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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗
NASA NTRS1971

A fast algorithm for the calculation of junction capacitance and its application for impurity profile determination

A fast algorithm is described which calculates the space charge layer width and junction capacitance for an arbitrary impurity profile and for plane, cylindrical and spherical junctions. The algorithm is based on the abrupt space charge edge (ASCE) approximation. A method to use the algorithm for the determination of impurity profiles for two-sided junctions is presented. An expression is derived for the built-in voltage to be used for capacitance calculations with the ASCE approximation. Experimental evidence is given that the algorithm permits very accurate capacitance calculations and also predicts the exact temperature dependence of the junction capacitance.

Deman, H. J. J.↗
NASA NTRS1972

A fast algorithm for the calculation of junction capacitance and its application for impurity profile determination.

A fast algorithm is described which calculates the space charge layer width and junction capacitance for an arbitrary impurity profile and for plane, cylindrical and spherical junctions. The algorithm is based on the abrupt space charge edge (ASCE) approximation. A method to use the algorithm for the determination of impurity profiles for two-sided junctions is presented. An expression is derived for the built-in voltage to be used for capacitance calculations with the ASCE approximation. Experimental evidence is given that the algorithm permits very accurate capacitance calculations and also predicts the exact temperature dependence of the junction capacitance.

De Man, H. J. J.↗
NASA NTRS2000

A New Fast Algorithm to Completely Account for Non-Lambertian Surface Reflection of The Earth

Surface bidirectional reflectance distribution function (BRDF) influences not only radiance just about the surface, but that emerging from the top of the atmosphere (TOA). In this study we propose a new, fast and accurate, algorithm CASBIR (correction for anisotropic surface bidirectional reflection) to account for such influences on radiance measured above TOA. This new algorithm is based on a 4-stream theory that separates the radiation field into direct and diffuse components in both upwelling and downwelling directions. This is important because the direct component accounts for a substantial portion of incident radiation under a clear sky, and the BRDF effect is strongest in the reflection of the direct radiation reaching the surface. The model is validated by comparison with a full-scale, vector radiation transfer model for the atmosphere-surface system. The result demonstrates that CASBIR performs very well (with overall relative difference of less than one percent) for all solar and viewing zenith and azimuth angles considered in wavelengths from ultraviolet to near-infrared over three typical, but very different surface types. Application of this algorithm includes both accounting for non-Lambertian surface scattering on the emergent radiation above TOA and a potential approach for surface BRDF retrieval from satellite measured radiance.

Qin, Wen-Han↗
NASA NTRS1986

Fast algorithm for calculating chemical kinetics in turbulent reacting flow

This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.

Radhakrishnan, K.↗
NASA NTRS1991

A fast algorithm for image-based ranging

Image-based ranging has emerged as a critical issue in the low altitude operation of flight vehicles such as rotorcraft and planetary landers. These flight regimes require ranging systems for recovering the geometry of the terrain and obstacles for use with guidance algorithms. The development of a ranging equation combining image irradiance together with various order spatial partial derivatives and the vehicle motion parameters is discussed. The ranging equation is in the form of a polynomial in scene depth. Two-dimensional linear filters are then used to compute the coefficients of this polynomial to result in a fast image-based ranging algorithm. Performance of the algorithm is demonstrated using laboratory images.

Menon, P. K. A.↗
NASA NTRS1991

A fast algorithm for control and estimation using a polynomial state-space structure

One of the major problems associated with the control of flexible structures is the estimation of system states. Since the parameters of the structures are not constant under varying loads and conditions, conventional fixed parameter state estimators can not be used to effectively estimate the states of the system. One alternative is to use a state estimator which adapts to the condition of the system. One such estimator is the Kalman filter. This filter is a time varying recursive digital filter which is based upon a model of the system being measured. This filter adapts the model according to the output of the system. Previously, the Kalman filter has only been used in an off-line capacity due to the computational time required for implementation. With recent advances in computer technology, it is becoming a viable tool for use in the on-line environment. A distributed Kalman filter implementation is described for fast estimation of the state of a flexible arm. A key issue, is the sensor structure and initial work on a distributed sensor that could be used with the Kalman filter is presented.

Shults, James R.↗
NASA NTRS1981

Theory and implementation of a fast algorithm linear equalizer

The theory and implementation of a multiplication-free linear mean-square error criterion equalizer for data transmission are considered. For many real-time signal processing situations, a large number of multiplications is objectionable. The linear estimation problem on a binary computer is considered where the estimation parameters are constrained to be powers of two and thus all multiplications are replaced by shifts. The optimal solution is obtained from an integer-programming-like problem except that the allowable discrete points are non-integers. The branch-and-bound algorithm is used to obtain the coefficients of the equalization TDL. Specific experimental performance results are given for an equalizer implemented with a 12 bit A/D device and a 8080 microprocessor.

Yan, T. Y.↗
NASA NTRS1984

Fast algorithms for combustion kinetics calculations: A comparison

To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature.

Radhakrishnan, K.↗
NASA NTRS1992

A fast algorithm for spectral differentiation

A simple algorithm is presented for matrix multiplication in just over half the number of operations entailed by the conventional algorithm, in cases where the matrix possesses the degree of symmetry widely exhibited by derivative matrices. The algorithm is used to multiply the Chebyshev derivative matrix by a vector. For the larger values of n, the ratio of execution times approached the expected value of 2.

Solomonoff, Alex↗
NASA NTRS1993

A fast algorithm for parallel computation of multibody dynamics on MIMD parallel architectures

In this paper the implementation of a parallel O(LogN) algorithm for computation of rigid multibody dynamics on a Hypercube MIMD parallel architecture is presented. To our knowledge, this is the first algorithm that achieves the time lower bound of O(LogN) by using an optimal number of O(N) processors. However, in addition to its theoretical significance, the algorithm is also highly efficient for practical implementation on commercially available MIMD parallel architectures due to its highly coarse grain size and simple communication and synchronization requirements. We present a multilevel parallel computation strategy for implementation of the algorithm on a Hypercube. This strategy allows the exploitation of parallelism at several computational levels as well as maximum overlapping of computation and communication to increase the performance of parallel computation.

Fijany, Amir↗
NASA NTRS1995

Fast algorithms for visualizing fluid motion in steady flow on unstructured grids

The plotting of streamlines is an effective way of visualizing fluid motion in steady flows. Additional information about the flowfield, such as local rotation and expansion, can be shown by drawing in the form of a ribbon or tube. In this paper, we present efficient algorithms for the construction of streamlines, streamribbons and streamtubes on unstructured grids. A specialized version of the Runge-Kutta method has been developed to speed up the integration of particle paths. We have also derived closed-form solutions for calculating angular rotation rate and radius to construct streamribbons and streamtubes, respectively. According to our analysis and test results, these formulations are two to four times better in performance than previous numerical methods. As a large number of traces are calculated, the improved performance could be significant.

Ueng, S. K.↗