Paper  Title  Page 

WEPOY050  A Differential Algebraic Framework for the Fast Indirect Boundary Element Method  3107 
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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 reexpressed 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 M^{2} ). 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.
* 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: 10551057. 

DOI •  reference for this paper ※ DOI:10.18429/JACoWIPAC2016WEPOY050  
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