ITERATIVE SOLVERS FOR PSEUDO-HERMITIAN EIGENPROBLEMS WITH APPLICATION TO LARGE-SCALE BETHE-SALPETER EQUATIONS

2024

COMISION DE LAS COMUNIDADES EUROPEA

I+D COLAB. COMPETITIVA

Román Moltó José Enrique

Eigenvalue problems lie at the core ot many physical applications and beyond. While otten hermitian matrices (HMs) appear, more in general, broader classes of matrices need to be studied. In the present proposal we consider the class of structured pseudo-hermitian matrices (SPHMs). SPHMs emerge, far example, when studying interacting particle-hole hamiltonians, whose eigenvalues and eigenvectors need to be computed to determine the optical properties of materials. Nowadays, when SPHMs need to be solved, algorithms far non-hermitian matrices (NHMs) are frequently used. Indeed, specific algorithms far SPHMs have been developed only far full diagonalization. Far the case of particle-hole hamiltonians, a specific iterative algorithm far SPHMs has also been developed. However, while the algorithm has been very successful, it does not give access to eigenvalues and eigenvectors of the matrices, which are often also needed. In this propasa! we will develop a novel algorithm able to provide, via an iterative approach, a subset of the eigenvalues and eigenvectors, specific far SPHMs. In doing so, we will systematically compare the performance of our algorithm against standard algorithms far NHMs, and also against algorithms far HMs (which can often be applied if an approximated version of the SPHM is considered). The comparison will be done both in serial and running with MPI and/or on GPUs. This novel algorithm far SPHMs will be directly coded inside the SLEPc library, thus ensuring that it will be made publicly available to the community and distributed. Moreover we will call it via a simple subroutine, which will be embedded in the yambo code. The latter is already interfaced with the SLEPc library, and this structure will ensure a smooth transition towards realistic applications in the future.