On parallel computing for stochastic optimization models and algorithms

167 p.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Parallel optical negabinary arithmetic based on logic operations

On the basis of signed-digit negabinary representation, parallel two-step addition and one-step subtraction can be performed for arbitrary-length negabinary operands.; The arithmetic is realized by signed logic operations and optically implemented by spatial encoding and decoding techniques. The proposed algorithm and optical system are simple, reliable, and practicable, and they have the property of parallel processing of two-dimensional data. This leads to an efficient design for the optical arithmetic and logic unit. (C) 1997 Optical Society of America.

Compact parallel optical modified-signed-digit arithmetic-logic array processor with electron-trapping device

A compact two-step modified-signed-digit arithmetic-logic array processor is proposed. When the reference digits are programmed, both addition and subtraction can be performed by the same binary logic operations regardless of the sign of the input digits. The optical implementation and experimental demonstration with an electron-trapping device are shown. Each digit is encoded by a single pixel, and no polarization is included. Any combinational logic can be easily performed without optoelectronic and electro-optic conversions of the intermediate results. The system is compact, general purpose, simple to align, and has a high signal-to-noise ratio. (C) 1999 Optical Society of America.

Solid-state optical parallel morphological processor

Based on birefringence, a building-block stacking technique is suggested in this paper. A solid-state optical morphological processor module is thus developed, which is an integration of a beam array generator submodule, an optical connector submodule, and a Pockels readout optical modulator. It is shown that the technique is compact in construction, simple for fabrication, and insensitive to the environment.

Parallel optical negabinary signed-digit computing: algorithm and optical implementation

Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

A hybrid-parallel framework for the nonlinear seismic analysis of very tall buildings

FRAME3D, a program for the nonlinear seismic analysis of steel structures, has previously been used to study the collapse mechanisms of steel buildings up to 20 stories tall. The present thesis is inspired by the need to conduct similar analysis for much taller structures. It improves FRAME3D in two primary ways.

First, FRAME3D is revised to address specific nonlinear situations involving large displacement/rotation increments, the backup-subdivide algorithm, element failure, and extremely narrow joint hysteresis. The revisions result in superior convergence capabilities when modeling earthquake-induced collapse. The material model of a steel fiber is also modified to allow for post-rupture compressive strength.

Second, a parallel FRAME3D (PFRAME3D) is developed. The serial code is optimized and then parallelized. A distributed-memory divide-and-conquer approach is used for both the global direct solver and element-state updates. The result is an implicit finite-element hybrid-parallel program that takes advantage of the narrow-band nature of very tall buildings and uses nearest-neighbor-only communication patterns.

Using three structures of varied sized, PFRAME3D is shown to compute reproducible results that agree with that of the optimized 1-core version (displacement time-history response root-mean-squared errors are ~〖10〗^(-5) m) with much less wall time (e.g., a dynamic time-history collapse simulation of a 60-story building is computed in 5.69 hrs with 128 cores—a speedup of 14.7 vs. the optimized 1-core version). The maximum speedups attained are shown to increase with building height (as the total number of cores used also increases), and the parallel framework can be expected to be suitable for buildings taller than the ones presented here.

PFRAME3D is used to analyze a hypothetical 60-story steel moment-frame tube building (fundamental period of 6.16 sec) designed according to the 1994 Uniform Building Code. Dynamic pushover and time-history analyses are conducted. Multi-story shear-band collapse mechanisms are observed around mid-height of the building. The use of closely-spaced columns and deep beams is found to contribute to the building's “somewhat brittle” behavior (ductility ratio ~2.0). Overall building strength is observed to be sensitive to whether a model is fracture-capable.

Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We demonstrate a full-range parallel Fourier-domain optical coherence tomography (FD-OCT) in which a tomogram free of mirror images as well as DC and autocorrelation terms is obtained in parallel. The phase and amplitude of two-dimensional spectral interferograms are accurately detected by using sinusoidal phase-modulating interferometry and a two-dimensional CCD camera, which allows for the reconstruction of two-dimensional complex spectral interferograms. By line-by-line inverse Fourier transformation of the two-dimensional complex spectral interferogram, a full-range parallel FD-OCT is realized. Tomographic images of two separated glass coverslips obtained with our method are presented as a proof-of-principle experiment.

Parallel plate interferometer with a reflecting mirror for measuring angular displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10(-8) rad. (C) 2007 The Optical Society of Japan.