  In this work, we consider parabolic models with dynamic boundary conditions
and parabolic bulk-surface problems in 3D. Such partial differential equations
based models describe phenomena that happen both on the surface and in the
bulk/domain. These problems may appear in many applications, ranging from cell
dynamics in biology, to grain growth models in polycrystalline materials. Using
Difference Potentials framework, we develop novel numerical algorithms for the
approximation of the problems. The constructed algorithms efficiently and
accurately handle the coupling of the models in the bulk and on the surface,
approximate 3D irregular geometry in the bulk by the use of only Cartesian
meshes, employ Fast Poisson Solvers, and utilize spectral approximation on the
surface. Several numerical tests are given to illustrate the robustness of the
developed numerical algorithms.
