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Since the early days of supercomputing, numerical algorithms have been the application with the highest demand for computing power anywhere. Many of today’s fastest computers in the world, as give in the TOP 500 list, are mostly used for the solution of huge systems of equations as they arise in the simulation of complex large scale problems in engineering and science.
Definitions for the uniform representation of d-dimensional matrices serial- ly in Morton-order (or Z-order) support both their use with cartesian indices, and their divide-and-conquer manipulation as quaternary trees. In the latter case, d-dimensional arrays are accessed as 2d-ary trees. This data structure is important because, at once, it relaxes serious problems of locality and latency, and the...
To solve large systems of linear equations with sparse matrices in parallel, there are three factors that contribute to the com- puting time: the numerical efficiency, the floating point performance, and the scalability. In this paper, we mainly consider the floating point performance. For large linear systems, multi-level techniques, like the cascadic conjugate gradient method (CCG), require significantly...
We present an approach for the efficient parallel solution of convection diffusion equations. Based on iterative nested dissection techniques [1] we extended these existing iterative algorithms to a solver based on nested dissection with incomplete elimination of the unknowns. Our elimination strategy is derived from physical properties of the con- vection diffusion equation, but is independent of...
The most common technique for the parallelization of multi- grid methods is grid partitioning. For such methods Brandt and Diskin have suggested the use of a variant of segmental refinement in order to re- duce the amount of inter-processor communication. A parallel multigrid method with this technique avoids all communication on the finest grid levels. This article will examine some features of this...
A new parallel partitioning algorithm for unstructured par- allel grid generation is presented. This new approach is based on a space- filling curve. The space-filling curve’s indices are calculated recursively and in parallel, thus leading to a very efficient and fast load distribution. The resulting partitions have good edge-cut and load balancing charac- teristics.
This paper analyzes the performance of a parallel solver for discrete-time periodic Riccati equations based on a sequence of orthog- onal reordering transformations of the monodromy matrices associated with the equations. A coarse-grain parallel algorithm is investigated on a Myrinet cluster.
For calibrating the vehicle model of a commercial vehicle dy- namics program a parameter estimation tool has been developed which relies on observations obtained from driving tests. The associated non- linear least-squares problem can be solved by means of mathematical op- timization algorithms most of them making use of first-order derivative information. While the complexity of the investigated...
Dictionary compression belongs to the class of lossless com- pression methods and is mainly used for compressing text files [1, 2, 3]. In this paper, we present a parallel algorithm for one of these coding methods, namely the LZ77 coding algorithm also known as a sliding- window coding algorithm. Although there exist PRAM algorithms [4, 5] for various dictionary compression methods, their rather irregular...
In this paper we describe a parallel version of the potential reduction algorithm for MIMD distributed memory machines, in which the computational kernels arising at each step of the algorithm are concurrently performed by using standard parallel software environments. This approach is shown to be very effective, in contrast to what happens in the active set strategies where the linear algebra computational...
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