In the past, reconfigurable computing has not been an option for accelerating scientific algorithms (which require complex floating-point operations) and other similar applications due to limited Field Programmable Gate Array (FPGA) density. However, the rapid increase of FPGA densities over the past several years has altered this situation. The central goal of the Reconfigurable Computing Appl...

K. Puri, G. Dietachmayer, P. Steinle, M. Dix, L. Rikus, L. Logan, M. Naughton, C. Tingwell, Y Xiao, V. Barras, I. Bermous, R. Bowen, L. Deschamps, C. Franklin, J. Fraser, T. Glowacki, B. Harris, J. Lee, T. Le, G. Roff, A. Sulaiman, H. Sims, X. Sun, Z. Sun, H. Zhu, M. Chattopadhyay, C. Engel Centre for Australian Weather and Climate Research, A partnership between CSIRO and the Bureau of Meteoro...

We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects or any other type of seeds. We then show that this system is well suited ...

The seismic imaging problem centers around mathematical and numerical techniques to create an accurate image of the earth’s subsurface, using recorded data from geophones that capture reflected seismic waves. Using a path integral approach, a wavefield extrapolater can be expressed as a limit of depth-sliced path steps through a variable velocity medium. An image is created from the correlation...

The algorithms behind a toolbox for approximating Lyapunov exponents of nonlinear differential systems by QR methods are described. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as integration for the Lyapunov exponents is carri...

The goal of this work is to show that the numerical solution of the obstacle scattering problem based on the modified Rayleigh conjecture (MRC) method is a competitive alternative to the boundary integral equations method, and that it has numerical advantages which may be especially important in threedimensional scattering problems with non-smooth domains, for example, with domains whose bounda...

This paper presents the implementation of a variational formulation of brittle fracture mechanics proposed by G.A. Francfort and J.-J. Marigo in 1998. The essence of the model relies on successive global minimizations of an energy with respect to any crack set and any kinematically admissible displacement field. We briefly present the model itself, and its variational approximation in the sense...

In this paper, we present an automated technique swati: Synthesizing Wordlengths Automatically Using Testing and Induction, which uses a combination of Nelder-Mead optimization based testing, and induction from examples to automatically synthesize optimal fixedpoint implementation of numerical routines. The design of numerical software is commonly done using floating-point arithmetic in design-...

We have observed, in a wide variety of circumstances, the difficulties posed by the need for temporary work storage in numerical algorithms. Practical implementations in such libraries as ACM’s Collected Algorithms (CALGO [1]) vary widely and frequently obscure the details of the algorithm itself. In this paper, we review typical practices and possible implementation solutions in various langua...

We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N -homoclinic orbit, for any N > 1 (if it exists nearby). This scheme is based on Lin’s method and it is robust and reliable. The method is implemented in AUTO/HomCont. A system of or...