A gridless technique for the solution of the integral form of the radiative heat flux equation for emitting and absorbing media is presented. The technique was developed to yield solutions of participating media radiative heat transfer in a manner compatible with numerical simulation of the flow and temperature field by gridless vortex and transport element methods, respectively. Additional utility for subgrid analyses, in conjunction with direct numerical simulation or reduced dimensional mixing and turbulence models is noted. Results are compared to established and newly developed closed-form solutions for transport with uniform properties in a planar media. Significant errors in alternative techniques that include simplifications of the governing equations are illustrated by direct comparison. Radiative transfer analyses of highly resolved temperature fields representative of single and multiple (150) flame sheets are performed. Multipole fast solvers for the exponential integrals in the radiative transfer equations are developed and are shown to yield reductions in CPU time of an order of magnitude for modest problem sizes (N∼O(1000)) and two orders of magnitude for large problems (N∼O(10000)). Additional improvements in computational efficiency are provided since the gridless formulation only requires a numerical representation of the portion of the domain with significant temperature gradients and the results are provided in the form of gradients of energy deposition.*This work was performed in part at Sandia National Laboratories, a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for theUSDepartment of Energy under contract no DE-AC04-94AL85000.