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In this work, we develop a cutting method for solving problems with movingand growing interfaces in 3D. This new method is able to resolve largedisplacement or deformation of immersed objects by combining the ArbitraryLagrangian-Eulerian method with only small local mesh deformation defined onthe reference domain, that is decomposed into the macro-elements. The linearsystem of algebraic equations arising after the temporal and spatialdiscretizations of a model parabolic interface heat-conduction-like problemwith vector-valued functions is solved by either an all-at-once or a segregatedalgebraic multigrid method.

Numerical simulation of parabolic moving and growing interface problems using small mesh deformation