Investigation of the Numerical Method of Finite Elements for Digital Computer Determination of Green's Functions.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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The feasibility of using the numerical method of finite elements for digital computer determinations of Greens functions was investigated in this thesis. A study of Poissons equation, the Helmholtz equation, and the diffusion equation in one and two dimensions was conducted using the CDC 6600 computer. Both Dirichlet and mixed boundary conditions were considered. The Greens functions numerically determined by the finite element method were compared with those found by the analytical method and the finite difference method for accuracy. The numerical and analytical Greens functions were also used in the solution of several boundary value problems, and the accuracy of the results were compared. The results of the study indicated that although for Poissons equation, the finite element method produced the same results as the finite difference method, the finite element method was more time consuming. For the Helmholtz and diffusion equations, the finite element method again required more computations, but in most cases gave greater accuracy.
- Numerical Mathematics