VL Rvachev called R-functions 'logically charged functions' because they encode complete
logical information within the standard setting of real analysis. He invented them in the …

Finite volume methods apply directly to the conservation law form of a differential equation
system; and they commonly yield cell average approximations to the unknowns rather than …

This article demonstrates how numerical methods for atmospheric models can be validated
by showing that they give the theoretically predicted rate of convergence to relevant …

In a general setting, the transfinite interpolation problem requires constructing a single
function f (x) that takes on the prescribed values and/or derivatives on some collection of …

We are concerned here with processing discontinuous functions from their spectral
information. We focus on two main aspects of processing such piecewise smooth data …

Abstract The R-Function Method (RFM) solution structure is a functional expression that
satisfies all given boundary conditions exactly and contains some undetermined functional …

Abstract Theory of R-functions [121 provides the methodology for constructing exact implicit
functions for any semianalytic set. This paper systematically explores and compares the …

(57) ABSTRACT A method and apparatus for mesh-free engineering analysis of geometric
models is described. The method and apparatus, which are preferably software-based and …

For a given set of points S, a Euclidean distance field is defined by associating with every
point p of Euclidean space Ed a value that is equal to the Euclidean distance from p to S …

Molecular dynamics is discussed from a mathematical perspective. The recent history of
method development is briefly surveyed with an emphasis on the use of geometric …