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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.09484 |
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| _version_ | 1866912182623535104 |
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| author | Stammer, Pia Burlacu, Tiberiu Wahl, Niklas Lathouwers, Danny Kusch, Jonas |
| author_facet | Stammer, Pia Burlacu, Tiberiu Wahl, Niklas Lathouwers, Danny Kusch, Jonas |
| contents | Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint.
For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Deterministic Dynamical Low-rank Approach for Charged Particle Transport Stammer, Pia Burlacu, Tiberiu Wahl, Niklas Lathouwers, Danny Kusch, Jonas Numerical Analysis Computational Physics Medical Physics Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint. For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches. |
| title | A Deterministic Dynamical Low-rank Approach for Charged Particle Transport |
| topic | Numerical Analysis Computational Physics Medical Physics |
| url | https://arxiv.org/abs/2412.09484 |