Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
Matrix computations (3rd ed.)
Locality of Reference in LU Decomposition with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A survey of out-of-core algorithms in numerical linear algebra
External memory algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
New Serial and Parallel Recursive QR Factorization Algorithms for SMP Systems
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Applying recursion to serial and parallel QR factorization leads to better performance
IBM Journal of Research and Development
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
Parallel out-of-core computation and updating of the QR factorization
ACM Transactions on Mathematical Software (TOMS)
Application of filter diagonalization method to numerical solution of algebraic equations
Proceedings of the 2009 conference on Symbolic numeric computation
PaCT'07 Proceedings of the 9th international conference on Parallel Computing Technologies
| Hi-index | 31.45 |
We present an out-of-core filter-diagonalization method which can be used to solve very large electronic structure problems within the framework of the one-electron pseudopotential-based methods. The approach is based on the following three steps. First, nonorthogonal states in a desired energy range are generated using the filter-diagonalization method. Next, these states are orthogonalized using the Householder QR orthogonalization method. Finally, the Hamiltonian is diagonalized within the subspace spanned by the orthogonal states generated in the second step. The main limiting step in the calculation is the orthogonalization step, which requires a huge main memory for large systems. To overcome this limitation we have developed and implemented an out-of-core orthogonalization method which allows us to store the states on disks without significantly slowing the computation. We apply the out-of-core filter-diagonalization method to solve the electronic structure of a quantum dot within the framework of the semiempirical pseudopotential method and show that problems which require tens of gigabytes to represents the electronic states and electronic density can be solved on a personal computer.