Parallel optimization with boundary elements and kernel independent fast multipole method

Igor Ostanin, Denis Zorin, Ivan Oseledets

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)154-162
Number of pages9
JournalInternational Journal of Computational Methods and Experimental Measurements
Volume5
Issue number2
DOIs
StatePublished - Jan 1 2017

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Parallel Optimization
Fast multipole Method
Surface integral
Boundary Elements
Discretization
Topological Derivative
kernel
Iteration
Topology Optimization
Process Optimization
Level Set
Optimization Techniques
Integral Equations
Partial differential equation
Directly proportional
Boundary Value Problem
Finite Element
Optimization
Shape optimization
Boundary value problems

Keywords

  • Kernel-independent fast multi-pole method
  • Topological-shape optimization

ASJC Scopus subject areas

  • Computational Mathematics
  • Computer Science Applications
  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mechanics

Cite this

Parallel optimization with boundary elements and kernel independent fast multipole method. / Ostanin, Igor; Zorin, Denis; Oseledets, Ivan.

In: International Journal of Computational Methods and Experimental Measurements, Vol. 5, No. 2, 01.01.2017, p. 154-162.

Research output: Contribution to journalArticle

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