A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains

We propose a fourth-order cut-cell method for solving Poisson’s equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, © optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature ©, we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method.