On efficient block Krylov-solvers for $\mathcal H^2$-matrices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908551833714688 |
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| author | Christophersen, Sven |
| author_facet | Christophersen, Sven |
| contents | Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative solvers are preferred over direct ones due to the cost-efficient matrix-vector multiplications they enable. Solving multiple systems of linear equations with the same hierarchical matrix naturally leads to block methods, which in turn make heavy use of BLAS level-3 functions such as GEMM. We present an efficient implementation of H^2-matrix-vector and H^2-matrix-matrix multiplication that fully exploits the potential of modern hardware in terms of memory and cache utilization. The latter is employed to accelerate block Krylov subspace methods, which we present later as the main results of this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_17257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On efficient block Krylov-solvers for $\mathcal H^2$-matrices Christophersen, Sven Numerical Analysis 65F55, 65F08, 65F10 Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative solvers are preferred over direct ones due to the cost-efficient matrix-vector multiplications they enable. Solving multiple systems of linear equations with the same hierarchical matrix naturally leads to block methods, which in turn make heavy use of BLAS level-3 functions such as GEMM. We present an efficient implementation of H^2-matrix-vector and H^2-matrix-matrix multiplication that fully exploits the potential of modern hardware in terms of memory and cache utilization. The latter is employed to accelerate block Krylov subspace methods, which we present later as the main results of this paper. |
| title | On efficient block Krylov-solvers for $\mathcal H^2$-matrices |
| topic | Numerical Analysis 65F55, 65F08, 65F10 |
| url | https://arxiv.org/abs/2509.17257 |