Abstract
The parquet formalism to calculate the two-particle Green’s functions of large systems requires the
solution of a large, sparse, complex system of quadratic equations. If Nf Matsubara frequencies are used for a
system of size Nc , and Newton’s method is used to solve the nonlinear system, the Jacobian system has O(8Nt^3 )
variables and O(40Nt^4 ) complex entries where Nt = Nc Nf . For Nt = 1024, the nonlinear system has over 8.5
billion degrees of freedom and the sparse Jacobian will require over 351 TBytes of memory. The Jacobian is very
expensive to store but the matrix-vector products can be computed directly. We are developing a highly scalable
parallel solver that uses both OpenMP and MPI to exploit the multicore nodes. We present initial scalability results
on the Cray XT5 that suggests the code can be scaled to solve larger problems with Nt ≥ 1024.
