A fictitious domain method with distributed Lagrange multipliers for the numerical simulation of particulate flow and its parallel implementation

this article the solution of the Laplacian for the pressure mesh that functions as preconditioner mentioned in the above algorithm is solved by a parallel multilevel Poisson solver, developed by Sarin and Sameh [9] Problem (3.8), the advection-diffusion problem, is solved by a least-squares/conjugategradient algorithm [2] with two or three iterations. The arisen linear system has been solved by the Jacobi iterative method which is easy to be parallelized. 5 Finally, problem (3.10) has the following - classical - saddle-point structur