The KiT-RT framework is an open source project for radiation transport written in C++ programming language.

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Special attention has been paid to the application of radiation therapy and treatment planning.

The framework provides rich deterministic solver types for different domain-specific problems.

A list of current supported models and equations is as follows.

- linear Boltzmann (:math:`S_N`) equation

- spherical harmonics (:math:`P_N`) equations

- entropy-closure moment (:math:`M_N`) equations

- continuous slowing down equation

Design philosophy

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The code hierarchy is designed as intuitive and neat as possible.

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Finite volume method is a proven approach for simulating conservation laws.

Compared with the existing open-source softwares, e.g. OpenFOAM, SU2 and Clawpack, Kit-RT holds the novelty through the following points:

- Comprehensive support for kinetic theory and phase-space equations

- radiation therapy

- Special focus on radiation therapy

- Lightweight design to ensure the flexibility for secondary development

How to get help?

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The software is being developed by members of the group `CSMM <https://www.scc.kit.edu/en/aboutus/rg-csmm.php>`_ at the Karlsruhe Institute of Technology (KIT).

If you are interested in using KiT-RT or are trying to figure out how to use it, please feel free to get in touch with `us <authors>`_.

If you are interested in using KiT-RT or are trying to figure out how to use it, please feel free to get in touch with `us <authors.html>`_.

Do open an issue or pull request if you have questions, suggestions or solutions.

where the left and right hand sides model particle transports and collisions correspondingly.

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@@ -46,16 +47,14 @@ In the KiT-RT solver, we are interested in the linear Boltzmann equation, where

Therefore, the Boltzmann can be simplified as the linear equation with respect to :math:`f`.

.. math::

:label: linbz

\partial_{t} f(v)+v \cdot \nabla_{x} f(v)=\int k\left(v, v^{\prime}\right)\left(f\left(v^{\prime}\right)-f(v)\right) d v^{\prime}-\tau f(v)

For convenience, it is often reformulated with polar coordinates :math:`\{r, \phi, \theta \}`.

.. math::

:label: porbz

&\left[\frac{1}{v(E)} \frac{\partial}{\partial t}+\Omega \cdot \nabla+\Sigma_t (r, E, t)\right] \psi(r, \Omega, E, t) \\

&\left[\frac{1}{v(E)} \partial_{t} +\Omega \cdot \nabla+\Sigma_t (r, E, t)\right] \psi(r, \Omega, E, t) \\

&=\int_{0}^{\infty} d E^{\prime} \int_{\mathcal R^2} d \Omega^{\prime} \Sigma_{s}\left(r, \Omega^{\prime} \bullet \Omega, E^{\prime} \rightarrow E\right) \psi\left(r, \Omega^{\prime}, E^{\prime}, t\right) + Q(r, \Omega, E, t)

The particle distribution :math:`\psi(r, \Omega, E, t)` here is often named as angular flux, :math:`\{\Sigma_s, \Sigma_t \}` are the scattering and total cross sections correspondingly, and :math:`Q` denotes a source term.

Here, we define :math:`\widetilde\Sigma_{t}(\widetilde E):=\Sigma_t(E(\widetilde E))` and :math:`\widetilde\Sigma_{s}(\widetilde E,\Omega\cdot\Omega'):=\Sigma_s(E(\widetilde E),\Omega\cdot\Omega')`. Finally, to obtain a positive sign in front of the energy derivative, we transform to