speclib.F90 File Reference

LIBRARY ROUTINES FOR SPECTRAL METHODS. More...

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Data Types
module	speclib

Detailed Description

LIBRARY ROUTINES FOR SPECTRAL METHODS.

Date

March 1989

Author

Einar Malvin Ronquit

ABBRIVIATIONS:

M   - Set of mesh points
Z   - Set of collocation/quadrature points
W   - Set of quadrature weights
H   - Lagrangian interpolant
D   - Derivative operator
I   - Interpolation operator
GL  - Gauss Legendre
GLL - Gauss-Lobatto Legendre
GJ  - Gauss Jacobi
GLJ - Gauss-Lobatto Jacobi

MAIN ROUTINES:

Points and weights:
ZWGL      Compute Gauss Legendre points and weights
ZWGLL     Compute Gauss-Lobatto Legendre points and weights
ZWGJ      Compute Gauss Jacobi points and weights (general)
ZWGLJ     Compute Gauss-Lobatto Jacobi points and weights (general)

Lagrangian interpolants:
HGL       Compute Gauss Legendre Lagrangian interpolant
HGLL      Compute Gauss-Lobatto Legendre Lagrangian interpolant
HGJ       Compute Gauss Jacobi Lagrangian interpolant (general)
HGLJ      Compute Gauss-Lobatto Jacobi Lagrangian interpolant (general)

Derivative operators:
DGLL      Compute Gauss-Lobatto Legendre derivative matrix
DGLLGL    Compute derivative matrix for a staggered mesh (GLL->GL)
DGJ       Compute Gauss Jacobi derivative matrix (general)
DGLJ      Compute Gauss-Lobatto Jacobi derivative matrix (general)
DGLJGJ    Compute derivative matrix for a staggered mesh (GLJ->GJ) (general)

Interpolation operators:
IGLM      Compute interpolation operator GL  -> M
IGLLM     Compute interpolation operator GLL -> M
IGJM      Compute interpolation operator GJ  -> M  (general)
IGLJM     Compute interpolation operator GLJ -> M  (general)

Other:
PNLEG     Compute Legendre polynomial of degree N
PNDLEG    Compute derivative of Legendre polynomial of degree N

Comments:
Note that many of the above routines exist in both single and
double precision. If the name of the single precision routine is
SUB, the double precision version is called SUBD. In most cases
all the "low-level" arithmetic is done in double precision, even
for the single precsion versions.

Useful references:

[1] Gabor Szego: Orthogonal Polynomials, American Mathematical Society, Providence, Rhode Island, 1939. [2] Abramowitz & Stegun: Handbook of Mathematical Functions, Dover, New York, 1972. [3] Canuto, Hussaini, Quarteroni & Zang: Spectral Methods in Fluid

Dynamics, Springer-Verlag, 1988.

Definition in file speclib.F90.