We consider three different ways of algorithmization of the Janashia-Lagvilava spectral factorization method. The first algorithm is faster than the second one, however, it is only suitable for matrices of low dimension. The second algorithm, on the other hand, can be applied to matrices of substantially larger dimension. The third algorithm is a superfast implementation of the method, but only works in the polynomial case under the additional restriction that the zeros of the determinant are not too close to the boundary. All three algorithms fully utilize the advantage of the method, which carries out spectral factorization of leading principal submatrices step-by-step. The corresponding results of numerical simulations are reported in order to describe the characteristic features of each algorithm and compare them to other existing algorithms.

With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process, is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners, compared to state-of-the-art ILU family of preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model - based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated on diverse heterogeneous multiclusters - platforms for which performance prediction is particularly challenging.

Abstract This paper describes Indiana University's implementation, performance testing, and use of a large high performance computing system. IU's Big Red, a 20.48 TFLOPS IBM e1350 BladeCenter cluster, appeared in the 27th Top500 list as the 23rd fastest supercomputer in the world in June 2006. In spring 2007, this computer was upgraded to 30.72 TFLOPS. The e1350 BladeCenter architecture, including two internal networks accessible to users and user applications and two networks used exclusively for system management, has enabled the system to provide good scalability on many important applications while being well manageable. Implementing a system based on the JS21 Blade and PowerPC 970MP processor within the US TeraGrid presented certain challenges, given that Intel‐compatible processors dominate the TeraGrid. However, the particular characteristics of the PowerPC have enabled it to be highly popular among certain application communities, particularly users of molecular dynamics and weather forecasting codes. A critical aspect of Big Red's implementation has been a focus on Science Gateways, which provide graphical interfaces to systems supporting end‐to‐end scientific workflows. Several Science Gateways have been implemented that access Big Red as a computational resource—some via the TeraGrid, some not affiliated with the TeraGrid. In summary, Big Red has been successfully integrated with the TeraGrid, and is used by many researchers locally at IU via grids and Science Gateways. It has been a success in terms of enabling scientific discoveries at IU and, via the TeraGrid, across the US. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we report on some computational experience in solving ocean acoustic propagation problems in three dimensions on supercomputers. The underlying Helmholtz equation is transformed into a parabolic-type equation in the Lee-Saad-Schultz model [5], which has a natural alternating direction implicit (ADI) implementation. We give estimates of the computing power required to solve problems with realistic sound velocity profiles. We then give performance results for the CRAY X-MP and for the computational kernel on the Intel hypercube (iPSC/2). We conclude with some remarks about architectural enhancements that would be beneficial to our application.