Moment-method calculations on apertures using basis singular functions

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

A Spectral Method on Tetrahedra Using Rational Basis Functions

A spectral method using fully tensorial rational basis functions on tetrahedron, obtained from the polynomials on the reference cube through a collapsed coordinate transform, is proposed and analyzed. Theoretical and numerical results show that the rational approximation is as accurate as the polynomial approximation, but with a more effective implementation.

A Note on the Finite Element Method with Singular Basis Functions

In this note, we make a few comments concerning the paper of Hughes and Akin [4]. Our primary goal is to demonstrate that the rate of convergence of numerical solutions of the finite element method with singular basis functions depends upon the location of additional collocation points associated with the singular elements.

Basis functions for electronic structure calculations on spheres.

We introduce a new basis function (the spherical Gaussian) for electronic structure calculations on spheres of any dimension D. We find general expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the D = 2 case, we show that spherical Gaussians are more efficient than spheri...

numerical solution of singular ivps of lane-emden type using integral operator and radial basis functions

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