Browsing by Subject "Tree data structures"

Now showing 1 - 3 of 3

Open Access
Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Fast and accurate solution of large-scale scattering problems obtained by integral-equation formulations for conducting surfaces is considered in this paper. By employing a parallel implementation of the multilevel fast multipole algorithm (MLFMA) on relatively inexpensive platforms. Specifically, the solution of a scattering problem with 33,791,232 unknowns, which is even larger than the 20-million unknown problem reported recently. Indeed, this 33-million-unknown problem is the largest integral-equation problem solved in computational electromagnetics.
Open Access
Online anomaly detection with nested trees
(Institute of Electrical and Electronics Engineers Inc., 2016) Delibalta, I.; Gokcesu, K.; Simsek, M.; Baruh, L.; Kozat, S. S.
We introduce an online anomaly detection algorithm that processes data in a sequential manner. At each time, the algorithm makes a new observation, produces a decision, and then adaptively updates all its parameters to enhance its performance. The algorithm mainly works in an unsupervised manner since in most real-life applications labeling the data is costly. Even so, whenever there is a feedback, the algorithm uses it for better adaptation. The algorithm has two stages. In the first stage, it constructs a score function similar to a probability density function to model the underlying nominal distribution (if there is one) or to fit to the observed data. In the second state, this score function is used to evaluate the newly observed data to provide the final decision. The decision is given after the well-known thresholding. We construct the score using a highly versatile and completely adaptive nested decision tree. Nested soft decision trees are used to partition the observation space in a hierarchical manner. We adaptively optimize every component of the tree, i.e., decision regions and probabilistic models at each node as well as the overall structure, based on the sequential performance. This extensive in-time adaptation provides strong modeling capabilities; however, it may cause overfitting. To mitigate the overfitting issues, we first use the intermediate nodes of the tree to produce several subtrees, which constitute all the models from coarser to full extend, and then adaptively combine them. By using a real-life dataset, we show that our algorithm significantly outperforms the state of the art. © 1994-2012 IEEE.
Open Access
Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
(IEEE, 2009-06) Ergül, Özgür; Gürel, Levent
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary conditions for the tangential electric and magnetic fields. Discretizations of large objects with dimensions of hundreds of wavelengths lead to dense matrix equations with hundreds of millions of unknowns. Solutions are performed iteratively, where the matrix-vector multiplications are performed efficiently by using the multilevel fast multipole algorithm (MLFMA). Solutions are also parallelized on a cluster of computers using a hierarchical partitioning strategy, which is well suited for the multilevel structure of MLFMA. Accuracy and efficiency of the implementation are demonstrated on electromagnetic problems involving as many as 205 million unknowns, which are the largest integral-equation problems ever solved in the literature.