Descript 
89 p 
Note 
Source: Dissertation Abstracts International, Volume: 5812, Section: B, page: 6614 

Supervisor: Kendall E. Atkinson 

Thesis (Ph.D.)The University of Iowa, 1997 

In this work, we present numerical methods for the solution of Fredholm integral equations of the second type, for smooth and piecewise smooth surfaces. We use a collocation method based on piecewise polynomial interpolation of the solution. We consider only collocation methods for which the collocation nodes are interior to each triangular face 

In Chapter II we give the general framework for collocation methods based on interpolation. We show that interpolation of degree r of the solution leads to an error in the collocation method of $O(h\sp{r+1}),$ where h is the mesh size of the triangulation, and so collocation methods of any given order can be developed 

In Chapter III we discuss superconvergent methods, as particular cases of the methods introduced in Chapter II. The radiosity equation is introduced, along with some of its properties. Next we discuss two superconvergent collocation methods based on piecewise quadratic interpolation, for the radiosity equation, followed by numerical examples. We conclude this chapter with giving generalized superconvergent methods based on interpolation of any degree r, considering separately the case where r is odd and the case where r is even 

In the following chapter the ideas described earlier are used for finding numerical solutions of the exterior Neumann problem, since in solving this problem we encounter integral equations whose properties are very similar to the ones of the radiosity equation. Considering collocation methods that use only interior nodes is especially useful in solving this problem. We describe a collocation method based on interpolation of the solution, for solving the integral equation derived from the exterior Neumann problem, giving numerical examples for the case of piecewise constant interpolation of the solution (centroid rule) 

In the concluding chapter, we draw some important and interesting conclusions as well as discuss some possible ideas for future work in this area 

School code: 0096 
Host Item 
Dissertation Abstracts International 5812B

Subject 
Mathematics


0405

Alt Author 
The University of Iowa

