ALBERT

Description: The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Description: A bidirectional horizontal-path optical link was demonstrated between Strawberry Peak (SP), Lake Arrowhead, California, and the JPL Table Mountain Facility (TMF), Wrightwood, California, during June and November of 1998. The 0.6-m telescope at TMF was used to broadcast a 4-beam 780-nm beacon to SP. The JPL-patented Optical Communications Demonstrator (OCD) at SP received the beacon, performed ne tracking to compensate for the atmosphere-induced beacon motion and retransmitted a 844-nm communications laser beam modulated at 40 to 500 Mb/s back to TMF. Characteristics of the horizontal-path atmospheric channel as well as performance of the optical communications link were evaluated. The normalized variance of the irradiance fluctuations or scintillation index delta2/I at either end was determined. At TMF where a single 844-nm beam was received by a 0.6-m aperture, the measured delta2/I covered a wide range from 0.07 to 1.08. A single 780-nm beam delta2/I measured at SP using a 0.09-m aperture yielded values ranging from 0.66 to 1.03, while a combination of four beams reduced the scintillation index due to incoherent averaging to 0.22 to 0.40. This reduction reduced the dynamic range of the fluctuations from 17 to 21 dB to 13 to 14 dB as compared with the OCD tracking sensor dynamic range of 10 dB. Predictions of these values also were made based on existing theories and are compared. Generally speaking, the theoretical bounds were reasonable. Discussions on the probability density function (PDF) of the intensity fluctuations are presented and compared with the measurements made. The lognormal PDF was found to agree for the weak scintillation regime as expected. The present measurements support evidence presented by earlier measurements made using the same horizontal path, which suggests that the aperture averaging effect is better than theoretically predicted.