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.
Zhao, A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces, Journal of Scientific Computing 63 (2015) 118–137
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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.