2026/07/28 by Hongyun Wang, Parthiv Seetharaman, Shannon E. Foley +1
#math-ph #math.MP
In electromagnetic heating and other applications, we need to compute the volume enclosed by an isosurface of the 3D temperature distribution that is numerically represented on a rectangular grid. This situation arises naturally when the temperature distribution is obtained by solving a partial differential equation numerically using a finite difference method. Given the temperature distribution on the 3D grid, the isosurface of a prescribed value is represented approximately by a triangulation, a collection of triangles with vertices on the grid lines. The vertices are determined by a linear interpolation to approximate the locations where the temperature is at the prescribed level. The region enclosed by the isosurface is approximated by that enclosed by the triangulation, which is a set of tetrahedrons. The enclosed volume is approximated by summing those of tetrahedrons. This volume approximation is analogous to approximating a curve using line segments and is limited in accuracy. In this study, we combine extrapolation with the triangulation approximation to develop a more accurate method for computing the volume enclosed by an isosurface of the 3D temperature distribution on a rectangular grid.