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[Licence| Download | New Version Template] aeyz_v1_0.tar.gz(9975 Kbytes)
Manuscript Title: FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation
Authors: D. Regnier, M. Verrière, N. Dubray, N. Schunck
Program title: FELIX-1.0
Catalogue identifier: AEYZ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 200(2016)350
Programming language: C++.
Computer: Intel Xeon, Intel Core.
Operating system: LINUX.
RAM: Memory usage depends on the number of nodes in the calculation mesh as well as on the degree of the interpolation polynomials. For a 1D calculation with linear polynomials on a mesh with 600 nodes, memory usage is approximately 3.3 MB; in a realistic simulation of fission on a 2D mesh with quadratic polynomials and 1.3 105 nodes, it reaches 1.5 GiB.
Keywords: FELIX, Finite element method, Generator coordinate method, Gaussian overlap approximation, Nuclear fission, Classification: 17.23 Fission and Fusion Processes.
Classification: 17.23.

External routines: The solver itself requires the BLAS and LAPACK libraries, and a Fortran compiler with OpenMP support. Building the documentation requires DoxyGen-1.8.6 or higher. Building the full set of tools also requires GSL, PETSc, SLEPc and Boost. In particular, environment variables PETSC_DIR, PETSC_ARCH, SLEPC_DIR and SLEPC_ARCH must be set.

Nature of problem:
Nuclear fission is a relatively slow process compared to the typical timescale of the intrinsic motion of the nucleons. In the adiabatic approximation, it can be described as a large amplitude collective motion driven by only a few collective degrees of freedom. In the time-dependent generator coordinate method (TDGCM), the nuclear wave-function is thus described as a time-dependent, linear superposition of basis functions in this collective space. Further assuming a Gaussian overlap approximation (GOA) for the basis functions, the time-dependent Schrödinger equation can be reduced into a local, time-dependent, Schrödinger-like equation in collective space. This is the TDGCM+GOA equation. Scission configurations are defined as a hyper-surface in the N-dimensional collective space. Fission fragment distributions are then computed by integrating over time the flux of the collective wave-packet across the scission hyper-surface. This microscopic approach to fission fragment distributions is fully quantum-mechanical.

Solution method:
FELIX solves the TDGCM+GOA equation by using the Galerkin finite element method to discretize the N-dimensional collective space, and the Crank-Nicolson scheme to solve for the time evolution. At each time step, this procedure requires solving a linear system of equation involving sparse, complex, symmetric matrices. FELIX employs an iterative QMR algorithm to perform matrix inversion.

Restrictions:
Although the program can operate in an arbitrary number of dimensions N, it has only been tested in practice on 1, 2 and 3 dimensional meshes.

Additional comments:
The code has checkpointing capabilities: the collective wave-function, norm a and energy kernels are stored on disk every n iterations, ensuring that the program can resume where it stops.

Running time:
Running time grows linearly with the number of time-steps requested by the user. It is also highly dependent on the number of nodes in the space mesh. Two periods of a 1D harmonic oscillator (600 nodes, 800 time steps) are typically computed in a few seconds on one thread of a Intel(R) Core(TM) i5 CPU. A 2-dimensional realistic case of fission (105 nodes, 105 time steps) requires roughly 10 hours on 10 threads of an Intel Xeon EP X5660 processor.