Efficient Eigensolver Methods For very large, sparse matrices using high performance computers

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Date/Time:Wednesday, 06 Apr 2016 from 4:10 pm to 5:00 pm
Location:Room 3 Physics Building
Contact:
Phone:515-294-8894
Channel:Nuclear Physics
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James P. Vary, Iowa State University. NOTE: This lecture is also a lecture in the High Performance Computing Seminar Series.

In order to solve forefront problems in quantum many-body theory, we need algorithms tailored for today's high performance computers. Expressing the quantum many-body problem as a Hamiltonian matrix in a basis representation produces the challenge of solving a large sparse matrix eigenvalue problem. The real-world problem of solving ab initio nuclear physics problems requires (1) ability to efficiently evaluate and store the non-vanishing matrix elements for a complicated strong interaction with three-particle interactions and Coulomb contributions, and (2) an efficient method to solve for the lowest 10-100 eigenvalues and eigenvectors for matrix dimensions exceeding one billion basis states.
I will concentrate on an efficient eigensolver based on the Lanczos algorithm suitable for high performance computers with hundreds of thousands of cores.