EJ-HEAT: A Fast Explicit Jump Harmonic Averaging Solver for the Effective Heat Conductivity of Composite Materials

  • The stationary heat equation is solved with periodic boundary conditions in geometrically complex composite materials with high contrast in the thermal conductivities of the individual phases. This is achieved by harmonic averaging and explicitly introducing the jumps across the material interfaces as additional variables. The continuity of the heat flux yields the needed extra equations for these variables. A Schur-complent formulation for the new variables is derived that is solved using the FFT and BiCGStab methods. The EJ-HEAT solver is given as a 3-page Matlab program in the Appendix. The C++ implementation is used for material design studies. It solves 3-dimensional problems with around 190 Mio variables on a 64-bit AMD Opteron desktop system in less than 6 GB memory and in minutes to hours, depending on the contrast and required accuracy. The approach may also be used to compute effective electric conductivities because they are governed by the stationary heat equation.

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Metadaten
Author:A. Wiegmann, A. Zemitis
URN (permanent link):urn:nbn:de:hbz:386-kluedo-17860
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (94)
Document Type:Report
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Creating Corporation:Fraunhofer ITWM
Tag:Stationary heat equation; discontinuous coefficients; effective thermal conductivity; explicit jump; microstructure simulatio; virtual material design
Stationary heat equation; discontinuous coefficients; effective thermal conductivity; explicit jump; microstructure simulatio; virtual material design
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:510 Mathematik

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