Exploiting Fine Block Triangularization and Quasilinearity in Differential-Algebraic Equation Systems
Provides a systematic approach for structural analysis of DAEs, benefiting researchers and practitioners in numerical simulation of differential-algebraic systems.
The paper derives a method for quasilinearity analysis of DAEs and combines it with fine block-triangularization to find minimal initial values for consistent initialization and enable block-wise derivative computation.
The $Σ$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form (BTF). This article derives a simple method for quasilinearity analysis of a DAE and combines it with its fine BTF to construct a method for finding the minimal set of initial values needed for consistent initialization and a method for a block-wise computation of derivatives for the solution to the DAE.