.05.006_BIB9 article-title: Numerical inversions of Laplace transforms publication-title: Commun. ACM doi: 10.1145/361953.361969 – volume: 25 start-page: 279 issue: 30 year: 1999 ident: 10.1016/j.envsoft.2004.05.006_BIB2 article-title: An implementation of a Fourier series method for the numerical inversion of the Laplace transform publication-title: ACM Trans. Math. Softw doi: 10.1145/326147.326148 – volume: 25 start-page: 2129 issue: 10 year: 1989 ident: 10.1016/j.envsoft.2004.05.006_BIB8 article-title: Interpretation of oscillatory water levels in observation wells during aquifer tests in fractured rock publication-title: Water Resour. Res doi: 10.1029/WR025i010p02129 – volume: 25 start-page: 306 issue: 30 year: 1999 ident: 10.1016/j.envsoft.2004.05.006_BIB3 article-title: Algorithm 796: a Fortran software package for the numerical inversion of the Laplace transform based on Fourier series method publication-title: ACM Trans. Math. Softw doi: 10.1145/326147.326149 – ident: 10.1016/j.envsoft.2004.05.006_BIB7 – ident: 10.1016/j.envsoft.2004.05.006_BIB6 – volume: 21 start-page: 1397 issue: 9 year: 1985 ident: 10.1016/j.envsoft.2004.05.006_BIB5 article-title: Type curve analysis of inertial effects in the response of a well to a slug test publication-title: Water Resour. Res doi: 10.1029/WR021i009p01397 – volume: 3 start-page: 357 issue: 3 year: 1982 ident: 10.1016/j.envsoft.2004.05.006_BIB4 article-title: An improved method for numerical inversion of Laplace transforms publication-title: SIAM J. Sci. Stat. Comput doi: 10.1137/0903022 – volume: 23 start-page: 89 issue: 1 year: 1976 ident: 10.1016/j.envsoft.2004.05.006_BIB1 article-title: Numerical inversion of Laplace transform using a Fourier series approximation publication-title: J. ACM doi: 10.1145/321921.321931 |
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| Title | Parallel Fortran-MPI software for numerical inversion of the Laplace transform and its application to oscillatory water levels in groundwater environments |
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