KFBI-ADI schemes achieve second-order accuracy and unconditional stability for 3D heat equations with irregular boundaries and interfaces, verified numerically and applied to Stefan problems with level sets.
Mayo, The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions, SIAM Journal on Numerical Analysis 21 (2) (1984) 285–299
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ADI schemes for heat equations with irregular boundaries and interfaces in 3D with applications
KFBI-ADI schemes achieve second-order accuracy and unconditional stability for 3D heat equations with irregular boundaries and interfaces, verified numerically and applied to Stefan problems with level sets.