xtess.f90 and xqtess.f90 are the revised Fortran codes in double and quadruple precision based on the original Fortran codes xtess.txt and xqtess.txt (Fukushima 2018).
They can accurately compute the gravitational field (i.e. gravitational potential, gravitational acceleration vector, and gravity gradient tensor) of a tesseroid both in double and quadruple precision no matter the computation point is located outside, near the surface of, on the surface of, or inside the tesseroid.
In the abstract of Fukushima (2018):
The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential.
The achievable precision is 14–15 digits for the potential, 9–11 digits for the acceleration vector, and 6–8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation.
The original sites of xtess.txt and xqtess.txt are:
- xtess.txt (Fortran program to compute the gravitational field of a tesseroid accurately in double precision)
- xqtess.txt (Fortran program to compute the gravitational field of a tesseroid accurately in quadruple precision)
If the Fortran code xtess.f90 (or xqtess.f90) runs on Linux system (e.g. Ubuntu) with the ifort, please use this command:
ifort xtess.f90 -o xtess &&
./xtess
or
ifort xqtess.f90 -o xqtess &&
./xqtess
If the Fortran code xtess.f90 (or xqtess.f90) runs on the macOS system with the ifort, please use this command:
ifort -L/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/lib xtess.f90 -o xtess &&
./xtess
or
ifort -L/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/lib xqtess.f90 -o xqtess &&
./xqtess
Regarding the installation of the ifort, please refer to the Intel® oneAPI Base & HPC Toolkit:
- Intel® oneAPI Base Toolkit: Essential oneAPI Tools & Libraries
- Intel® oneAPI HPC Toolkit: Cluster & HPC Development Tools
- Fukushima T (2018) Accurate computation of gravitational field of a tesseroid. Journal of Geodesy 92(12):1371–1386, https://doi.org/10.1007/s00190-018-1126-2
- Deng XL (2023) Corrections to: “Accurate computation of gravitational field of a tesseroid” by Fukushima (2018) in J. Geod. 92(12):1371–1386. Journal of Geodesy 97(1):8, 1-7. https://doi.org/10.1007/s00190-022-01673-2