| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 103 === The subject of this thesis is the application of the multi-grid method to solve Neumann boundary condition and the elliptic equations with discontinuous or highly oscillating coefficients. Numerical discretization is based on fi ve-point finite difference method. First, we discuss a special case which is ill-posed. When we execute the multi-grid method in this case, whether the coarse-grid correction problem is solvable or not is an issue which we need to discuss. To avoid a situation that the coarse-grid correction problem is not solvable and ensure that the multi-grid method works, we develop a theory to choose the restriction operator. Because of the discontinuous and highly oscillating coefficient, we employ a new interpolation operator which is dependent on the diffusion coefficient of the elliptic equation to improve the rate of convergence. Finally, we display some numerical results and compare it with other iterative methods. With these results, the multi-grid method appears to be feasible and efficient on solving Neumann boundary condition and the elliptic equations with highly oscillating coefficients.
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