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arXiv · 2607.25994

Accurate Computation of Activated Volume in Electromagnetic Heating

Hongyun Wang·Parthiv Seetharaman·Shannon E. Foley·Hong Zhou
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Abstract

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.

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Hongyun Wang, Parthiv Seetharaman, Shannon E. Foley, Hong Zhou. 2026-07-28. Accurate Computation of Activated Volume in Electromagnetic Heating. https://arxiv.org/abs/2607.25994

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