Skeletonization accelerated solution of crank-nicolson method for solving three-dimensional parabolic equation

Parabolic equation models discretized with the finite difference method have been extensively studied for a long time. However, several explicit and implicit schemes exist in the literature. The advantage in explicit schemes is its simplicity, while its disadvantage is conditional stability. On the other hand, implicit schemes are unconditionally stable but require special treatment for a fast and accurate solution such as the Crank-Nicolson (CN) method. This method becomes computationally intensive for problems with dense meshes. The resulting matrix from the CN in two and three-dimensional cases requires high computational resources. This paper applies hierarchical interpolative factorization (HIF) to reduce the computational cost of the CN method. Numerical experiments are conducted to validate the proposed HIF acceleration.