Numerical Implementation of Inactive Elements in Balancing Domain Decomposition Method and Its Application to Metal Additive Manufacturing Simulation

Numerical implementation of inactive elements in balancing domain decomposition method is presented. The inactive elements cause floating degrees of freedom, which make the coefficient matrix of the linear system of equations singular. Regularization methods for matrices related to the Schur complement, the diagonal scaling preconditioner, balancing domain decomposition (BDD) method and the BDD with diagonal scaling (BDD-DIAG) method are derived. The present numerical implementation showed good convergence performance in a numerical test of metal additive manufacturing simulation.