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Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set
Chandra Saravanan1, Yihan Shao, Roi Baer
1Department of Chemistry, University of California, Berkeley, California 94720, USA.
Journal of Computational Chemistry
|March 13, 2003
Summary
A new sparse matrix multiplication method using multiatom blocks significantly speeds up calculations. This approach, optimized with Basic Linear Algebra Subroutines (BLAS), achieves up to 10x faster performance for linear-scaling methods.
Area of Science:
- Computational chemistry
- Materials science
- Scientific computing
Background:
- Developing linear-scaling methods requires efficient matrix multiplication.
- Atom-centered basis functions are commonly used in computational chemistry.
- Conventional sparse matrix multiplication can be a bottleneck.
Purpose of the Study:
- To report a novel sparse matrix multiplication scheme utilizing multiatom blocks.
- To enhance the efficiency of linear-scaling methods in computational chemistry.
- To optimize performance by balancing computational trade-offs.
Main Methods:
- Implementation of a sparse matrix multiplication scheme with multiatom blocks.
- Leveraging highly optimized Basic Linear Algebra Subroutines (BLAS) for efficiency.
- Investigating the impact of block size on computational performance.
Main Results:
- The multiatom blocking scheme offers significant speedups compared to element-by-element methods.
- Optimal block sizes were determined to be between 40 and 100 basis functions.
- Achieved 55-75% of peak machine performance on an IBM RS6000 workstation.
- Demonstrated up to 10 times faster computation for blocked sparse matrix multiplications.
Conclusions:
- The multiatom block sparse matrix multiplication is a valuable tool for linear-scaling methods.
- The method provides substantial computational gains for various molecular systems.
- Optimal block size selection is crucial for maximizing performance and minimizing sparsity loss.
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