Exploiting Fine Block Triangularization and Quasilinearity in Differential-Algebraic Equation Systems
Nedialko S. Nedialkov, Guangning Tan, and John D. Pryce
TL;DR
This paper introduces a novel approach combining quasilinearity analysis with fine block-triangularization of DAE systems to improve initial value determination and derivative computation.
Contribution
It presents a simple quasilinearity analysis method integrated with fine BTF to optimize initialization and derivative calculations in DAE systems.
Findings
Efficient minimal initial value set determination
Block-wise derivative computation method
Enhanced structural analysis of DAE systems
Abstract
The -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.
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Taxonomy
TopicsModeling and Simulation Systems · Numerical methods for differential equations · Model Reduction and Neural Networks