A GPU-Accelerated Semi-Implicit Method for Large-Scale Nonlinear Eddy-Current Problems Using Adaptive Time Step Control

A transient magnetic vector potential formulation for nonlinear eddy-current problems and spatial finite element discretization form a system of nonlinear algebraic differential equations. Using Rosenbrock-Wanner (ROW) time integration methods, the system of nonlinear functions is solved with a series of linear systems of equations where the Jacobian matrix is kept constant during the entire time step. This makes ROW methods error-prone to larger time step sizes, wherefore the time step size must be controlled adaptively. To improve accuracy and reliability, the Jacobian matrix is determined exactly during the time step. For highly efficient simulations of large-scale problems, the process is accelerated using parallel computing and graphic processing units (GPUs).