Lazy K-way linear combination kernels for efficient runtime sparse Jacobian matrix evaluations in C++

Abstract

The most notoriously expensive component to develop, extend, and maintain within implicit PDAE-based predictive simulation software is the Jacobian evaluation component. While the Jacobian is invariably sparse, its structure and dimensionality are functions of the point of evaluation. The application of Automatic Differentiation to develop these tools is highly desirable. The challenge presented is in providing implementations that treat dynamic sparsity efficiently without requiring the developer to have any a priori knowledge of sparsity structure. Under the context of dynamic sparse Operator Overloading implementations, we develop a direct sparse lazy evaluation approach. In this approach, an efficient runtime variant of the classic Expression Templates technique is proposed to support sparsity. The second aspect is the development of two alternate multi-way Sparse Vector Linear Combination kernels that yield efficient runtime sparsity detection and evaluation. © 2012 Springer-Verlag.