TITLE:
Accurate Computation of Activated Volume in Electromagnetic Heating
AUTHORS:
Hongyun Wang, Parthiv Seetharaman, Shannon E. Foley, Hong Zhou
KEYWORDS:
Electromagnetic Heating, Skin Activated Volume, Isosurface, Triangulation, Extrapolation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
25,
2026
ABSTRACT: In electromagnetic heating and other applications, it is necessary 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 tetrahedra. The enclosed volume is approximated by summing the contribution of these tetrahedra. This volume approximation is analogous to approximating a curve using line segments and is limited to second-order accuracy. In this study, we combine extrapolation with the triangulation approximation to develop a more accurate method for computing the volume of the region in which the temperature is above a given threshold.