Gaussian basis functions for highly oscillatory scattering wavefunctions
نویسندگان
چکیده
منابع مشابه
Gaussian basis functions for solving differential equations
We derive approximate numerical solutions for an ordinary differential equation common in engineering using two different types of basis functions, polynomial and Gaussian, and a maximum discrepancy error measure. We compare speed and accuracy of the two solutions. The basic finding for our example is that while Gaussian basis functions can be used, the computational effort is greater than that...
متن کاملGaussian Radial Basis Functions for Simulation Metamodeling
This paper presents a novel approach for developing simulation metamodels using Gaussian radial basis functions. This approach is based on some recently developed mathematical results for radial basis functions. It is systematic, explicitly controls the underfitting and overfitting tradeoff, and uses a fast computational algorithm that requires minimal human involvement. This approach is illust...
متن کاملComputing Integrals of Highly Oscillatory Special Functions Using Complex Integration Methods and Gaussian Quadratures
An account on computation of integrals of highly oscillatory functions based on the so-called complex integration methods is presented. Beside the basic idea of this approach some applications in computation of Fourier and Bessel transformations are given. Also, Gaussian quadrature formulas with a modified Hermite weight are considered, including some numerical examples.
متن کاملStable Gaussian radial basis function method for solving Helmholtz equations
Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems. They are often referred to as a meshfree method and can be spectrally accurate. In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion. We develop our approach in two-dimensional spaces for so...
متن کاملStable Computations with Gaussian Radial Basis Functions
Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly illconditioned as the RBF shape parameter becomes small, corresponding to flat RBFs. Two stable approaches that overco...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics B: Atomic, Molecular and Optical Physics
سال: 2018
ISSN: 0953-4075,1361-6455
DOI: 10.1088/1361-6455/aab19f