FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs

FATODE is a FORTRAN library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities. The paper describes the capabilities, implementation, code organization, and usage of this package. FATODE implements four families of methods -- explicit Runge-Kutta for nonstiff problems and fully implicit Runge-Kutta, singly diagonally implicit Runge-Kutta, and Rosenbrock for stiff problems. Each family contains several methods with different orders of accuracy; users can add new methods by simply providing their coefficients. For each family the forward, adjoint, and tangent linear models are implemented. General purpose solvers for dense and sparse linear algebra are used; users can easily incorporate problem-tailored linear algebra routines. The performance of the package is demonstrated on several test problems. To the best of our knowledge FATODE is the first publicly available general purpose package that offers forward and adjoint sensitivity analysis capabilities in the context of Runge Kutta methods. A wide range of applications are expected to benefit from its use; examples include parameter estimation, data assimilation, optimal control, and uncertainty quantification

An Algorithmic Framework for Efficient Large-Scale Circuit Simulation Using Exponential Integrators

We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes it capable of simulating stiff nonlinear circuit system at a large scale. In this framework, the system's nonlinearity is treated with exponential Rosenbrock-Euler formulation. The matrix exponential and vector product is computed using invert Krylov subspace method. Our proposed method has several distinguished advantages over conventional formulations (e.g., the well-known backward Euler with Newton-Raphson method). The matrix factorization is performed only for the conductance/resistance matrix G, without being performed for the combinations of the capacitance/inductance matrix C and matrix G, which are used in traditional implicit formulations. Furthermore, due to the explicit nature of our formulation, we do not need to repeat LU decompositions when adjusting the length of time steps for error controls. Our algorithm is better suited to solving tightly coupled post-layout circuits in the pursuit for full-chip simulation. Our experimental results validate the advantages of our framework.Comment: 6 pages; ACM/IEEE DAC 201