Analysis of Hierarchical Compression Parallel Solver for BEM Problems on Intel Xeon CPUs
We compare the performance of traditional Gaussian elimination with a solver utilizing hierarchical compression of the matrix. The test problems are obtained by Boundary Element Method (BEM) simulation of laminar flow around airfoils. The most computationally expensive part of the BEM algorithm is to solve the arising system of linear algebraic equations. The related dense matrix can be compressed using a Hierarchically Semi-Separable (HSS) representation. This significantly lowers the computational complexity of the solution method, thus allowing faster overall execution.
The performance of STRUMPACK library implementation of HSS and the MKL direct solver is compared on Intel Xeon architecture. At the end, we examine the accuracy of the HSS approximation using the (exact) results of Gaussian elimination as a reference solution.
The partial support by the Bulgarian NSF Grant DN 12/2 is acknowledged. The firs author is also supported trough Bulgarian Academy of Sciences Program for support of Ph.D. Students.
We acknowledge the opportunity to run the numerical tests on the HPC cluster AVITOHOL  of the Institute of Information and Communication Technologies, Bulgarian Academy of Sciences.
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