News
2007
Our seminar series focuses on all aspects of electromagnetics and
acoustics (theory/computational/experimental).
The key motivation being:
(i) expose our students to research in related areas
(ii) enhance the visibility of this group
(iii) provide a forum for
discussion and possibly collaboration.
Details are as follows Day: Tuesday; Jan 9th Time: 3:00 - 4:00 pm Place: 1235 Anthony Hall The title and abstract for the first seminar is as follows: Speaker: B. Shanker; ECE, MSU
*Title: An O(N) Method for Computing of Potentials of the Form for all real *
The need to compute potentials of the form O(N) for occur in a variety of areas ranging from electromagnetics to biophysics to molecular dynamics to astrophysics, etc. For instance, Coulomb, London, Lennard-Jones, H-bonds are of the form = 1, 5, 6 (and 12), 10, respectively. For systems with source/observation points, the cost of computing these potentials scales proportional to . Methods to overcome this computational bottleneck have been a topic of research for while. For instance, the fast multipole method (FMM) and their cousins--tree codes--have revolutionized the computation of electrostatic potentials (). Here, the reduction in computational cost is achieved using a multipole-representation for the Green's function. However, framing these in terms of Cartesian harmonics provides several advantages: It is possible (i) to exploit symmetry; (ii) to construct a methodology wherein the errors are /independent/ of the height of the tree; (iii) to combine different potential functions together; and (iv) to extended to other potential functions. This talk will first focus on construction of classical FMM using Cartesian harmonics, and then extend this for potentials where . Several numerical results will be presented to demonstrate the accuracy and efficiency of the proposed scheme. We will also demonstrate how this scheme can be extended to Yukawa (shielded Coulomb), lattice-gas, Gauss potentials, and low-frequency Helmholtz potentials.
