Solving Two-Dimensional Partial Differential Equations on Vector and Scalar Machines

TTGR is a Fortran program that solves time-varying partial differential equations on a rectangle. TTGR uses fixed tensor product Galerkin B-splines, nonuniform meshes and higher order approximations. The algorithm sequentially reduces the partial differential equation to an ordinary differential equation to a nonlinear system and finally to a linear system. Difficult problems which require enormous resources with a standard finite element or finite difference method are quite tractable with the Galerkin approach. Central to the method is the construction and solution of a linear system. Partly because so much effort has been expended to increase the speed of linear equation solvers and partly because of the nature of the equations themselves, the construction of the Galerkin equations often is more costly than the solution of these equations.