47,935 research outputs found
A high-accuracy optical linear algebra processor for finite element applications
Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced
A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs
In this work, possibility of simulating biological organs in realtime using
the Boundary Element Method (BEM) is investigated. Biological organs are
assumed to follow linear elastostatic material behavior, and constant boundary
element is the element type used. First, a Graphics Processing Unit (GPU) is
used to speed up the BEM computations to achieve the realtime performance.
Next, instead of the GPU, a computer cluster is used. Results indicate that BEM
is fast enough to provide for realtime graphics if biological organs are
assumed to follow linear elastostatic material behavior. Although the present
work does not conduct any simulation using nonlinear material models, results
from using the linear elastostatic material model imply that it would be
difficult to obtain realtime performance if highly nonlinear material models
that properly characterize biological organs are used. Although the use of BEM
for the simulation of biological organs is not new, the results presented in
the present study are not found elsewhere in the literature.Comment: preprint, draft, 2 tables, 47 references, 7 files, Codes that can
solve three dimensional linear elastostatic problems using constant boundary
elements (of triangular shape) while ignoring body forces are provided as
supplementary files; codes are distributed under the MIT License in three
versions: i) MATLAB version ii) Fortran 90 version (sequential code) iii)
Fortran 90 version (parallel code
SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction
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-environments such as Matlab. However, these
designs are often implemented using fixed-point arithmetic for speed and
efficiency reasons especially in embedded systems. The fixed-point
implementation reduces implementation cost, provides better performance, and
reduces power consumption. The conversion from floating-point designs to
fixed-point code is subject to two opposing constraints: (i) the word-width of
fixed-point types must be minimized, and (ii) the outputs of the fixed-point
program must be accurate. In this paper, we propose a new solution to this
problem. Our technique takes the floating-point program, specified accuracy and
an implementation cost model and provides the fixed-point program with
specified accuracy and optimal implementation cost. We demonstrate the
effectiveness of our approach on a set of examples from the domain of automated
control, robotics and digital signal processing
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