Partitioned Transient Analysis Procedures for Coupled-Field Problems: Accuracy Analysis

Partitioned solution procedures for direct time integration of second-order coupled-field systems are studied from the standpoint of accuracy. These procedures are derived by three formulation steps: implicit integration of coupled governing equations, partitioning of resulting algebraic systems and extrapolation on the right-hand partition. It is shown that the combined effect of partition, extrapolation, and computational paths governs the choice of stable extrapolators and preservation of rigid-body motions. Stable extrapolators for various computational paths are derived and implementation-extrapolator combinations which preserve constant-velocity and constant-acceleration rigid-body motions are identified. A spectral analysis shows that the primary error source introduced by a stable partition is frequency distortion. Finally, as a guide to practical applications, the advantages and shortcomings of five specific partitions are discussed.

Partitioned Transient Analysis Procedures for Coupled-Field Problems: Stability Analysis

A general partitioned transient analysis procedure is proposed, which is amenable to a unified stability analysis technique. The procedure embodies two existing implicit-explicit procedures and one existing implicit-implicit procedure. A new implicit-explicit procedure is discovered, as a special case of the general procedure, that allows degree-by-degree implicit or explicit selections of the solution vector and can be implemented within the framework of the implicit integration packages. A new element-by-element implicit-implicit procedure is also presented which satisfies program modularity requirements and enables the use of single-field implicit integration packages to solve coupled-field problems.