Large scale iterative solvers by combining FMM and H-matrices

2017 Fiscal Year Final Research Report

• Project/Area Number: 16H05859
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: High performance computing
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Yokota Rio 東京工業大学, 学術国際情報センター, 准教授 (20760573)
• Research Collaborator: Li Xiaoye S. Lawrence Berkeley National Laboratory ; Keyes David E. King Abdullah University of Science and Technology
• Project Period (FY): 2016-04-01 – 2018-03-31
• Keywords: H行列 / FMM / GPU / LU分解

Outline of Final Research Achievements

In FY2016, we extended the FMM to H-matrices and developed a LU decomposition code using H-matrices. The dual tree traversal of exaFMM was used to determine the block cluster tree for arbitrary admissibility conditions, which allowed tasked based parallelization of the compression part of the H-matrix code. In FY2017, we further optimized inner kernels of the H-matrix code and compared H-matrices with multigrid for real applications. The use of batched MAGMA enabled us to maximize the performance of GPUs even for small matrices. The advantage of H-matrices over multigrid depends on the condition number of the matrix, while the H-matrix becomes advantageous as the degree of parallelism increases.

Free Research Field

高性能計算