|WEPOY050||A Differential Algebraic Framework for the Fast Indirect Boundary Element Method||3107|
|SUPSS064||use link to see paper's listing under its alternate paper code|
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 (miterations M2 ). Accelerating with the fast multipole method (FMM) can reduce this to O(M) if miterations << 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: 1055-1057.
|DOI •||reference for this paper ※ DOI:10.18429/JACoW-IPAC2016-WEPOY050|
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