(WHPC03) Solving the Schrödinger Eigenproblem with PUMA
Women in HPC Poster
Scientific Software Development
TimeTuesday, June 18th12:30pm - 5pm CEST
DescriptionIn this presentation we are concerned with the efficient approximation of the Schrödinger eigenproblem on general triclinic cells using an orbital-enriched flat-top partition of unity method (PUM).
To this end, we present the PUMA software framework, an MPI-parallel implementation of the flat-top PUM, which allows the user to access its full approximation power by employing arbitrary, problem-dependent enrichment functions. Furthermore, PUMA provides both a variational mass lumping scheme and a stability transformation that handles occurring stability problems in the resulting system matrices.
As an application example, we show the effective utilization of PUMA for the Schrödinger eigenproblem, where we observe a significant reduction of DOFs needed to obtain chemical accuracy compared to non-enriched approaches for model problems. Furthermore, due to the mass lumping scheme and stabilization we only have to solve a stable standard eigenvalue problem instead of a generalized eigenvalue problem. We show results obtained on the Drachenfels cluster at Fraunhofer SCAI. As more realistic physical problems can become very large, a more efficient parallel integration scheme as well as an optimized eigenvalue solver are interesting future challenges.