### Uittreksel

Originele taal-2 | Engels |
---|---|

Pagina's (van-tot) | 739-771 |

Aantal pagina's | 33 |

Tijdschrift | Journal of Scientific Computing |

Volume | 68 |

Nummer van het tijdschrift | 2 |

Vroegere onlinedatum | 11 feb 2016 |

DOI's | |

Status | Gepubliceerd - aug 2016 |

### Vingerafdruk

### Citeer dit

*Journal of Scientific Computing*,

*68*(2), 739-771. https://doi.org/10.1007/s10915-015-0157-6

}

*Journal of Scientific Computing*, vol. 68, nr. 2, blz. 739-771. https://doi.org/10.1007/s10915-015-0157-6

**A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics.** / van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

AU - van Lith, B.S.

AU - ten Thije Boonkkamp, J.H.M.

AU - IJzerman, W.L.

AU - Tukker, T.W.

PY - 2016/8

Y1 - 2016/8

N2 - A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell’s law or the law of specular reflection. Solutions to Liouville’s equation should be constant along curves defined by the Hamiltonian system when the right-hand side is zero, i.e., no absorption or collisions. This consideration allows us to derive a new jump condition, enabling us to construct a first-order accurate scheme. Essentially, the correct physics is built into the solver. The scheme is tested in a two-dimensional optical setting with two test cases, the first using a single jump in the refractive index and the second a compound parabolic concentrator. For these two situations, the scheme outperforms the more conventional method of Monte Carlo ray tracing.

AB - A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell’s law or the law of specular reflection. Solutions to Liouville’s equation should be constant along curves defined by the Hamiltonian system when the right-hand side is zero, i.e., no absorption or collisions. This consideration allows us to derive a new jump condition, enabling us to construct a first-order accurate scheme. Essentially, the correct physics is built into the solver. The scheme is tested in a two-dimensional optical setting with two test cases, the first using a single jump in the refractive index and the second a compound parabolic concentrator. For these two situations, the scheme outperforms the more conventional method of Monte Carlo ray tracing.

U2 - 10.1007/s10915-015-0157-6

DO - 10.1007/s10915-015-0157-6

M3 - Article

VL - 68

SP - 739

EP - 771

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 2

ER -