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Register a new userFELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation
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We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N $geq$ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.
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It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two $alpha$ particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $Omega$ on the extruded domain $mathcal{C}=Omegatimes[0,infty)$ following Caffarelli and Silvestre (2007). The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyls law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions show that the approach is quasi-optimal in terms of complexity.
The new matrix element generator AMEGIC++ is introduced, dedicated to describe multi-particle production in high energy particle collisions. It automatically generates helicity amplitudes for the processes under consideration and constructs suitable, efficient integration channels for the multi-channel phase space integration. The corresponding expressions for the amplitudes and the integrators are stored in library files to be linked to the main program.
We introduce an open-source package called QTraj that solves the Lindblad equation for heavy-quarkonium dynamics using the quantum trajectories algorithm. The package allows users to simulate the suppression of heavy-quarkonium states using externally-supplied input from 3+1D hydrodynamics simulations. The code uses a split-step pseudo-spectral method for updating the wave-function between jumps, which is implemented using the open-source multi-threaded FFTW3 package. This allows one to have manifestly unitary evolution when using real-valued potentials. In this paper, we provide detailed documentation of QTraj 1.0, installation instructions, and present various tests and benchmarks of the code.
A monolithic coupling between the material point method (MPM) and the finite element method (FEM) is presented. The MPM formulation described is implicit, and the exchange of information between particles and background grid is minimized. The reduced information transfer from the particles to the grid improves the stability of the method. Once the residual is assembled, the system matrix is obtained by means of automatic differentiation. In such a way, no explicit computation is required and the implementation is considerably simplified. When MPM is coupled with FEM, the MPM background grid is attached to the FEM body and the coupling is monolithic. With this strategy, no MPM particle can penetrate a FEM element, and the need for computationally expensive contact search algorithms used by existing coupling procedures is eliminated. The coupled system can be assembled with a single assembly procedure carried out element by element in a FEM fashion. Numerical results are reported to display the performances and advantages of the methods here discussed.
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