4 research outputs found
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
MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks
We proposed MATEX, a distributed framework for transient simulation of power
distribution networks (PDNs). MATEX utilizes matrix exponential kernel with
Krylov subspace approximations to solve differential equations of linear
circuit. First, the whole simulation task is divided into subtasks based on
decompositions of current sources, in order to reduce the computational
overheads. Then these subtasks are distributed to different computing nodes and
processed in parallel. Within each node, after the matrix factorization at the
beginning of simulation, the adaptive time stepping solver is performed without
extra matrix re-factorizations. MATEX overcomes the stiff-ness hinder of
previous matrix exponential-based circuit simulator by rational Krylov subspace
method, which leads to larger step sizes with smaller dimensions of Krylov
subspace bases and highly accelerates the whole computation. MATEX outperforms
both traditional fixed and adaptive time stepping methods, e.g., achieving
around 13X over the trapezoidal framework with fixed time step for the IBM
power grid benchmarks.Comment: ACM/IEEE DAC 2014. arXiv admin note: substantial text overlap with
arXiv:1505.0669