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Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin
Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin
Theses and Dissertations
In this thesis, a treecode implementing Hermite interpolation is constructed to approximate a summation of pairwise interactions on large data sets. Points are divided into a hierarchical tree structure and the interactions between points and well-separated clusters are approximated by interpolating the kernel function over the cluster. Performing the direct summation takes O(N^2) time for system size N, and evidence is presented to show the method presented in this paper scales with O(N logN) time. Comparisons between this method and existing ones are made, highlighting the relative simplicity and adaptability of this process. Parallelization of the computational step is implemented …
Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin
Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin
Theses and Dissertations
In this thesis, a treecode implementing Hermite interpolation is constructed to approximate a summation of pairwise interactions on large data sets. Points are divided into a hierarchical tree structure and the interactions between points and well-separated clusters are approximated by interpolating the kernel function over the cluster. Performing the direct summation takes O(N^2) time for system size N, and evidence is presented to show the method presented in this paper scales with O(N logN) time. Comparisons between this method and existing ones are made, highlighting the relative simplicity and adaptability of this process. Parallelization of the computational step is implemented …
An Adapative Treecode-Accelerated Boundary Integral Solver For Computing The Electrostatics Of A Biomolecule, Andrew Joseph Szatkowski
An Adapative Treecode-Accelerated Boundary Integral Solver For Computing The Electrostatics Of A Biomolecule, Andrew Joseph Szatkowski
Theses and Dissertations
The Poisson-Boltzmann equation (PBE) is a widely-used model in the calculation of electrostatic potential for solvated biomolecules. PBE is an interface problem defined in the whole space with the interface being a molecular surface of a biomolecule, and has been solved numerically by finite difference, finite element, and boundary integral methods. Unlike the finite difference and finite element methods, the boundary integral method works directly over the whole space without approximating the whole space problem into an artificial boundary value problem. Hence, it is expected to solve PBE in higher accuracy. However, so far, it was only applied to a …