A Cyclic-Symmetry-Based Partitioned IG-SBFEM for Steady-State Heat Conduction Analysis

A reduced-order isogeometric scaled boundary finite element method (IG-SBFEM) is developed for solving steady-state heat conduction problems by exploiting cyclic symmetry. First, the IG-SBFEM formulation is established in a symmetry-adapted reference coordinate system. It is then demonstrated that the eigenvalue and coefficient matrices in the IG-SBFEM equations possess a block-circulant structure, which can be transformed into block-diagonal form using an orthogonal basis. Consequently, the eigenvalue problem and system equations can be decomposed into a series of independent subproblems with smaller solution scale, and computational cost can effectively be reduced. Furthermore, a Lagrange-multiplier-based strategy is proposed to effectively accommodate temperature constraints that do not exhibit cyclic symmetry. Several numerical examples are provided to highlight the accuracy, efficiency, and applicability of the proposed method.