Direct and approximate algorithmic methods for solving self-adjoint elliptic PDEs in three-space dimensions
The finite difference discretization of a class of three-dimensional self-adjoint elliptic partial differential equations leads to the solution of a linear system of equations with a large sparse symmetric coefficient matrix which has seven occupied diagonals. After factorization into \(LDL^ T\) with L lower unit triangular and D diagonal the system can be solved by forward-backward substitution. The exact factorization can be considered as a special case of a described approximate factorization where the amount of fill in within the envelope is prescribed for the factor L. Two FORTRAN routines are given, LDL 3D for the factorization and FBS 3D for the computation of the solution. A numerical example is reported on.
scientific article; zbMATH DE number 3856343