472 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
Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources
Light incident on a layer of scattering material such as a piece of sugar or
white paper forms a characteristic speckle pattern in transmission and
reflection. The information hidden in the correlations of the speckle pattern
with varying frequency, polarization and angle of the incident light can be
exploited for applications such as biomedical imaging and high-resolution
microscopy. Conventional computational models for multi-frequency optical
response involve multiple solution runs of Maxwell's equations with
monochromatic sources. Exponential Krylov subspace time solvers are promising
candidates for improving efficiency of such models, as single monochromatic
solution can be reused for the other frequencies without performing full
time-domain computations at each frequency. However, we show that the
straightforward implementation appears to have serious limitations. We further
propose alternative ways for efficient solution through Krylov subspace
methods. Our methods are based on two different splittings of the unknown
solution into different parts, each of which can be computed efficiently.
Experiments demonstrate a significant gain in computation time with respect to
the standard solvers.Comment: 22 pages, 4 figure
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations
Recently, ParaExp was proposed for the time integration of linear hyperbolic
problems. It splits the time interval of interest into sub-intervals and
computes the solution on each sub-interval in parallel. The overall solution is
decomposed into a particular solution defined on each sub-interval with zero
initial conditions and a homogeneous solution propagated by the matrix
exponential applied to the initial conditions. The efficiency of the method
depends on fast approximations of this matrix exponential based on recent
results from numerical linear algebra. This paper deals with the application of
ParaExp in combination with Leapfrog to electromagnetic wave problems in
time-domain. Numerical tests are carried out for a simple toy problem and a
realistic spiral inductor model discretized by the Finite Integration
Technique.Comment: Corrected typos. arXiv admin note: text overlap with arXiv:1607.0036
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