### Abstract

Kinetic equations have proven to be useful models in different applications as, e.g., neutron transport,

gas dynamics, semiconductors, photon propagation, opinion dynamics or biological network

formation. One of the key challenges in the numerical simulation of kinetic equations is their highdimensionality.

For instance, in neutron transport, the solution depends in general on three spatial,

three angular and one temporal variable. Based on the mixed variational formulation analyzed in

[1] we will present a strategy for the design of efficient numerical approximation schemes. The formulation

of [1] incorporates boundary conditions in a weak sense. Unfortunately, the bilinear form

corresponding to the boundary conditions couples spatial and angular variables in a non-smooth way

rendering a tensor product approximation not straight-forward. As a remedy we introduce an absorbing

layer and consider a perturbed variational problem which leads to matrices with tensor product

structure. Hence, even in the full tensor product approximation, the resulting discrete operators can

be stored efficiently. We provide corresponding error estimates for our approach.

gas dynamics, semiconductors, photon propagation, opinion dynamics or biological network

formation. One of the key challenges in the numerical simulation of kinetic equations is their highdimensionality.

For instance, in neutron transport, the solution depends in general on three spatial,

three angular and one temporal variable. Based on the mixed variational formulation analyzed in

[1] we will present a strategy for the design of efficient numerical approximation schemes. The formulation

of [1] incorporates boundary conditions in a weak sense. Unfortunately, the bilinear form

corresponding to the boundary conditions couples spatial and angular variables in a non-smooth way

rendering a tensor product approximation not straight-forward. As a remedy we introduce an absorbing

layer and consider a perturbed variational problem which leads to matrices with tensor product

structure. Hence, even in the full tensor product approximation, the resulting discrete operators can

be stored efficiently. We provide corresponding error estimates for our approach.

Original language | English |
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Pages | 356-356 |

Publication status | Published - 28 Sep 2017 |

Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017 |

### Conference

Conference | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 |
---|---|

Abbreviated title | ENUMATH |

Country | Norway |

City | Voss |

Period | 25/09/17 → 29/09/17 |

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## Cite this

Schlottbom, M., Botchev, M. A., & Egger, H. (2017).

*An approach for the efficient solution of the time-dependent linear Boltzmann equation*. 356-356. Abstract from European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway.