FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

TL;DR

FELIX-2.0 is an improved finite element solver for the time-dependent generator coordinate method with Gaussian overlap approximation, enabling more efficient and flexible quantum many-body system simulations, especially in nuclear fission studies.

Contribution

This paper introduces version 2.0 of FELIX, featuring advanced numerical methods, support for new finite element types, and a redesigned workflow for improved performance and accuracy.

Findings

FELIX-2.0 can solve generalized TDGCM+GOA equations with a metric term.

The new version achieves about 20 times faster calculations for Pu240 fission mass distributions.

Benchmark results show high accuracy with spectral element methods at higher polynomial degrees.

Abstract

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schr\"odinger equation in a multi-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solves the collective Schr\"odinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank-Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of Pu240 and Fm256. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fission mass distributions of Pu240, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).