AI 中文总结
研究电磁加热中三维温度分布等值面所围体积计算问题，核心方法是结合外推法与三角剖分近似，主要贡献是开发出更精确计算该体积的方法。
AI 中文摘要
在电磁加热等应用中，需要计算三维温度分布等值面所包围的体积，该温度分布由有限差分法数值求解偏微分方程得到。给定三维网格上的温度分布，规定值的等值面由三角剖分近似表示，顶点通过线性插值确定。等值面所围区域由三角剖分所围区域近似，其为一组四面体。通过对四面体体积求和近似封闭体积，但这种体积近似精度有限。本研究将外推法与三角剖分近似相结合，开发出一种更精确的方法来计算矩形网格上三维温度分布等值面所围体积。
英文摘要
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.
Comments24 pages, 10 figures, preprint
