FISHPAK

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 73 articles , 2 standard articles )

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  1. Li, Zhilin; Qiao, Zhonghua; Tang, Tao: Numerical solution of differential equations. Introduction to finite difference and finite element methods (2018)
  2. 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)
  3. 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)
  4. Hu, Wei-Fan; Lai, Ming-Chih; Seol, Yunchang; Young, Yuan-Nan: Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method (2016)
  5. Ji, Haifeng; Chen, Jinru; Li, Zhilin: A new augmented immersed finite element method without using SVD interpolations (2016)
  6. Shi, Lingling; Čanić, Sunčica; Quaini, Annalisa; Pan, Tsorng-Whay: A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation (2016)
  7. Hu, Wei-Fan; Lai, Ming-Chih; Young, Yuan-Nan: A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations (2015)
  8. Li, Zhilin: On convergence of the immersed boundary method for elliptic interface problems (2015)
  9. Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray: A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions (2015)
  10. Chen, Kuan-Yu; Lai, Ming-Chih: A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant (2014)
  11. Hu, Wei-Fan; Kim, Yongsam; Lai, Ming-Chih: An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows (2014)
  12. Hu, Wei-Fan; Lai, Ming-Chih: An unconditionally energy stable immersed boundary method with application to vesicle dynamics (2013)
  13. 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)
  14. Jayathilake, P.G.; Tan, Zhijun; Le, D.V.; Lee, H.P.; Khoo, B.C.: Three-dimensional numerical simulations of human pulmonary cilia in the periciliary liquid layer by the immersed boundary method (2012)
  15. 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)
  16. Chen, Kuan-Yu; Feng, Ko-An; Kim, Yongsam; Lai, Ming-Chih: A note on pressure accuracy in immersed boundary method for Stokes flow (2011)
  17. Krasnov, Dmitry; Zikanov, Oleg; Boeck, Thomas: Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number (2011)
  18. Li, Zhilin; Lai, Ming-Chih: New finite difference methods based on IIM for inextensible interfaces in incompressible flows. (2011)
  19. Nicolás, Alfredo; Báez, Elsa; Bermúdez, Blanca: From cat’s eyes to disjoint multicellular natural convection flow in tall tilted cavities (2011)
  20. Gallizio, Federico; Iollo, Angelo; Protas, Bartosz; Zannetti, Luca: On continuation of inviscid vortex patches (2010)

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