Efficient mesh generation utilizing an adaptive body centered cubic mesh

Abstract

To generate a mesh in a physical domain, an initial mesh of a polygonal domain that approximates the physical domain is introduced. The initial mesh is formed by using a Body Centered Cubic (BCC) lattice that can give a more efficient node ordering for the matrix vector multiplication. An optimization problem is then considered for the displacement on the initial mesh points, which maintains a good quality of triangles while aiming at fitting the initial mesh to the boundary of the physical domain. In the optimization problem, a mesh quality function is employed. The Fréchet derivative of the objective function vanishes at the optimal solution and it gives a resulting nonlinear algebraic system for the optimal solution. The nonlinear algebraic system can be solved by using the Picard or Newton method. To resolve the complexity in the physical domain, a very fine initial mesh is often required but the solution time for the nonlinear algebraic system becomes problematic. To overcome this limitation, adaptively refined grid cells for the initial BCC mesh can be used and iterative solvers combined with a domain decomposition preconditioner can be used for solving the algebraic system in the Picard or Newton method. The use of iterative solvers with a domain decomposition preconditioner gives a parallel meshing algorithm that makes the proposed scheme more efficient for large scale problems. Numerical results for various test models are included.