Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma. (English) Zbl 1349.76453
Summary: We consider numerical modeling of the Farley-Buneman instability in the Earth’s ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed.
The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.
The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 82D10 | Statistical mechanics of plasmas |
| 86A25 | Geo-electricity and geomagnetism |
Keywords:
high-dimensional problems; DMRG; MPS; tensor train format; ionospheric irregularities; plasma waves and instabilities; Vlasov equation; hybrid methodsSoftware:
MatlabReferences:
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