Showing papers on "Basis function published in 1983"

Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations

Abstract: An algorithm based on the method of integral equations to simulate the electromagnetic responses of three-dimensional bodies in layered earths has been developed. The inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric tensor Green's function appropriate to a layered earth, and it is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic tensor Green's functions over the scattering currents. Efficient evaluation of the tensor Green's functions is a major consideration in reducing computation time. We find that tabulation and interpolation of the six electric and five magnetic Hankel transforms defining the secondary Green's functions is perferable to any direct Hankel transform calculation using linear filters. A comparison of responses over elongate three-dimensional (3-D) bodies with responses over two-dimensional (2-D) bodies of identical cross-section using plane wave incident fields is the only check available on our solution. Agreement is excellent; however, the length that a 3-D body must have before departures between 2-D transverse electric and corresponding 3-D signatures are insignificant depends strongly on the layering. The 2-D transverse magnetic and corresponding 3-D calculations agree closely regardless of the layered host. (Author)

Computation of electron repulsion integrals using the Rys quadrature method

Abstract: Following an earlier proposal to evaluate electron repulsion integrals over Gaussian basis functions by a numerical quadrature based on a set of orthogonal polynomials (Rys polynomials), a computational procedure is outlined for efficient evaluation of the two-dimensional integrals Ix, Iy, and Iz. Compact recurrence formulas for the integrals make the method particularly fitted to handle high-angular-momentum basis functions. The technique has been implemented in the HONDO molecular orbital program.

The Fourier transforms of some exponential‐type basis functions and their relevance to multicenter problems

Abstract: We analyze the properties of Slater‐type functions (STFs) and B functions with respect to the Fourier transformation which is one of the most important methods for the evaluation of multicenter integrals Although B functions have a much more complicated structure than STFs, their Fourier transform is probably the simplest of all expontential‐type basis functions Accordingly, in multicenter integrals, B functions seem to have much more attractive properties than STFs We demonstrate this by analyzing shifting operators which make it possible to increase quantum numbers of the orbitals Again we find that the shifting operators of B functions can be applied much more easily and yield much more compact results than the corresponding operators for STFs We also show that the extremely compact convolution and Coulomb integrals of B functions are direct consequences of the simple Fourier transform of B functions

Analytic second derivative techniques for self-consistent-field wave functions. A new approach to the solution of the coupled perturbed hartree-fock equations

Abstract: A new method for the solution of the coupled perturbed Hartree-Fock equations is outlined which avoids the four-index transformation of electron repulsion integrals. This allows the extension of analytic energy second derivative methods to large molecular systems. The new approach has been implemented for both closed- and open-shell molecules and a number of test cases considered, including as many as 96 contracted gaussian basis functions. The time required for the determination of all cartesian force constants varies from 8% to 65% of that required for analytic gradient techniques.

Edge And Line Detection in Multidimensional Noisy Imagery Data

Abstract: Detection of edges and lines in multidimensional data is an important operation in a number of image processing applications. The multidimensional picture function is a sampling of the underlying reflectance function of the objects in the scene with the noise added to the true function values. Edges and lines refer to places in the image where there are jumps in the values of the function or its derivatives. The multidimensional greytone surface is expanded as a weighted sum of basis functions. Using multidimensional orthogonal polynomial basis functions, expressions are developed for the coefficients of the fitted quadrautic and cubic surfaces. The parameters of the fitted surfaces are obtained when there is a rotation in the coordinate system. Assuming the noise is Gaussian, statistical tests are devised for the detection of significant edges and lines. Direction isotropic properties of the fitted surfaces are described. For computational efficiency, recursive relations are obtained between the parameters of the fitted surfaces of successive neighborhoods. Furthermore, experimental results are presented by applying the developed theory to multiband Landsat-Imagery Data.

A proposed upstream weight numerical method for simulating pollutant transport in groundwater

Abstract: An alternative upstream weighting numerical method is proposed to simulate the transport process in groundwater under a variety of conditions. The discretized system of the solute transport equations is derived from the integral form that expresses the balance of mass in each element. An upstream weight that depends on the local Peclet number is directly added to the basis functions. When convective transport dominates the dispersive transport, this technique can eliminate the oscillation of solutions efficiently, with only a nominal increase of computation effort over that of the general linear triangular Galerkin finite element method. The accuracy of the proposed numerical model is tested against two classical problems for which analytical solutions exist. The agreement is nearly exact. An additional numerical example is used to illustrate the applicability of this model.

Iterative Solution of Systems Originating from Integral Equations and Surface Interpolation

Abstract: A simple procedure for generating diagonal dominance in certain linear systems is presented, and the iterative solution of the transformed systems is discussed. The method is presented for systems encountered in the numerical solution of Fredholm equations of the first kind with singular kernels, and for systems arising in the interpolation of surfaces by certain sets of radial functions. In the second case the method provides new sets of basis functions generalizing in some sense the univariate B-splines.

An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios

Abstract: The recently developed iterative extended boundary condition method (IEBCM) has been used to compute the internal fields induced in homogeneous, axisymmetric, lossy dielectric objects of large aspect ratios when exposed to incident planewave radiation. Calculations were made for both the E- and k-polarization cases. The computed results for a prolate spheroidal model of an average man are found to be accurate for frequencies up to 300 MHz, while the use of the popular EBCM [1] was found to be essentially restricted to frequencies less than 70 MHz for these models and exposure conditions. The applicability of the IEBCM to composite bodies has also been examined by studying the irradiation of a capped cylindrical object. This composite object was first partitioned into several overlapping spherical subregions, and, alternatively, into two spherical subregions overlapping with a central cylindrical subregion. Spherical harmonics were used to represent the internal fields in the spherical subregions, while cylindrical expansions were utilized in the cylindrical subregions. It is shown that the second partitioning scheme is more computationally efficient and thereby suggests that the basis functions used to represent the subregional fields should be compatible with the subregional geometry. The new IEBCM, therefore, is a very valuable procedure which provides the opportunity of using the mixed basis functions in the solution.

A Cloud Physical Parameterization Method Using Movable Basis Functions: Stochastic Coalescence Parcel Calculations

Abstract: Numerical simulations of stochastic coalescence in a parcel framework are presented using a series of distribution functions. The equations governing the distribution parameter tendencies are derived using a variational approach with constraints. Solutions with two and three log-normal distribution functions are compared with a conventional benchmark model and the distribution model is shown to produce accurate solutions. Although only coalescence is considered within this paper, the procedures for including further physical processes is discussed. All of the simulations presented use the log-normal distribution although the method is general enough that it could be adapted to use other distributions such as the gamma distribution. A decrease in the number of dependent variables by as much as by a factor of 10 as well as an equivalent reduction in computation time required for the treatment of the coalescence equation makes the distribution model attractive for multi-dimensional cloud model simul...

Augmented Gaussian-orbital basis for atomic-cluster calculations within the density-functional formalism: Application to Cu 2

Abstract: The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse Gaussian-orbital tails are matched continuously and differentiably to inner-atom numeric radial functions at the atomic-sphere radius. Major advantages of Gaussian-orbital basis sets are acquired without the need for numerous Gaussians of large exponent for the core region. The numeric functions used inside the atom permit essentially exact solutions for that region. Procedures are described which recover use of the efficient integral algorithms for the Gaussian-orbital-tail matrix elements. The interactions over the structured inner-atom region are treated by efficient integrand smoothing and integration procedures for the sphere. The new augmented Gaussian basis removes the primary limitations on the use of Gaussian orbitals for heavy atoms. As an illustration the method is applied to the copper dimer in an all-electron framework within the local-spin-density approximation (LSDA). The calculated binding energy, equilibrium separation, and first ionization potential of ${\mathrm{Cu}}_{2}$ are within 2% of experiment within the $X\ensuremath{\alpha}$ model. Excitation energies are better described within more recent refined exchange-correlation functionals. These all-electron results show the LSDA model predicts a slightly contracted bond length for ${\mathrm{Cu}}_{2}$, consistent with bulk LSDA calculations for the $3d$ transition-metal series.

An economical technique for forcing convergence in conventional SCF methods

Abstract: We present an economical technique for ensuring convergence of the open‐ and closed‐shell SCF methods. In this technique, the number of operations required is proportional to the square of the number of basis functions and all the employed quantities are present in any conventional SCF procedure. We test their efficacy with several numerical calculations.

Estimation of a remote sensing system point-spread function from measured imagery

Abstract: A general approach to identifying the point spread function (PSF) of a remotely sensed scene is demonstrated in terms of a step function for an abrupt change in the gray level along the row or column of the image data The estimate of the PSF is made in terms of a finite sum of basis functions, employing a sequence of rectangular pulses covering the spatial extent of the PSF The approximation, if narrow impulses are employed, provides accurate fidelity to the PSF The method becomes practical when the geometrical structure of the scene elements producing the measured response is known The field boundary is obtained through consideration of the differing intensities on each side of the boundary, which is a step discontinuity The mathematical procedure for the technique is provided, together with a sample problem from Landsat-4 Thematic Mapper data Atmospheric blurring and electronic effects on the overall PSF and the cubic convolution resampling effects are noted

Calibration procedure in dual-energy scanning using the basis function technique

Abstract: We present a technique to simplify the calibration procedure of the dual‐energy scanning, using aluminum (AL) and plastic (PL) as basis materials In essence, this method determines the ‘‘basis functions’’ of the basis materials at the chosen energies This technique replaces the two‐dimensional calibration procedure, which is tedious, by two simple one‐dimensional calibration steps In addition, this technique also provides an alternative approach for solving the dual‐energy problem

Automatic computation of optimum origins of the poles in the multiple multipole method (MMP-Method)

Abstract: This paper gives a strategy to calculate the optimum origins of the poles in the multiple multipole method, which contains as a special case the charge method (method of images). The field, given finally as a linear combination of basis functions f i is built up one function after another. For each basis function one has to solve a nonlinear problem in two or three independent variables.

Near-Hartree-Fock energies and geometries of the hydrogen clusters H n + (n(odd) ≤ 13) obtained with floating basis sets

Abstract: The H n + clusters,n (odd) ≤ 13, are used to test the performance of an extreme approach with floating basis functions. Near-Hartree-Fock energies and structures are obtained by optimizing the positions of the nuclei and of nearly all basis functions independently with relatively small basis sets ofs- type functions only. Advantages and disadvantages of this approach are discussed.

Representations of global supersymmetries for all N

Abstract: The authors present the global supersymmetry rules for the fundamental representation of N-extended supersymmetry for all N and an associated invariant quadratic Lagrangian. This is achieved by the use of a suitable set of basis functions defined in terms of the spinor generators acting on the vacuum state of the representation. These basis functions allow the action of the generators on them to be obtained explicitly, as well as their internal symmetry properties. Specific examples are given of this for N=3, 4, 6 and 8.

On the ritz penalty method for solving the control of a diffusion equation

Abstract: The study of the finite-element method for the solution of a variety of complicated scientific problems has enjoyed a period of intense activity and stimulation, because of its simplicity in concept and elegance in development. These qualities have led eventually to its growing acceptance as a promising technique equipped with a powerful mathematical basis. The finite-element method operates on the subdomain principle; this means that the domain of the equation to be solved is usually divided into a number of separate regions or subdomains. The unknown solution function is then approximated in each subdomain by some functions, generally known as pyramid functions or basis functions.

Symmetry-adapted functions: molecular vibrations

Abstract: A method is developed for the construction of symmetry-adapted molecular functions which are consistent with a given set of 3-jm symbols (or coupling coefficients) No irreducible representation matrices or projection operators are required because all group theoretic basis information is contained in the 3-jm symbols for the molecular symmetry group The authors use this information to construct basis functions for the permutation representation of the molecule and then use point group 3-jm symbols to combine this permutation structure with a set of xyz displacements to give irreducible basis functions for the molecular vibrations The molecular SF6 is used as an example

Signal subspace algorithms for emitter location and multidimensional spectral estimation

Abstract: The signal subspace approach was introduced by Schmidt for locating narrowband emitters from a sensor array. The multichannel data is considered to be elements in a vector space and used to determine a subspace containing information on emitter location. The array characteristics determine a manifold in this space representing prior knowledge and the minimization of a distance function between the signal subspace and the array manifold determine the emitter locations. The method exhibits superior performance over existing methods. In this thesis, the generalization of the signal subspace approach is obtained for the wideband emitter location problem using rational modeling. A general theory for the application of signal subspace algorithms to multidimensional spectral estimation is also developed. The work in this thesis provide the theoretical background for a new class of high resolution spectral estimation algorithms. Two different generalizations of the signal subspace approach to the wideband emitter location problem are presented. The first method uses a rational vector space framework to define the signal subspace and the array manifold based on rational models of the array outputs. Minimization of the signal subspace - array manifold distance gives emitter location estimates. The resulting algorithms provide high resolution asymptotically exact wideband emitter location estimates ideally suited for the application of fast multichannel rational modeling methods. Detailed simulation results are given for a simple implementation. The second method models the emitters as AR or ARMA linear systems driven by white noise. This allows characterization of the array outputs by the behavior at emitter poles and the definition of a signal subspace and an array manifold for each pole. Minimization of the signal subspace - array manifold distance at each pole provides location estimates. Simulation results are given to illustrate the algorithm performance. The generalization of the signal subspace approach to multidimensional spectral estimation is based on the representation of multidimensional signals as combinations of parametrized basis functions with deterministic or stochastic coefficients. The general theory is given and related to some existing spectral estimation methods resulting in signal subspace interpretations and extensions. It is also applied to the problem of multidimensional generalized harmonic retrieval resulting in new high resolution algorithms.

Computation of the resonant frequency of a dielectric resonator by a differential method

Abstract: A differential method to compute, with high accuracy, the resonant frequency of a dielectric body with an axis of revolution and placed between two conducting plates is described. The propagation equations, projected on a Fourier basis, are integrated by the Adams-Moulton predictor-corrector algorithm and matched to the modified Bessel expansion of the field. Numerical results obtained for the cylinder shape are compared with those obtained by a modal theory, exhibiting an accuracy better than 10−4. Results for a dielectric sphere are given as another application.

The simulated ab initio molecular orbital (SAMO) method. VII. Extended basis sets for molecules and polymers

Abstract: The simulated ab initio molecular orbital SAMO method has been extended to study the use of basis sets larger than minimum basis sets for hydrocarbon molecules and polymers. Inclusion of polarization functions leads to no new features but the diffuse nature of double zeta basis sets requires, for the simulation of molecular properties, larger pattern molecules than was previously the case. For polymers, the approximations made within the ab initio crystal orbital method are comparable to those made in the SAMO method and the results are correspondingly closely similar. The problem of near linear dependence in the basis set for polymers is thoroughly discussed. This study opens up the SAMO method to the utilization of a wider range of extended basis function.

Mathematical model of an electrocardiogram based on new basis functions

Abstract: This paper deals with a mathematical model of an electrocardiogram (ECG) based on new basis functions The functions of different orders are given for various segments in the form of polynomial expressions The coefficients of the polynomials have been found using the Gauss-Jordan elimination method The ECG wave pattern has been represented in terms of proposed basis functions and model parameters The main advantages of the model are the accurate representation of the ECG wave, fewer parameters to he measured and stored, ease of categorization of parameters and applicability to computer aided diagnosis

A Study of the Parametric Uniform B-spline Curve and Surface

Abstract: This paper explains the parametric uniform B-spline curve and surface representations. The parametric representation is discussed, the properties of the B-spline basis functions is presented. Various end conditions and boundary conditions are described in order to enable the B-spline user to select which of the many options would be appropriate for a particular application. Efficient algorithms are designed and analyzed for B-spline basis function evaluation, and for the evaluation and perturbation of both B-spline curves and surfaces. Finally, difference techniques to accomplish this are also developed.

Modification of Welge's method of shock front location in Buckley-Leverett problem for non-zero initial condition

Abstract: To establish the accuracy of a numeric solution to the Buckley-Leverett equation, a comparison with the analytic solution normally is sought. However, difficulties arise when a zero-initial saturation over the space domain, normally imposed on the analytic solution, is to be expressed numerically while incorporating a non-zero boundary condition. For example, the finite element method using a Chapeau basis function by necessity generates a ramp initial condition. This study provides a modification to the Welge method for an appropriate location of the shock-front on the basis of mass conservation for non-zero initial condition.

Exponential factor optimization in characteristic function method for electrically charged particles

Abstract: In this work, the simplest basis function on hyperspherical coordinates with an optimization parameter is used to construct the characteristic function for a system of electrically charged particles. The first three coefficients of the serial expansion of the characteristic function in powers of eigenvalue parameter are evaluated in terms of well-known functions. The construction of a Pade table for this expansion with the aid of these coefficients, a theoretical discussion, the optimization of the exponential parameter, evaluation of ground state energies for certain systems, and finally comparison of accuracy increments due to optimization for several systems complete the work.