ABSTRACT
The analysis of transient wave scattering from rigid bodies using integral equation-based techniques is computationally intensive: if carried out using classical schemes, the evaluation of the velocity potential on the surface of a three-dimensional scatterer, represented in terms of Ns spatial basis functions for Nt time steps, requires O(NtNs2) operations. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions. It has been shown that incorporation of the PWTD algorithm into integral equation-based solvers in a two-level setting reduces the computational complexity of a transient analysis to O(NtNs1.5 logNs). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in O(NtNslog2Ns) operations using O(NtNs) memory. Numerical examples that demonstrate the efficacy of the multilevel implementation are also presented.
ABSTRACT
A novel algorithm for fast computation of tomographic image projections is presented. The method comprises a decomposition of an image into subimages followed by an aggregation of projections computed for the subimages. The multilevel domain decomposition algorithm is formulated as a recursive procedure. The computational cost of the proposed algorithm is comparable to that of FFT-based techniques while it appears to be more flexible than the latter. Numerical results demonstrate the effectiveness of the method.
ABSTRACT
We present a new procedure for localizing simultaneously active multiple brain sources that overlap in both space and time on EEG recordings. The source localization technique was based on a spatio-temporal model and a genetic algorithm search routine. The method was successfully applied to the localization of two dipole sources from several sets of simulated potentials with various signal-to-noise ratios (SNR). The different SNR values resembled evoked responses and epileptic spikes as commonly seen in the laboratory. Results of the simulation studies yielded localization accuracy ranging from 0.01 to 0.07 cm with an SNR of 10; from 0.02 to 0.26 cm with an SNR of 5; and from 0.06 to 0.73 cm when the SNR was equal to 2. Additionally, two sets of simulations were based on the dipole arrangements and time activities of data obtained during electrical stimulation of the median nerve in human subjects. These studies yielded localization accuracy within 0.1 cm. We also studied the localization accuracy of the algorithm using a physical model incorporating potential measurements of two current dipoles embedded in a sphere. In this situation the algorithm was successful in localizing the two simultaneously active sources to within 0.07-0.15 cm.
Subject(s)
Algorithms , Computer Simulation , Electroencephalography , Models, Genetic , Brain/physiology , Electric Stimulation , Electrodes, Implanted , Electromagnetic Fields , Evoked Potentials/physiology , Humans , Reproducibility of ResultsABSTRACT
Spatial structures created by pulsed field interactions with surface-bound two-level systems are considered. Superresolved pattern formation is possible by the use of extra degrees of freedom programmed in the time-domain field.
