Efficient Numerical Integration for Postprocessing and Matrix Assembly of Finite-Element Subdomains

The efficiency of numerical integration methods for finite-element analysis (FEA) is investigated. The focus of this paper, within the context of traditional FEA, is the postprocessing operation of numerical integration over a subdomain containing potentially large numbers of elements. Improvements to the efficiency of such operations directly increase the efficacy of the assembly process for the mass and stiffness matrices of a generalized family of macroelements. The analogous postprocessing and matrix assembly methods are refined such that repeated computations are eliminated, effectively treating a large number of traditionally separate numerical integrations as one full-domain integral. Electromagnetic applications are tested to demonstrate the reduction in computational cost of the method. Results demonstrate increased efficiency as higher order basis functions and larger numbers of elements are employed.