TY - JOUR
T1 - Parallel optimization with boundary elements and kernel independent fast multipole method
AU - Ostanin, Igor
AU - Zorin, Denis
AU - Oseledets, Ivan
N1 - Funding Information:
Authors gratefully acknowledge the financial support from Russian National Foundation under the grant 15-11-00033. I.O acknowledges the financial support from the Russian Foundation of Basic Research under grant 16-31-60100.
Funding Information:
ACKNOWLEDGEMENT Authors gratefully acknowledge the financial support from Russian National Foundation under the grant 15-11-00033. I.O acknowledges the financial support from the Russian Foundation of Basic Research under grant 16-31-60100.
Publisher Copyright:
© 2017 WIT Press.
PY - 2017
Y1 - 2017
N2 - We propose a new framework for topology optimization based on the boundary element discretization and kernel-independent fast multipole method (KIFMM). The boundary value problem for the considered partial differential equation is reformulated as a surface integral equation and is solved on the domain boundary. Volume solution at selected points is found via surface integrals. At every iteration of the optimization process, the new boundary is extracted as a level set of a topological derivative. Both surface and volume solutions are accelerated using KIFMM. The obtained technique is highly universal, fully parallelized, it allows achieving asymptotically the best performance with the optimization iteration complexity proportional to a number of surface discretization elements. Moreover, our approach is free of the artifacts that are inherent for finite element optimization techniques, such as “checkerboard” instability. The performance of the approach is showcased on few illustrative examples.
AB - We propose a new framework for topology optimization based on the boundary element discretization and kernel-independent fast multipole method (KIFMM). The boundary value problem for the considered partial differential equation is reformulated as a surface integral equation and is solved on the domain boundary. Volume solution at selected points is found via surface integrals. At every iteration of the optimization process, the new boundary is extracted as a level set of a topological derivative. Both surface and volume solutions are accelerated using KIFMM. The obtained technique is highly universal, fully parallelized, it allows achieving asymptotically the best performance with the optimization iteration complexity proportional to a number of surface discretization elements. Moreover, our approach is free of the artifacts that are inherent for finite element optimization techniques, such as “checkerboard” instability. The performance of the approach is showcased on few illustrative examples.
KW - Kernel-independent fast multi-pole method
KW - Topological-shape optimization
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U2 - 10.2495/CMEM-V5-N2-154-162
DO - 10.2495/CMEM-V5-N2-154-162
M3 - Article
AN - SCOPUS:85070220576
SN - 2046-0546
VL - 5
SP - 154
EP - 162
JO - International Journal of Computational Methods and Experimental Measurements
JF - International Journal of Computational Methods and Experimental Measurements
IS - 2
ER -