FMM CMSC 878R/AMSC 698R Lecture 22 Outline . Adaptive Multilevel FMM - Brief Historical Review - Statement of the Problem for Adaptive MLFMM - Data Structure . Determination of the Target Box Set . Building of D-tree . Building of C-forest - AMLFMM Algorithm . Upward Pass . Downward Pass . Final Summation Summary of requirements for functions that can be used in FMM Summary of requirements for functions that can be used in FMM (2) Both Types of Function Representations Considered satisfy these requirements When using the diagonal forms of translation operators, we understand that representing vectors A and B are samples of the signature function at the quadrature nodes and S- and R- basis functions are samples of the singular and regular kernel at the same nodes. Operation ° means weighted dot product (with the quadrature weights). Adaptive Multilevel FMM Some History: . J. Carrier, L. Greengard & V. Rokhlin, A fast adaptive multipole algorithm for particle simulations. ...