  We provide an analytical solution of the heat equation in the half-space
subject to a moving Gaussian heat flux with piecewise constant parameters. The
solution is of interest in powder bed fusion applications where these
parameters can be used to control the conduction of heat due to a scanning beam
of concentrated energy. The analytical solution is written in a dimensionless
form as a sum of integrals over (dimensionless) time. For the numerical
computation of these integrals we suggest a quadrature scheme that utilizes
pre-calculated look-up tables for the required quadrature orders. Such a scheme
is efficient because the required quadrature orders are strongly dependent on
the parameters in the heat flux. The possibilities of using the obtained
computational technique for the control and optimization of powder bed fusion
processes are discussed.
