Document Type
Conference Proceeding
Publication Date
6-3-2005
Abstract
For a given partial differential equation, such as Poisson’s equation in two dimensions, stipulating the null-space component of the solution is sometimes a useful alternative to specifying boundary conditions in order to determine a unique solution. To implement this approach computationally, we need a sparse and well-conditioned representation of the null space of the relevant differential operator. We discuss how the null-space method works and present an explicit formula for generating a sparse null basis for a uniform, finite-difference discretization of Laplacian operator on the unit square. The formula makes use of a triangular array which has the large Schroeder numbers on its diagonal. We also consider the conditioning of such a basis and demonstrate the use of the basis in a numerical procedure for computing an approximate solution to the patrol differential equation.
Recommended Citation
VanderZee, Hanna, "Explicit Null Space of Discrete Laplacian" (2005). ACMS Conference Proceedings 2005. 20.
https://pillars.taylor.edu/acms-2005/20
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