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The parallel tiled WZ factorization algorithm for multicore architectures

Bylina Beata, Bylina Jarosław

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 2

407--419

The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal theoretical speedup implied by Amdahl’s law.

Parallel FDTD simulation using Task Parallel Library (TPL)

Bolesta I., Demchuk A.

Journal of Applied Computer Science

2016

Vol. 24, nr 2

7--16

The finite-difference time-domain (FDTD) is a numerical analysis technique used for solving computational electrodynamic problems. The nature of the FDTD method is that simulation of big and complicated electromagnetic field problems requires a vast amount of computer operational memory and runtime. Parallel-processing techniques have been broadly applied to FDTD to accelerate the simulations. The parallelism of the FDTD algorithm is based on a fact that the computational domain can be divided into parts (sub-domains), and each processor in a parallel system deals with one or several sub-domains. The FDTD algorithm belongs to data parallelism model and can be effectively implemented on shared memory system architecture. The parallel FDTD method was implemented using TPL library. The Task Parallel Library (TPL) is a library for .NET that makes easy to parallelize the program using the advantages of .NET Framework. The speedup metrics of parallel FDTD algorithm were calculated and compared with Amdahl’s estimated speedup.