We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an efficient distributed parallelization with respect to time and with a one-directional communication pattern. On top, we apply a task-based shared memory parallelization and Single Instruction Multiple Data vectorization. In the numerical tests we observe high efficiencies of our parallelization approach.


  1. boundary element method
  2. space-time
  3. heat equation
  4. FMM
  5. parallelization
  6. HPC

MSC codes

  1. 65M38
  2. 65Y05
  3. 35K05

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: C320 - C345
ISSN (online): 1095-7197


Submitted: 29 June 2021
Accepted: 24 March 2022
Published online: 4 August 2022


  1. boundary element method
  2. space-time
  3. heat equation
  4. FMM
  5. parallelization
  6. HPC

MSC codes

  1. 65M38
  2. 65Y05
  3. 35K05



Funding Information

MOE Czech : 90140
Austrian Science Fund https://doi.org/10.13039/501100002428 : 4033-N32
Grantová Agentura České Republiky https://doi.org/10.13039/501100001824 : 19-29698L

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