26,660 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
Focal-plane wavefront sensing with high-order adaptive optics systems
We investigate methods to calibrate the non-common path aberrations at an
adaptive optics system having a wavefront-correcting device working at an
extremely high resolution (larger than 150x150). We use focal-plane images
collected successively, the corresponding phase-diversity information and
numerically efficient algorithms to calculate the required wavefront updates.
The wavefront correction is applied iteratively until the algorithms converge.
Different approaches are studied. In addition of the standard Gerchberg-Saxton
algorithm, we test the extension of the Fast & Furious algorithm that uses
three images and creates an estimate of the pupil amplitudes. We also test
recently proposed phase-retrieval methods based on convex optimisation. The
results indicate that in the framework we consider, the calibration task is
easiest with algorithms similar to the Fast & Furious.Comment: 11 pages, 7 figures, published in SPIE proceeding
Correcting soft errors online in fast fourier transform
While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage
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