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| Title | A Differential Algebraic Framework for the Fast Indirect Boundary Element Method | |||||
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| Abstract | Beam physics at the intensity frontier must account for the beams' realistic surroundings on their dynamics in an accurate and efficient manner. Mathematically, the problem can be expressed as a Poisson PDE with given boundary conditions. Commonly, the Poisson boundary value problem is solved locally within many volume elements. However, it is known the PDE may be re-expressed as indirect bound- ary integral equations (BIE) which give a global solution*. By solving the BIEs on M surface elements, we arrive at the indirect boundary element method (iBEM). Iteratively solving this dense linear system of form Ax = b scales like (m_{i}terations M² ). Accelerating with the fast multipole method (FMM) can reduce this to O(M) if m_{i}terations << M. For N evaluation points, the total complexity would be O(M) + O(N) or O(N) with N = M. We have implemented a constant element version of this fast iBEM based on our previous work with the FMM in the differential algebraic (DA) framework**. This implementation is to illustrate the flexibility and accuracy of our method. A future version will focus on allowing for higher order elements. | |||||
| Footnotes & References | * Sauter, S. and C. Schwab. Boundary Element Methods (2011) ** Abeyratne, S., S. Manikonda, and B. Erdelyi. "A novel differential algebraic adaptive fast multipole method." IPAC 2013: 1055-1057. |
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| Paper | download WEPOY050.PDF [0.772 MB / 3 pages] | |||||
| Export | download ※ BibTeX ※ LaTeX ※ Text/Word ※ RIS ※ EndNote | |||||
| Conference | IPAC2016, Busan, Korea | |||||
| Series | International Particle Accelerator Conference (7th) | |||||
| Proceedings | Link to full IPAC2016 Proccedings | |||||
| Session | Poster Session | |||||
| Date | 11-May-16 16:00–18:00 | |||||
| Main Classification | 05 Beam Dynamics and Electromagnetic Fields | |||||
| Sub Classification | D11 Code Developments and Simulation Techniques | |||||
| Keywords | multipole, simulation, space-charge, framework, controls | |||||
| Publisher | JACoW, Geneva, Switzerland | |||||
| Editors | Christine Petit-Jean-Genaz (CERN, Geneva, Switzerland); Dong Eon Kim (PAL, Pohang, Republic of Korea); Kyung Sook Kim (PAL, Pohang, Republic of Korea); In Soo Ko (POSTECH, Pohang, Republic of Korea); Volker RW Schaa (GSI, Darmstadt, Germany) | |||||
| ISBN | 978-3-95450-147-2 | |||||
| Published | June 2016 | |||||
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