FISHPAK swMATH ID: 8012 Software Authors: Adams, J.; Swarztrauber, P.; Sweet, R Description: Algorithm 541. FISHPAK: A package of Fortran subprograms for the solution of separable elliptic partial differential equations. FISHPACK contains a collection of Fortran77 subroutines that solve second- and fourth-order finite difference approximations to separable elliptic Partial Differential Equations (PDEs). These include Helmholtz equations in cartesian, polar, cylindrical, and spherical coordinates, as well as more general separable elliptic equations. The solvers use the cyclic reduction algorithm. When the problem is singular, a least-squares solution is computed. Singularities induced by the coordinate system are handled, including at the origin r=0 in cylindrical coordinates, and at the poles in spherical coordinates. Test programs are provided for the 19 solvers. Each serves two purposes: as a template to guide you in writing your own codes utilizing the FISHPACK solvers, and as a demonstration on your computer that you can correctly produce FISHPACK executables. The FISHPACK library and programs are intended to be installed on your computer using the Makefile provided when you download the files in this distribution. The Makefile builds the library and driver executables under the compiler you specify when you run ”make”. If your application requires solution of nonseparable elliptic PDEs, or a mix of separable and nonseparable ones, consider using the MUDPACK library instead of FISHPACK. MUDPACK uses multigrid iteration to approximate separable and nonseparable elliptic PDEs. The software is available on NCAR’s web pages. If you are solving separable elliptic PDEs only, and prefer Fortran90 syntax, then you may want to use FISHPACK90, also available on NCAR’s web pages. Both FISHPACK and FISHPACK90 have the same functionality. Homepage: http://www2.cisl.ucar.edu/resources/legacy/fishpack Related Software: IIMPACK; MUDPACK-2; MUDPACK; Matlab; LAPACK; FFTW; ELLPACK; LINPACK; EISPACK; ASCL; CMMEXP; hwsplr.f; HFFT; CLAWPACK; PoisFFT; SERRG2; Algorithm 527; BEMLIB; DiffSharp; GEMMW Cited in: 110 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Efficient Fortran subprograms for the solution of elliptic partial differential equations. Zbl 0467.65044Adams, John C.; Swarztrauber, Paul N.; Sweet, Roland A. 1981 Efficient Fortran subprograms for the solution of separable elliptic partial differential equations \([D3]\). Zbl 0419.35043Swarztrauber, Paul N.; Sweet, Roland A. 1979 all top 5 Cited by 173 Authors 18 Lai, Mingchih 13 Pan, Tsorng-Whay 10 Glowinski, Roland 10 Li, Zhilin 9 Hu, Wei-Fan 9 Khoo, Boo Cheong 9 Tan, Zhijun 6 Lim, Kian-Meng 5 Le, Duc-Vinh 4 Adams, John Conway 4 Boeck, Thomas 4 Schumacher, Jörg 3 Chang, Chien-Cheng 3 Krasnov, Dmitry 3 Sweet, Roland A. 3 Wang, Weiyi 3 Zheng, Zhongquan Charlie 2 Báez, Elsa 2 Bermúdez, Blanca 2 Bialecki, Bernard 2 Chang, Sinchung 2 Chen, Kuanyu 2 Feng, Hongsong 2 Gallizio, Federico 2 Kim, Yongsam 2 Li, Jing-Rebecca 2 Lin, Te-Sheng 2 Lin, Wen-Wei 2 Łukaniszyn, Marian 2 Nicolás, Alfredo 2 Peraire, Jaime 2 Périaux, Jacques F. 2 Prinz, Sebastian 2 Qiao, Zhonghua 2 Shi, Lingling 2 Swarztrauber, Paul N. 2 Tseng, Yu-Hau 2 Tseng, Yu-Hou 2 Wang, Desheng 2 Xu, Jianjun 2 Young, Yuan-Nan 2 Zhao, Hongkai 2 Zhao, Shan 2 Zikanov, Oleg Yu. 1 Abbasi, Aida 1 Abboudi, Said 1 Adamczyk, John J. 1 Akhtari, Ali Akbar 1 Anderson, Christopher R. 1 Balbás, Jorge 1 Bandaru, Vinodh 1 Barbosa Mota, J. P. 1 Barros, Saulo R. M. 1 Bartzis, John G. 1 Beaugendre, Héloïse 1 Bennett, Andrew F. 1 Biegler, Lorenz T. 1 Bini, Dario Andrea 1 Boisvert, Ronald F. 1 Brush, Lucien N. 1 Cai, Qin 1 Calhoun, Donna A. 1 Čanić, Sunčica 1 Chang, Che-Chia 1 Chen, Guo 1 Chen, Jinru 1 Chen, Shih-Di 1 Chiu, Shang-Huan 1 Chu, Chin-Chou 1 Chua, B. S. 1 Cocle, Roger 1 Daeninck, Goéric 1 Dai, Chen-Yang 1 Deng, Shaozhong 1 Deville, Michel O. 1 Dhall, Sudarshan K. 1 Dongarra, Jack J. 1 Dryja, Maksymilian 1 Eichfelder, Gabriele 1 Fairweather, Graeme 1 Feldman, Yuri 1 Feng, Ko-An 1 Fuka, Vladimír 1 Galdi, Giovanni Paolo 1 Goulas, Apostolos 1 Greengard, Leslie F. 1 Grigoriadis, Dimokratis G. E. 1 Guo, Aixia 1 Haldenwang, Pierre 1 Hao, Jian 1 He, Guowei 1 He, Jiwen 1 Helzel, Christiane 1 Huang, Huaxiong 1 Huang, Junjie 1 Huang, Shih-Lin 1 Iollo, Angelo 1 Ito, Kazufumi 1 Jayathilake, P. G. 1 Ji, Haifeng ...and 73 more Authors all top 5 Cited in 39 Serials 33 Journal of Computational Physics 10 Computers and Fluids 6 Applied Mathematics and Computation 5 Computer Methods in Applied Mechanics and Engineering 4 Communications in Computational Physics 3 Computers & Mathematics with Applications 3 Numerical Algorithms 3 SIAM Journal on Scientific Computing 3 East Asian Journal on Applied Mathematics 2 Computer Physics Communications 2 ACM Transactions on Mathematical Software 2 Applied Numerical Mathematics 2 COMPEL 2 Journal of Scientific Computing 2 International Journal of Computational Fluid Dynamics 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Fluids 1 Journal of Fluid Mechanics 1 Periodica Mathematica Hungarica 1 Physics Letters. A 1 Mathematics of Computation 1 BIT 1 Computing 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Chinese Annals of Mathematics. Series B 1 Physica D 1 Applied Mathematics Letters 1 Journal of Non-Newtonian Fluid Mechanics 1 Computational Optimization and Applications 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Advances in Computational Mathematics 1 European Journal of Mechanics. B. Fluids 1 Computational Geosciences 1 Optimization and Engineering 1 CMES. Computer Modeling in Engineering & Sciences 1 Computational Methods in Applied Mathematics 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris all top 5 Cited in 17 Fields 72 Fluid mechanics (76-XX) 65 Numerical analysis (65-XX) 39 Partial differential equations (35-XX) 7 Biology and other natural sciences (92-XX) 6 Mechanics of deformable solids (74-XX) 4 Computer science (68-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Operations research, mathematical programming (90-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Citations by Year