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Manuscript Title: A finite element program package for axisymmetric vector field problems.
Authors: A. Konrad, P. Silvester
Program title: AXISYMM-VECTOR-HELMHOLTZ-FINTEL6
Catalogue identifier: ACSE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 9(1975)193
Programming language: Fortran.
Computer: IBM 360/75, IBM 370/158.
Operating system: OS/360 WITH HASP-II.
Program overlaid: yes
RAM: 50K words
Word size: 32
Keywords: Plasma physics, Electromagnetics, Axisymmetric, Poisson, Heat transfer, Electrostatics, Electron optics, Vector field, Helmholtz, Linear accelerator Cavities, Bessel, Laplace, Finite element, Collisionless plasma.
Classification: 10, 19.3.

Subprograms used:
Cat Id Title Reference
ACSC_v1_0 AXISYMM-SCALAR-HELMHOLTZ-FINTEL6 CPC 5(1973)438
ACSD_v1_0 GENERATE CPC 5(1973)438
ACSF_v1_0 VECTR-FINTEL6 BLK-DATA-GENERATOR CPC 9(1975)194

Nature of problem:
The following types of problems can be solved with the program:- electromagnetic field problems requiring solution to the one-component vector Poisson or Helmholtz equation in cylindrical co-ordinates with no azimuthal variation (e.g. transformer problems, unsaturated magnetic lens problems , linear accelerator cavities), -electric field problems requiring azimuthally periodic solutions to the scalar Laplace , Poisson or Helmholtz equation, i.e. solutions to the generalized Bessel equation of order m), -a host of mathematically related problems which fall in the above two categories (e.g. heat and fluid problems).

Solution method:
The generalized Bessel equation of order m, derivable from the vector Helmholtz equation from m=1 under the assumption of one vector component in the azimuthal direction and no azimuthal variation, or derivable from the scalar Helmholtz equation under the assumption of azimuthal periodicity, is solved by high-order polynomial triangular finite- element method using an approximation technique which avoids singularities of the 1/r type at the axis of symmetry.

Restrictions:
Since the AXISYMM-VECTOR-HELMHOLTZ-FINTEL6 program is closely modelled after the previously published scalar finite element programs, the same restrictions apply. The computations, as in the scalar case, are carried out in single precision arithmetic. For large problems round- off errors may accumulate during the solution of the matrix eigenvalue equation. This of course depends on the word length of the computer used.

Unusual features:
Most program features closely resemble those of the scalar programs. Since computers may not accept the block data subprograms supplied with the program, a FORTRAN program (VECTR-FINTEL 6-BLK-DATA-GENERATOR) which punches out the complete block data subprograms is made available to the users.

Running time:
The running times are similar to those cited in Comp. Phys. Commun. 5(1973)437 and can be estimated from the running times of the matrix equation solving subroutines.