Veezhinathan Kamakoti

Industries in general and automotive industries in particular, use Finite Element Analysis (FEA) for better solutions to the engineering problems they encounter. The reliability of the Finite Element method can be improved to a larger extent by Adaptive Finite Element Analysis (AFEA). As we look towards increasingly accurate solutions, the process becomes computationally intensive and requires parallel and economic high-performance scientific computing environments to solve them. In this paper we present a parallel implementation of AFEA on a cluster of workstations and illustrate its efficiency and scalability with examples. In this process, we have developed a user-friendly environment for Parallel Distributed computing which is portable on top of both Parallel Virtual Machine (PVM) and Message Passing Interface (MPI) message passing layers. We have addressed the issues of the several stages in AFEA from a parallel computing perspective that includes Domain decomposition, Parallel Mesh generation, Parallel Finite Element Analysis using a Substructuring technique and Load balancing.

We present an efficient and simple randomized parallel algorithm, for finding the Closest Pair, in a set of n points in D - dimensional space, where (D≥2) is a fixed constant and the distances are measured in Lt metrics, 1≤t≤∞.

In this paper, we present optimal O(log n) time, O(n/log n) processor EREW PRAM parallel algorithms for finding the connected components, cut vertices, and bridges of a permutation graph. We also present an O(log n) time, O(n) processor, CREW PRAM model parallel algorithm for finding a Breadth First Search (BFS) spanning tree of a permutation graph rooted at vertex 1 and use the same to derive an efficient parallel algorithm for the All Pairs Shortest Path problem on permutation graphs. © 1995 Academic Press, Inc.

In this paper we present the new data structure Colored Sector Search Tree (CSST) for solving the Nearest-Foreign-Neighbor Query Problem (NFNQP): Given a set S of n colored points in ℝD, where D ≥ 2 is a constant, and a subset Sʹ ⊂ Sʹ stored in a CSST, for any colored query point q ∈ IRD a nearest foreign neighbor in Sʹ, i.e. a closest point with a different color, can be reported in O(log n(log log n)D−1) time w.r.t. a polyhedral distance function that is defined by a star-shaped polyhedron with O(1) vertices; note that this includes the Minkowski metrics d1 and d∞. It takes a preprocessing time of O(n(log n)D−1) to construct the CSST. Points from S can be inserted into the set Sʹ and removed from Sʹ in O(log n(log log n)D−1) time. The CSST uses O(n(log n)D−1) space. We present an application of the data structure in the parallel simulation of solute transport in aquifer systems by particle tracking. Other applications may be found in GIS (geo information systems) and in CAD (computer aided design). To our knowledge the CSST is the first data structure to be reported for the NFNQP.

We solve the difficult part of constructing a binary tree from its inorder and preorder traversals, finding the (right-son, parent) pairs, and outline an optimal parallel algorithm in the EREW PRAM model for constructing the binary tree. © 1992.