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DTSTAMP:20220812T074334Z
LOCATION:Nairobi Room
DTSTART;TZID=Europe/Stockholm:20220627T170000
DTEND;TZID=Europe/Stockholm:20220627T173000
UID:submissions.pasc-conference.org_PASC22_sess131_msa208@linklings.com
SUMMARY:Exascale Simulations via the Submatrix Matrix Method
DESCRIPTION:Minisymposium\n\nExascale Simulations via the Submatrix Matrix
  Method\n\nKühne\n\nWe present the submatrix method and a novel linear-sca
 ling electronic-structure method in conjunction with approximate computing
 , as well as the implementation of the technique in CP2K [1]. Even though 
 initially proposed for inverse p-th roots [2], it has recently been recogn
 ized that the submatrix method represents a general method to approximate 
 arbitrary matrix functions such as the matrix-sign function of large spars
 e matrices [3]. The matrix-sign function is the essential workhorse of lin
 ear-scaling electronic-structure theory, and we present an intuitive chemi
 cal justification for the accuracy of the submatrix method. We will discus
 s the efficient implementation of the submatrix method into CP2K with a sp
 ecial focus on limiting communication between compute nodes. The resulting
  compute kernel is the sign function of a relatively small but dense matri
 x. Our optimized implementation with a simple diagonalization-based evalua
 tion of the sign function of the submatrices outperforms the Newton-Schulz
  sign iteration in initial results [4], especially for larger cutoffs of m
 atrix elements. This observation shows that the submatrix method will be a
  valuable tool in the context of approximate computing [5]. <br /><br />[1
 ] https://doi.org/10.1063/5.0007045<br />[2] https://doi.org/10.1145/32181
 76.321823<br />[3] https://doi.org/10.1109/SC41405.2020.00084<br />[4] htt
 ps://doi.org/10.1016/j.parco.2022.102920<br />[5] https://doi.org/10.3390/
 computation8020039\n\nDomain: Chemistry and Materials, Life Sciences, Phys
 ics
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