A line input (LI) model has been developed, which makes the accurate modeling of powder bed processes more computationally efficient. Goldak's ellipsoidal model has been used extensively to model heat sources in additive manufacturing (AM), including lasers and electron beams. To accurately model the motion of the heat source, the simulation time increments must be small enough such that the source moves a distance smaller than its radius over the course of each increment. When the source radius is small and its velocity is large, a strict condition is imposed on the size of time increments regardless of any stability criteria. In powder bed systems, where radii of 0.1 mm and velocities of 500 mm/s are typical, a significant computational burden can result. The line heat input model relieves this burden by averaging the heat source over its path. This model allows the simulation of an entire heat source scan in just one time increment. However, such large time increments can lead to inaccurate results. Instead, the scan is broken up into several linear segments, each of which is applied in one increment. In this work, time increments are found that yield accurate results (less than 10% displacement error) and require less than 1/10 of the central processing unit (CPU) time required by Goldak's moving source model. A dimensionless correlation is given that can be used to determine the necessary time increment size that will greatly decrease the computational time required for any powder bed simulation while maintaining accuracy.