SCPACK
Numerical Computation of Schwarz-Christoffel Conformal Maps

SCPACK is a FORTRAN77 program which implements the Schwarz-Christoffel conformal map from a disk to a polygon, which may contain vertices at infinity.

Licensing:

The package may be freely copied and used, but reference to the paper by Nick Trefethen should be given in any publications arising from its use.

Languages:

SCPACK is available in a FORTRAN77 version.

Reference:

1. Tobin Driscoll, Lloyd Trefethen,
   Schwarz-Christoffel Mapping,
   Cambridge, 2002,
   ISBN: 0-521-80726-3,
   LC: QA360.D75.
2. Nick Trefethen,
   Numerical Computation of the Schwarz-Christoffel Transformation,
   SIAM Journal of Scientific and Statistical Computing,
   Volume 1, 1980, pages 82-102.

Source Code:

• scpack.f, the source code.
• scpack_sub.f, the source code for utility routines.
• scpack.sh, commands to compile the source code.

Examples and Tests:

• scpack_prb.f, a sample calling program.
• scpack_prb.sh, commands to compile and run the sample program.
• scpack_prb_output.txt, the output from a run of the sample program.

• scpack_prb.xy, an XY file containing node coordinates.
• scpack_prb.xyl, an XYL file listing the indices of nodes that form lines.
• scpack_prb.png, a PNG image of the grid created by XYL_DISPLAY.

List of Routines:

• QINIT computes nodes and weights for Gauss-Jacobi quadrature.
• SCSOLV computes parameters for the Schwarz-Christoffel mapping.
• WSC computes forward map w(zz)
• ZSC computes the inverse map Z(WW) by Newton iteration.
• ZFODE computes the function ZDZDT needed by ODE in ZSC.
• CHECK checks geometry of the problem.
• YZTRAN transforms y(k) to z(k).
• SCFUN is the function whose zero must be found in SCSOLV.
• SCOUTP prints K, W(K), TH(K), BETAM(K) and Z(K).
• SCTEST tests the computed map for accuracy.
• ZQUAD computes the line integral of ZPROD.
• ZQUAD1 computes half of the line integral of ZPROD.
• DIST determines the distance from zz to the nearest singularity z(k).
• ZQSUM computes the integral of ZPROD.
• ZPROD computes a Schwarz-Christoffel integrand.
• RPROD computes the absolute value of a Schwarz-Christoffel integrand.
• NEARZ returns information about the nearest prevertex.
• ANGLES computes external angles.
• COUNT0 ?
• COUNT ?

You can go up one level to the FORTRAN77 source codes.