Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Solving partial differential equations using sinc methods
Abstract
Sinc methods, since their introduction, have shown great theoretical promise as highly accurate methods for a wide range of numerical tasks. They have proven to have exponential convergence for ordinary differential equations and partial differential equations. However, there are few large-scale numerical implementations of sinc methods due to the density and size of the resulting matrix equations. We have developed a package, SincLib, which provides significant computational improvements for sinc-based PDE solutions in n-dimensions. We apply these speedups to several problems on different types of computational hardware. We additionally discuss domain decomposition as a method for attacking problems which are not differentiable at points. Throughout the dissertation, we apply our work to problems arising from the Schrödinger equation and the Poisson equation.
Subject Area
Mathematics|Computer science
Recommended Citation
Bockelman, Brian Paul, "Solving partial differential equations using sinc methods" (2008). ETD collection for University of Nebraska-Lincoln. AAI3315327.
https://digitalcommons.unl.edu/dissertations/AAI3315327