519 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
A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
We develop an algorithm for computing the solution of a large system of
linear ordinary differential equations (ODEs) with polynomial inhomogeneity.
This is equivalent to computing the action of a certain matrix function on the
vector representing the initial condition. The matrix function is a linear
combination of the matrix exponential and other functions related to the
exponential (the so-called phi-functions). Such computations are the major
computational burden in the implementation of exponential integrators, which
can solve general ODEs. Our approach is to compute the action of the matrix
function by constructing a Krylov subspace using Arnoldi or Lanczos iteration
and projecting the function on this subspace. This is combined with
time-stepping to prevent the Krylov subspace from growing too large. The
algorithm is fully adaptive: it varies both the size of the time steps and the
dimension of the Krylov subspace to reach the required accuracy. We implement
this algorithm in the Matlab function phipm and we give instructions on how to
obtain and use this function. Various numerical experiments show that the phipm
function is often significantly more efficient than the state-of-the-art.Comment: 20 pages, 3 colour figures, code available from
http://www.maths.leeds.ac.uk/~jitse/software.html . v2: Various changes to
improve presentation as suggested by the refere
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