K. Esselink, "The order of Appel's algorithm," Inform. Processing Lett., vol. 41, pp. 141--147, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....particle. There are two types of algorithms for the body problem: the hierarchical algorithm of Appel [1] and the multipole algorithm of Greenberg and Rohklin [6] When Appel first published his paper, he thought the time complexity was . Later, a careful analysis shows the time complexity is [4]. At about the same time, Greengard and Rohklin [6] proposed the multipole algorithm and proved its time complexity is . FastCap is based on the multipole algorithm, while our algorithm is based on Appel s algorithm [1] and a radiosity algorithm [8] Hanrahan et al. 8] used the ideas in Appel s ....

....representation of the coefficient matrix would require 64 entries. However, the block matrix has only 40 entries. Furthermore, if we use uniform grid discretization, then there would be a total of 16 panels and 256 entries. Esselink proved the number of interactions in the above algorithm is [4]. Callahan and Kosaraju show that under a Fig. 3. Potential coefficient matrix with block entries. very general condition, algorithms similar to ours contain interactions [2] We now give an intuitive explanation of why the block matrix contains block entries. For simplicity, consider panels of ....

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K. Esselink, "The order of Appel's algorithm," Inform. Processing Lett., vol. 41, pp. 141--147, 1992.

.... of algorithms for the n body problem: the hierarchical algorithm of Appel [1] 1985) and the multipole algorithm of Greenberg and Rohklin [5] 1987) When Appel first published his paper, he thought the time complexity was O(n log n) Later, a careful analysis shows the time complexity is O(n) [3]. At about the same time, Greengard and Rohklin [5] proposed the multipole algorithm, and proved its time complexity is O(n) The capacitance extraction algorithm FastCap is related to the multipole algorithm, while our algorithm is related to Appel s algorithm [1] and a radiosity algorithm [7] ....

....of the tree. Therefore, each node in the tree interacts with a constant number of other nodes, and the total number of block entries is O(n) Esselink did a detailed analysis on the number of interactions by Appel s algorithm for the general case, and compared it with the multipole algorithm [3]. In Figure 2, it shows that each panel undergoes a constant number of interactions with other panels, regardless of their level in the tree. Large panels that are far apart interact directly, in the same way that small panels near each other interact directly. Finally, we analyze the relationship ....

K. Esselink, "The order of Appel's algorithm," Information Processing Letters, Vol. 41, 1992, 141--147.

....roughly spherical cells. Some care is taken to construct a good set of cells which minimize the higher order multipole moments of the cells. The MAC is based on the size of interacting cells. The method was originally thought to be O(N log N) but has more recently been shown to be O(N) [2]. The Barnes Hut (BH) algorithm [3] uses a regular, hierarchical cubical subdivision of space (an oct tree in three dimensions) A two dimensional illustration of such a tree (a quad tree) is show in Fig. 1. Construction of BH trees is much faster than construction of Appel trees. In the BH ....

K. Esselink, "The order of Appel's algorithm," Information Processing Let., vol. 41, pp. 141--147, 1992.

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