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
Verfasserangaben:A. Wiegmann, A. Zemitis
URN (Permalink):urn:nbn:de:hbz:386-kluedo-17860
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (94)
Dokumentart:Bericht
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2006
Jahr der Veröffentlichung:2006
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Urhebende Körperschaft:Fraunhofer ITWM
Datum der Publikation (Server):17.10.2006
Freies Schlagwort / 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
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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