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 Author Micula, Sanda Title Numerical methods for the radiosity equation and related problems Descript 89 p Note Source: Dissertation Abstracts International, Volume: 58-12, 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 58-12B Subject Mathematics 0405 Alt Author The University of Iowa
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