Rapid simulation of the time-dependent diffusion coefficient in complex materials
Michael D Prange, Vladimir Druskin, David Linton Johnson and Lawrence M Schwartz
2011 J. Phys. A: Math. Theor. 44 395203 doi:10.1088/1751-8113/44/39/395203
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A finite-difference approach is presented for the analysis of the time-dependent diffusion coefficient for general heterogeneous materials that are either cavity-enclosed or periodic. In the bulk material, diffusivity and volume relaxivity are accounted for. The interaction of the diffusive medium with non-diffusive inclusions is modeled via a surface relaxivity. The time dependence is modeled using matrix exponentials that are shown to be efficiently evaluated using a Krylov-subspace approach. For a 3D model grid composed of M voxels of diffusive material (voxels containing non-diffusive material are not stored in the kernel matrix), the memory requirement is 15 M and the computational time complexity for two large-scale example models is shown to be of order M 1.39 and M 1.10. Error estimate formulas are presented that can be used to guide the choice of domain grid resolution. Richardson extrapolation is shown to be effective in lo...
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