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.

References in zbMATH (referenced in 103 articles , 2 standard articles )

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  1. Wang, Xue; Rui, Hongxing: An efficient augmented approach algorithm for incompressible Stokes problems on staggered Cartesian grids (2022)
  2. Feng, Hongsong; Long, Guangqing; Zhao, Shan: FFT-based high order central difference schemes for Poisson’s equation with staggered boundaries (2021)
  3. Leng, X.-Y.; Krasnov, D.; Li, B.-W.; Zhong, J.-Q.: Flow structures and heat transport in Taylor-Couette systems with axial temperature gradient (2021)
  4. Molins, Sergi; Soulaine, Cyprien; Prasianakis, Nikolaos I.; Abbasi, Aida; Poncet, Philippe; Ladd, Anthony J. C.; Starchenko, Vitalii; Roman, Sophie; Trebotich, David; Tchelepi, Hamdi A.; Steefel, Carl I.: Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set (2021)
  5. Prinz, Sebastian; Thomann, Jana; Eichfelder, Gabriele; Boeck, Thomas; Schumacher, Jörg: Expensive multi-objective optimization of electromagnetic mixing in a liquid metal (2021)
  6. Sela, Rafi; Zemach, Efi; Feldman, Yuri: A semi-implicit direct forcing immersed boundary method for periodically moving immersed bodies: a Schur complement approach (2021)
  7. Wang, Weiyi; Tan, Zhijun: A simple 3D immersed interface method for Stokes flow with singular forces on staggered grids (2021)
  8. Feng, Hongsong; Zhao, Shan: FFT-based high order central difference schemes for three-dimensional Poisson’s equation with various types of boundary conditions (2020)
  9. Xu, Jian-Jun; Shi, Weidong; Hu, Wei-Fan; Huang, Jun-Jie: A level-set immersed interface method for simulating the electrohydrodynamics (2020)
  10. Costa, Pedro: A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows (2018)
  11. Hu, Wei-Fan; Lai, Ming-Chih; Misbah, Chaouqi: A coupled immersed boundary and immersed interface method for interfacial flows with soluble surfactant (2018)
  12. Li, Zhilin; Qiao, Zhonghua; Tang, Tao: Numerical solution of differential equations. Introduction to finite difference and finite element methods (2018)
  13. Nicholson, Bethany L.; Wan, Wei; Kameswaran, Shivakumar; Biegler, Lorenz T.: Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems (2018)
  14. Prinz, Sebastian; Boeck, Thomas; Schumacher, Jörg: Large eddy simulation of hydrodynamic and magnetohydrodynamic channel flows with a collocated finite-volume scheme and improved subgrid-scale modeling (2018)
  15. Tsai, Liang-Hsia; Chang, Chien-Cheng; Pan, Tsorng-Whay; Glowinski, Roland: Numerical study of the wall effect on particle sedimentation (2018)
  16. Guo, Aixia; Pan, Tsorng-Whay; He, Jiwen; Glowinski, Roland: Numerical methods for simulating the motion of porous balls in simple 3D shear flows under creeping conditions (2017)
  17. Le, Duc-Vinh; Khoo, Boo-Cheong: A moving-least-square immersed boundary method for rigid and deformable boundaries in viscous flow (2017)
  18. Bandaru, Vinodh; Boeck, Thomas; Krasnov, Dmitry; Schumacher, Jörg: A hybrid finite difference-boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds number (2016)
  19. Hu, Wei-Fan; Lai, Ming-Chih; Seol, Yunchang; Young, Yuan-Nan: Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method (2016)
  20. Ji, Haifeng; Chen, Jinru; Li, Zhilin: A new augmented immersed finite element method without using SVD interpolations (2016)

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