zbMATH — the first resource for mathematics

MUDPACK: Multigrid portable FORTRAN software for the efficient solution of linear elliptic partial differential equations. (English) Zbl 0685.65091
Author’s summary: MUDPACK is a package of portable FORTRAN subprograms which use multigrid iteration for solving real or complex elliptic partial differential equations. The solution regions are rectangles in two dimensions and boxes in three dimensions. Any combination of periodic, Dirichlet, and mixed-derivative boundary conditions is allowed. The equations are automatically discretized using second-order finite differencing. The package will vectorize on Cray computers. Examples are given which demonstrate ease of use, efficiency, and applicability to a wide range of problems.
Reviewer: S.F.McCormick

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35J25 Boundary value problems for second-order elliptic equations
65Yxx Computer aspects of numerical algorithms
Full Text: DOI
[1] Gentzsch, W., Vectorization of computer programs with applications to computational fluid dynamics, (), 246
[2] Forester, H.; Witsch, K., Multigrid software for the solution of elliptic problems on rectangular domains: MG (release 1), (), Multigrid Methods
[3] Stuben, K., A multi-grid program to solve delta U − c(x, y)U = f(x, y) on omega),U = g(x, y) (on omega), on nonrectangular bounded domains omega, ()
[4] Brandt, A., Multilevel adaptive solutions to boundary value problems, Math. comp., 31, 333-390, (1977) · Zbl 0373.65054
[5] Hackbush, W.; Trottenberg, U., Multigrid methods, (1982), Springer-Verlag Berlin
[6] Jespersen, D., Multigrid methods for partial differential equations, (), 270-318 · Zbl 0594.65077
[7] McCormick, S., Multigrid methods, () · Zbl 0517.65083
[8] Briggs, W., A multigrid tutorial, (1987), SIAM Philadelphia · Zbl 0659.65095
[9] Fulton, S.; Ciesielski, R.; Schubert, W., Multigrid methods for elliptic problems: A review, Monthly weather rev., 114, 943-959, (1986)
[10] Pizzo, V., Numerical modeling of solar magnetostatic structures bounded by current sheets using multigrid methods, ()
[11] D. Haidvogel, H. wilkin, and R. Roung, A semi-spectral primitive equation model using vertical sigma and orthogonal curvilinear horizontal coordinates, J. Comput. Phys., to appear. · Zbl 0718.76077
[12] Gross, B., Semi-geostrophic flow over orography in a stratified rotating atmosphere, (), 139
[13] Buzbee, B.; Golub, G.; Nielson, C., On direct methods for solving Poisson’s equations, SIAM J. numer. anal., 7, 627-656, (1970) · Zbl 0217.52902
[14] Swarztrauber, P., Fast Poisson solvers, (), 319-369 · Zbl 0597.65084
[15] Adams, J.; Swarztrauber, P.; Sweet, R., Efficient \scfortran subprograms for the solution of elliptic partial differential equations, (), 187-191
[16] Handbook of Mathematical Functions, Nat. Bur. Standards Appl. Math. Ser. 55, p. 884.
[17] V. Pereyerea, High Order Difference Solution of Differential Equations, Report STAN-CS:73-348. Computer Science Dept., Stanford Univ., Stanford, Calif.
[18] Adams, J., New software for elliptic partial differential equations, CF notes 55, (Nov. 1978)
[19] Adams, J., Fortran subprograms for finite-difference formula, J. comput. phys., 26, 113-116, (1978) · Zbl 0364.65070
[20] Schaffer, S., Higher order multigrid methods, Math. comp., 43, 89-115, (July 1987)
[21] Thole, C.; Trottenberg, U., Basic smoothing procedures for the multigrid treatment of elliptic 3-D operators, Appl. math. comput., 19, 333-345, (1986) · Zbl 0612.65065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.