FIDISOL (Finite difference solver) is a program package for the solution of nonlinear systems of 2-D and 3-D elliptic and parabolic differential equations subject to arbitrary nonlinear boundary conditions on a rectangular domain. The solution method is a variable stepsize/variable order finite difference method. This paper is a survey of the project at the University of Karlsruhe in which the principles of developing a fully vectorized program package designed as a data flow algorithm for vector computers are obtained. Included are iterative solvers for large sparse linear systems. For details the reader is referred to a paper by the authors and {\itH. Muller} [The FIDISOL program package, Internal Report No.27/85, Computer Center, University of Karlsruhe, 75 Karlsruhe, FRG (1985)].

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Schönauer, Willi; Häfner, Hartmut: Numerical experiments to optimize the use of (I)LU preconditioning in the iterative linear solver package LINSOL (2002)
  2. Houstis, Elias N.; Rice, John R.; Weerawarana, Sanjiva; Catlin, Ann Christine; Papachiou, P.; Wang, KoYang; Gaitatzes, Margaret: PELLPACK: A problem solving environment for PDE based applications on multicomputer platforms (2000)
  3. Heyouni, M.; Sadok, H.: On a variable smoothing procedure for Krylov subspace methods (1998)
  4. Houstis, E. N.; Rice, J. R.; Weerawarana, S.; Catlin, A. C.; Papachiou, P.; Wang, K.-Y.; Gaitatzes, M.: PELLPACK: A problem-solving environment for PDE-based applications on multicomputer platforms (1998)
  5. Schönauer, Willi; Weiss, Rüdiger: An engineering approach to generalized conjugate gradient methods and beyond (1995)
  6. Weiss, Rüdiger: Properties of generalized conjugate gradient methods (1994)
  7. Schönauer, W.; Weiss, R.; Sternecker, P.: Polyalgorithms with automatic method selection for the iterative solution of linear equations and eigenproblems. (With discussion) (1992)
  8. Ortega, James M.; Voigt, Robert G.; Romine, Charles H.: A bibliography on parallel and vector numerical algorithms (1990)
  9. Ierotheou, C. S.; Richards, C. W.; Cross, M.: Vectorization of the SIMPLE solution procedure for CFD problems. I: A basic assessment (1989)
  10. Schönauer, W.; Weiß, R.: Efficient vectorizable PDE solvers (1989)
  11. Schönauer, Willi; Schnepf, Eric: FIDISOL: A `black box’ solver for partial differential equations (1988)
  12. Schönauer, Willi; Schnepf, Eric: Software considerations for the “black box” solver FIDISOL for partial differential equations (1987)