Finite Element Solution of a Self-Adjoint Transport Equation in One Dimension.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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A self-adjoint form of the transport equation was derived, and expressed as an extremization integral. The finite element equations were derived from the extremization integral for the one-dimensional time independent homogeneous transport equation with isotropic scatter. These equations were implemented in FORTRAN on a VAX 11780 and used to solve a simple benchmark problem. The finite element solution, for a small mesh of 32 elements, was compared to results from a numerical technique known as Ln. The solutions differed by about 35 percent. Larger meshes were not run because an automatic mesh refinement routine was not available. The large difference between the Ln solution and the finite difference solution is attributed to residual errors in the coding of the finite element equations for the scatter terms. Author
- Numerical Mathematics
- Computer Programming and Software