This paper presents a methodology for aiding a scientific programmer to evaluate the performance of parallel programs on advanced architectures. It applies well-defined design of experiments methods to the identification of relations among different levels in the process of mapping computational operations to high-performance computing systems. Statistical analysis is used for studying different factors that affect the mapping process of scientific computing algorithms to advanced architectures. In particular, a case study on the numerical solution of finite element methods for the analysis of conformal antennas for electromagnetic radiation applications was used to test the proposed methodology. The use of statistics for identification of relationships among factors has formalized the solution of the problem and this novel approach allows unbiased conclusions about results. Subset selection based on principal components was used to determine the subset of metrics required to explain the behavior of the system.