The Nonrecursive Plating Algorithm (NRPA) for Computing the Total Radiative Exchange Factors in Enclosures

Abstract

Many numerical methods for computing radiation exchange in enclosures are based on the computation of direct exchange areas (DEAs) and total exchange areas (TEAs). Excessively long computation times can be associated with TEAs computation. Among the best performing methods, the plating algorithm (PA) computes TEAs from DEAs based on a set of simple recursive equations. An efficient CPU and GPU parallelization of the PA are represented. Nevertheless, PA computation complexity is O(N ³). A novel formulation, the nonrecursive plating algorithm (NRPA), is introduced. It allows the computation of TEAs with a single nonrecursive step. Its equations are formulated by identification to the PA equations giving TEAs from DEAs, requiring one simple assumption. The NRPA is then written in matrix form as mainly a square matrix multiplication operation. Based on advancement in matrix multiplication computation, the NRPA complexity is proven to be O(N ^2.38) for the number of multiplications. CPU and GPU NRPA are implemented based on the optimized linear algebra library BLAS for CPU and cuBLAS for GPU CUDA programs. NRPA is found to highly outperform PA in both CPU and GPU computation times. Finally, a test enclosure is considered and serves to validate the accuracy of the NRPA by comparison to the PA.