D302: Fast Partial Differential Equation Solver

Author(s): R.C. Le Bail	Library: MATHLIB
Submitter:	Submitted: 20.03.1972
Language: Fortran	Revised: 01.12.1981

ELPAHY uses fast Fourier transform techniques for the solution, over a rectangular domain, of the following elliptic, parabolic or hyperbolic part differential equation:

where is the unknown function, the known source term, and given coefficients. A large variety of boundary conditions can be specified on the sides of the rectangle.

Structure:

SUBROUTINE subprogram
User Entry Names: ELPAHY
Internal Entry Names: NEWRO, ELANAL, ESOLVE, SYNT, MFT
External References: RFT
COMMON Block Names and Lengths: /FW1/ 774, /FW2/ 100

Usage:

    CALL ELPAHY(F,NX,NY,DX,DY,C,IBX,BWEST,BEAST,JBY,BSOUTH,BNORTH)

F

(REAL) Two-dimensional array, dimensioned (NX,NY) in the calling program. On input it contains the source term and on return it contains the unknown function .

NX

(INTEGER) Number of divisions along X. NX must be of the form .

NY

(INTEGER) Number of divisions along Y.

DX

(REAL) Mesh spacing along X.

DY

(REAL) Mesh spacing along Y.

C

(REAL) One-dimensional array of dimension 3, containing the coefficients .

IBX

(INTEGER) Controls the type of boundary conditions on the left (BWEST) and right (BEAST) sides of the rectangular domain:
Imposed periodicity along x; BWEST, BEAST not given.
Given derivative on either vertical side.
Given value on either vertical side.
Given value on the left side, given derivative on the right side.

BWEST

(REAL) One-dimensional array of size NY containing values or derivatives for the left side; the interpretation depends on IBX.

BEAST

(REAL) One-dimensional array of size NY containing values or derivatives for the right side; the interpretation depends on IBX.

JBY

(INTEGER) Controls the type of boundary conditions on the lower (BSOUTH) und upper (BNORTH) sides of the rectangular domain:
Elliptic equation ( ):
Given value on both lower and upper sides.
Given derivative on both lower and upper sides.
Given value on lower side, given derivative on upper side.
Given derivative on lower side, given value on upper side.
Parabolic equation ( ):
Specify BSOUTH array only. (If y=time, BSOUTH are initial values and the future BNORTH cannot be specified).
Given value on lower side.
Given derivative on lower side.
Hyperbolic equation ( ):
The BSOUTH array specifies the value, the BNORTH array the derivative.
.

BSOUTH

(REAL) One-dimensional array of size NX containing values or derivatives for the lower side; the interpretation depends on JBY.

BNORTH

(REAL) One-dimensional array of size NX containing values or derivatives for the upper side; the interpretation depends on JBY.

Notes:

If , specify COMMON /FWORK/ of length 6*NX and COMMON /FW1/ of length 6*NX in the calling program. If , specify COMMON /FW2/ of length 2*NY. In either case, make sure your program is loaded before ELPAHY (D302) (this is automatic unless you recompile D302 in the same job).

References:

1. R.C. Le Bail, Use of fast Fourier transforms for solving partial differential equations in physics, J. Comput. Phys. 9 (1972) 440-465

A copy of Ref. 1 is available.