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Semiempirical Molecular Dynamics (SEMD) I: Midpoint-Based Parallel Sparse Matrix-Matrix Multiplication Algorithm for

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This study introduces a new, efficient parallel algorithm for sparse matrix-matrix multiplication, improving performance and scalability for electronic structure calculations. The method achieves near-perfect linear scaling and constant time complexity.

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Area of Science:

  • Computational Chemistry
  • Numerical Analysis
  • High-Performance Computing

Background:

  • Sparse matrix-matrix multiplication is crucial for electronic structure theory.
  • Existing methods face challenges in performance and scalability.

Purpose of the Study:

  • To present a novel, efficient, and massively parallel sparse matrix-matrix multiplication algorithm.
  • To demonstrate its suitability for matrices with decay and its application in electronic structure theory.

Main Methods:

  • Algorithm inspired by the midpoint method, exploiting data locality.
  • Massively parallel implementation suitable for matrices with decay.
  • Application in constructing density matrices for Hartree-Fock, density functional theory, and semiempirical Hamiltonians.

Main Results:

  • Achieves better performance and scalability compared to state-of-the-art methods.
  • Demonstrates near-perfect linear scaling up to a characteristic matrix length.
  • Achieves linear scaling with system size and constant time complexity regarding memory.

Conclusions:

  • The novel algorithm offers significant improvements in efficiency and scalability for sparse matrix-matrix multiplication.
  • It is highly effective for density matrix construction in electronic structure calculations.
  • The implementation scales effectively to large process counts (up to 185,193).