A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1-dimensional and 2-dimensional systems

Source coding by efficient selection of ground states clusters

In this letter, we show how the Survey Propagation algorithm can be generalized to include external forcing messages, and used to address selectively an exponential number of glassy ground states. These capabilities can be used to explore efficiently the space of solutions of random NP-complete constraint satisfaction problems, providing a direct experimental evidence of replica symmetry breaking in large-size instances. Finally, a new lossy data compression protocol is introduced, exploiting as a computational resource the clustered nature of the space of addressable states.Comment: 4 pages, 4 figure

Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis

The frequency-domain fast boundary element method (BEM) combined with the exponential window technique leads to an efficient yet simple method for elastodynamic analysis. In this paper, the efficiency of this method is further enhanced by three strategies. Firstly, we propose to use exponential window with large damping parameter to improve the conditioning of the BEM matrices. Secondly, the frequency domain windowing technique is introduced to alleviate the severe Gibbs oscillations in time-domain responses caused by large damping parameters. Thirdly, a solution extrapolation scheme is applied to obtain better initial guesses for solving the sequential linear systems in the frequency domain. Numerical results of three typical examples with the problem size up to 0.7 million unknowns clearly show that the first and third strategies can significantly reduce the computational time. The second strategy can effectively eliminate the Gibbs oscillations and result in accurate time-domain responses