Load-balanced parallel banded-system solvers

AbstractSolving banded systems is important in the applications of science and engineering. This paper presents a load-balancing strategy for solving banded systems in parallel when the number of processors used is small. An optimization-based load-balancing analysis is given to determine how many loads should be assigned to each processor in order to minimize the time requirement. Some experimentations are carried out on the nCUBE 2E multiprocessor to demonstrate the speedup advantage of the proposed load-balancing strategy. The speedup improvement ratio ranges from 47% to 66% (from 12% to 24%) when using 4 (8) processors

Implementation of parallel tridiagonal solvers for a heterogeneous computing environment

Tridiagonal diagonally dominant linear systems arise in many scientific and engineering applications. The standard Thomas algorithm for solving such systems is inherently serial, forming a bottleneck in computation. Algorithms such as cyclic reduction and SPIKE reduce a single large tridiagonal system into multiple small independent systems which are solved in parallel. We develop portable cyclic reduction and the SPIKE algorithm for Open Computing Language implementations on a range of co-processors in a heterogeneous computing environment, including field programmable gate arrays, graphics processing units and other multi-core processors. We evaluate these designs in the context of solver performance, resource efficiency and numerical accuracy. References Altera. Implementing FPGA design with the OpenCL standard. Technical report, Altera Inc., November 2013. http://www.altera.com/literature/wp/wp-01173-opencl.pdf Altera. Altera SDK for OpenCL: Best practices guide. 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