TY - RPRT
A1 - Wiegmann, A.
A1 - Zemitis, A.
T1 - EJ-HEAT: A Fast Explicit Jump Harmonic Averaging Solver for the Effective Heat Conductivity of Composite Materials
N2 - 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 94
KW - Stationary heat equation
KW - effective thermal conductivity
KW - explicit jump
KW - discontinuous coefficients
KW - virtual material design
KW - microstructure simulatio
KW - Stationary heat equation
KW - effective thermal conductivity
KW - explicit jump
KW - discontinuous coefficients
KW - virtual material design
KW - microstructure simulatio
Y1 - 2006
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1786
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-17860
ER -