Ideally, want to have non-uniform implementation, but with Nlog(N) complexity
Compressed convolution by ABP
Drawback: double number of slices needed
For multi-turn wake, empty bucket sampling needed
How does it work?
Induced voltage only needed on the points where the line density is not zero
Introducing a MASKING of the data -> can cut the wakefield data
Calculate convolution on compressed data
For the relevant bins, the results are the same
For other locations, data is not correct => CANNOT use it for beam with LOSSES
Performance test:
Full convolution with 5 bucket bunch spacing vs. full conv with 15 bucket bunch spacing vs compressed convolution: compressed convolution performs best of all
The smaller the spacing, the less the improvement
Remarks on wake calculation
N. Mounet: exact analytical wake calculation can be approximated by cubic Hermitian interpolation
example: resistive wall impedance is not correctly represented by standard FFT, while analytical approximation is correct
Drawback: analytical expression of the impedance needed
For cases where the impedance is known, but wake cannot be calculated
Implementation in BLonD: Ivan will make a first implementation