Parallel Shared-Memory Isogeometric Residual Minimization (iGRM) for Three-Dimensional Advection-Diffusion Problems

In this paper, we present a residual minimization method for three-dimensional isogeometric analysis simulations of advection-diffusion equations. First, we apply the implicit time integration scheme for the three-dimensional advection-diffusion equation. Namely, we utilize the Douglas-Gunn time integration scheme. Second, in every time step, we apply the residual minimization method for stabilization of the numerical solution. Third, we use isogeometric analysis with B-spline basis functions for the numerical discretization. We perform alternating directions splitting of the resulting system of linear equations, so the computational cost of the sequential LU factorization is linear [Formula: see text]. We test our method on the three-dimensional simulation of the advection-diffusion problem. We parallelize the solver for shared-memory machine using the GALOIS framework.