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 49 articles , 1 standard article )

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  1. Ji, Haifeng; Chen, Jinru; Li, Zhilin: A new augmented immersed finite element method without using SVD interpolations (2016)
  2. Li, Zhilin: On convergence of the immersed boundary method for elliptic interface problems (2015)
  3. Hu, Wei-Fan; Lai, Ming-Chih: An unconditionally energy stable immersed boundary method with application to vesicle dynamics (2013)
  4. Pan, Tsorng-Whay; Huang, Shih-Lin; Chen, Shih-Di; Chu, Chin-Chou; Chang, Chien-Cheng: A numerical study of the motion of a neutrally buoyant cylinder in two dimensional shear flow (2013)
  5. Lai, Ming-Chih; Hu, Wei-Fan; Lin, Wen-Wei: A fractional step immersed boundary method for Stokes flow with an inextensible interface enclosing a solid particle (2012)
  6. Chen, Kuan-Yu; Feng, Ko-An; Kim, Yongsam; Lai, Ming-Chih: A note on pressure accuracy in immersed boundary method for Stokes flow (2011)
  7. Li, Zhilin; Lai, Ming-Chih: New finite difference methods based on IIM for inextensible interfaces in incompressible flows. (2011)
  8. Nicolás, Alfredo; Báez, Elsa; Bermúdez, Blanca: From cat’s eyes to disjoint multicellular natural convection flow in tall tilted cavities (2011)
  9. Li, Zhilin; Lai, Ming-Chih; He, Guowei; Zhao, Hongkai: An augmented method for free boundary problems with moving contact lines (2010)
  10. Pan, Tsorng-Whay; Shi, Lingling; Glowinski, Roland: A DLM/FD/IB method for simulating cell/cell and cell/particle interaction in microchannels (2010)
  11. Hao, Jian; Pan, Tsorng-Whay; Glowinski, Roland; Joseph, Daniel D.: A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach (2009)
  12. Le, D.V.; White, J.; Peraire, J.; Lim, K.M.; Khoo, B.C.: An implicit immersed boundary method for three-dimensional fluid-membrane interactions (2009)
  13. Li, Jing-Rebecca; Calhoun, Donna; Brush, Lucien: Efficient thermal field computation in phase-field models (2009)
  14. Nicolás, Alfredo; Bermúdez, Blanca; Báez, Elsa: Effects of the Rayleigh number and the aspect ratio on 2D natural convection flows (2009)
  15. Tan, Zhijun; Lim, K.M.; Khoo, B.C.: A fast immersed interface method for solving Stokes flows on irregular domains (2009)
  16. Tan, Zhijun; Lim, K.M.; Khoo, B.C.: An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries (2009)
  17. Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q.N.: Optimal superconvergent one step quadratic spline collocation methods (2008)
  18. Chen, Guo; Li, Zhilin; Lin, Ping: A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow (2008)
  19. Cocle, Roger; Winckelmans, Grégoire; Daeninck, Goéric: Combining the vortex-in-cell and parallel fast multipole methods for efficient domain decomposition simulations (2008)
  20. Lai, Ming-Chih; Tseng, Hsiao-Chieh: A simple implementation of the immersed interface methods for Stokes flows with singular forces (2008)

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