Efficient FORTRAN subprograms for the solution of elliptic partial differential equations (abstract)

Abstract

The purpose of this paper is to describe technical note, NCAR TN/IA-109, which is intended to provide scientists with a package of computer programs which make use of current methods for solving elliptic partial differential equations. Computer models of geophysical processes often require the numerical solution of elliptic partial differential equations. This is particularly true for models which make use of stream functions, velocity potentials, or vorticity equations, or in which the pressure of an incompressible fluid is computed. The numerical solution of elliptic equations can be a formidable programming task. Also, the equations are often time-dependent, requiring repeated solutions and, hence, considerable computing resources. Efficient, reliable, and well-documented computer subroutines for solving such equations are needed. With recent advances in computing methods, it became apparent to the authors that a very large class of elliptic equations (separable) could be solved rapidly and with minimal storage. Of particular importance was the fact that, as a result of work on singular problems, this class was free of special cases for which solutions could not be obtained numerically.