Quadrature over curved surfaces by extrapolation

Quadrature over Curved Surfaces by Extrapolation

In this paper we describe and justify a method for integrating over curved surfaces. This method does not require that the Jacobian be known explicitly. This is a natural extension of extrapolation (or Romberg integration) for planar squares or triangles.

Numerical quadrature over smooth, closed surfaces.

The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detai...

Extrapolation-based Boundary Element Quadrature

Mesh Generation Methods Over Plane and Curved Surfaces

In this paper, a set of mesh generation methods over plane and curved surfaces is presented. The surfaces can be plane, just defined by their boundary (as cylinders or cones), quadrics, surfaces of revolution or a combination of these by means of a multiblock definition. The basic method for plane surfaces and those defined by their boundary is based on a advancing front / algebraic combined te...

Generation of quadrilateral mesh over analytical curved surfaces

An automatic adaptive quadrilateral mesh conversion scheme for the generation of adaptive refinement meshes over analytical curved surfaces is proposed. The starting point of the quadrilateral mesh generator is a background triangular mesh of the curved surface. By a carefully controlled process to merge two triangles at a time the triangular mesh can be completely converted to quadrilaterals. ...