<title>Simulation comparisons on diffusion equation</title>

Abstract

Near IR laser is being explored in clinic diagnosis of early-stage cancer. Diffusion equation is used as the mathematical model to describe photon propagation inside human tissues. In this paper, two numerical algorithms, ADI and FEM, are applied in solving the diffusion equation. All the algorithms reach a satisfactory precision on a human- tissue model of realistic size. Results form simulation and experimental are compared and show a good match. Further analysis on algorithm convergence for both spatial grid size and time step also shows the algorithmic stability. The multigrid version of both ADI and FEM are developed to save computational time and memory. The multigrid algorithms use fine grid size in the region of interest and coarse grid size elsewhere. Parallelization implementation is completed for all the algorithms in both share-memory mode and message passing mode. Numerical simulation experiments show that all simulators can serve as computed experiments, i.e. an alternative to physical experiments.