On the reduction of computational costs in eigenfunction expansions of multidimensional diffusion problems

Analytical or hybrid numerical‐analytical solutions of multidimensional diffusion problems involve the evaluation of nested multiple infinite summations, which require the computation of eigenvalues and related quantities, from associated auxiliary eigenvalue‐type problems. A substantial reduction of the total computational effort in the construction of the final solution for the original potential can be achieved through the proper reorganization of the multiple summations into a single series representation. Such reordering of terms should be carefully accomplished, in order to account for the most significant contributions to the final numerical result, up to a truncated finite order that meets the user prescribed tolerance for the relative error. Presents an algorithm for an optimized scheme with consequent reduction on the number of eigenquantities to be evaluated. This approach is illustrated through representative two and three‐dimensional transient heat conduction problems.