This paper studies a general method for estimating the length of a parametric curve using only samples of points. We show that by making a special choice of points, namely the Gauss-Lobatto nodes, weâ€¦ (More)

In this paper, we develop a new method for estimating the area of a parametric surface using only a rectangular grid of point samples in order to avoid explicit differentiation of the surface. Theâ€¦ (More)

A well-known method of estimating the length of a parametric curve in ${\mathbb {R}}^d$ is to sample some points from it and compute the length of the polygon passing through them. In this paper weâ€¦ (More)

The accurate and efficient tracing of streamlines is fundamental to any streamline-based simulation method. For grids with irregular cell geometries, such as corner-point grids with faults orâ€¦ (More)

Streamline tracing on irregular grids requires reliable interpolation of velocity fields. We propose a new method for direct streamline tracing on polygon and polytope cells. While some numericalâ€¦ (More)

In this paper we make a thorough study of the use of the finite element method to numerically compute harmonic maps from parametric surfaces to the plane. There are essentially two choices to be madeâ€¦ (More)

The subject of this paper is the investigation of the Magnus expansion of a solution of the linear diierential equation y 0 = a(t)y, y(0) 2 G, where G is a Lie group and a : R + ! g, g being the Lieâ€¦ (More)