Authors
G. Sadaka, P. Jolivet, E. G. Charalampidis and I. Danaila
Abstract
We present and distribute a parallel finite-element toolbox written in the free software FreeFem++ for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions.
The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFem++ with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method.
Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFem++ with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states.
Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox’s results with known theoretical and numerical findings that have been reported in the literature.
Supplemental material: 3D one-component BEC continuation
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3D one-component BEC with single-charged vortex-line configuration
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Real part ωr and imaginary part ωi of eigenvalues
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3D one-component BEC with vortex-ring with two (oppositely charged) vortex-line handles configuration
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Real part ωr and imaginary part ωi of eigenvalues
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Supplemental material: 2D two-component BEC continuation
The dark-bright soliton state
Snapshots of the solution of the 1st component
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Snapshots of the solution of the 2nd component
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Real and imaginary part of eigenvalues
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The ground state and soliton necklace state
Snapshots of the solution of the 1st component
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Snapshots of the solution of the 2nd component
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Real and imaginary part of eigenvalues
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The ground state and multipole state
Snapshots of the solution of the 1st component
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Snapshots of the solution of the 2nd component
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Real and imaginary part of eigenvalues
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Supplemental material: 3D two-component BEC continuation
The dark-bright soliton stripe (with the ground state in ϕ1 and the planar dark soliton in ϕ2)
Snapshots of the solution of the 1st component
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Snapshots of the solution of the 2nd component
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Real and imaginary part of eigenvalues
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The vortex-ring-bright state (with the ground state in ϕ1 and the vortex-ring state in ϕ2)
Snapshots of the solution of the 1st component
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Snapshots of the solution of the 2nd component
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Real and imaginary part of eigenvalues
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